5370-nd016, bulletin 5370 color cvim module math-pak option … · 2014-07-18 · analysis and...

ALLEN-BRADLEY

Bulletin 5370 Color CVIM ModuleMATH-PAK Option(Catalog No. 5370–CMPK)

User’s Manual

ALLEN-BRADLEY

Solid state equipment has operational characteristics differing from those ofelectromechanical equipment. “Application Considerations for Solid StateControls” (Publication SGI-1.1) describes some important differencesbetween solid state equipment and hard–wired electromechanical devices.Because of this difference, and also because of the wide variety of uses forsolid state equipment, all persons responsible for applying this equipmentmust satisfy themselves that each intended application of this equipment isacceptable.

In no event will the Allen-Bradley Company be responsible or liable forindirect or consequential damages resulting from the use or application ofthis equipment.

The examples and diagrams in this manual are included solely for illustrativepurposes. Because of the many variables and requirements associated withany particular installation, the Allen-Bradley Company cannot assumeresponsibility or liability for actual use based on the examples and diagrams.

No patent liability is assumed by Allen-Bradley Company with respect to useof information, circuits, equipment, or software described in this manual.

Reproduction of the contents of this manual, in whole or in part, withoutwritten permission of the Allen-Bradley Company is prohibited.

1993 Allen-Bradley Company, Inc.

Important User Information

A–BColor CVIM MATH-PAKUser’s Manual

Table of Contents

i

Chapter 1Chapter Objectives 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manual Contents 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intended Audience 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notice of Attention 1–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Related Publications 1–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trademarks 1–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 2Chapter Objectives 2–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MATH-PAK Preview 2–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Definition of a Formula 2–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How Formula Results Are Applied 2–2. . . . . . . . . . . . . . . . . . . . . . . . . Accessing the MATH-PAK Features 2–4. . . . . . . . . . . . . . . . . . . . . . . . Copy and Paste Functions 2–5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Runtime Displays 2–5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3Chapter Objectives 3–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Installing the MATH-PAK Option 3–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 4Chapter Objectives 4–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formula Definition: Basic Steps 4–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selecting a Formula 4–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Selecting the Formula Number(s) 4–3. . . . . . . . . . . . . . . . . . . . . . . . . . Defining a Formula 4–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Accessing the Formula Entry Keyboard 4–5. . . . . . . . . . . . . . . . . . . . . Using the Formula Entry Keyboard 4–7. . . . . . . . . . . . . . . . . . . . . . . . .

Example Formula Entry 4–9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Edit / Control Keys 4–10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Example of Formula Editing 4–11. . . . . . . . . . . . . . . . . . . . . . . . . . Operands 4–12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Entering Constants as Operands 4–16. . . . . . . . . . . . . . . . . . . . . . . . Operators 4–17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Operator Execution Hierarchy 4–20. . . . . . . . . . . . . . . . . . . . . . . . . Operator Usage 4–21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Mathematical Operators 4–21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistical Operators 4–29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Logical Operators 4–33. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conditional Operators 4–35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Additional Formula Examples 4–35. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flagging Consecutive Rejects 4–35. . . . . . . . . . . . . . . . . . . . . . . . .

Using This Manual

Introduction to theMATH–PAK Option

Installation

Defining Formulas

Color CVIM MATH-PAKUser’s Manual

Table of Contents

ii

Chapter 4 (continued)Creating a Shift Register 4–36. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Naming a Formula 4–37. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enabling / Disabling a Formula 4–38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Copy and Paste 4–39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Example Copy and Paste 4–41. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Setting Range Limits and Assigning Outputs 4–41. . . . . . . . . . . . . . . . . . . .

Entering Range Limits for Formulas 4–43. . . . . . . . . . . . . . . . . . . . . . . . Inspection Statistics Table 4–44. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Example Range Limit Setting 4–45. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Assigning Range Limits to Results Output Lines 4–46. . . . . . . . . . . . . . Enabling Results and Range Limits for Corresponding Tools 4–47. . . . .

Chapter 5Chapter Objectives 5–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis Functions 5–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistics (Learn Mode) for Failed Tools 5–2. . . . . . . . . . . . . . . . . . . . . . . . Runtime Displays 5–3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Runtime Tools Displays 5–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I/O Page 5–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results and Stat1 Page Displays 5–5. . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix AObjective A–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formula Data Replaces Tool Data A–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results Blocks A–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Configuration Blocks A–6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discrete Bits A–9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Index

Tables1.A Chapter Descriptions 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.A Formula numbers and corresponding gage/window numbers 4–3. . 4.B Edit / Control Keys 4–10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.C Operand Definitions 4–14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.D Operator Definitions 4–18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Formula numbers and corresponding gage/window numbers A–1. . A.2 Results Block 1 – Formula/Tool Results A–3. . . . . . . . . . . . . . . . . . A.3 Results Block 2 – Formula/Tool Results A–4. . . . . . . . . . . . . . . . . . A.4 Results Block 3 – Formula/Tool Results A–6. . . . . . . . . . . . . . . . . . A.5 Configurations block numbering for formulas 1–56

(and corresponding tools) A–7. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Defining Formulas

Analysis Functions andRuntime Displays

Color CVIMCommunications with MATH-PAK Installed


Table of Contents

iii

Tables (continued)A.6 Configuration blocks 46–77 – for formulas 9–16, 25–32, 41–56

(gages 1–32) – fault and warning ranges A–8. . . . . . . . . . . . . . . . . . A.7 Configuration blocks (even numbered, 110–156) for formulas 1–8,

17–24, 33–40 (windows 1–24) – fault and warning ranges A–9. . . . A.8 Discrete Input Bits for formulas and corresponding tools A–10. . . . .

Figures2.1 Color image vs. gray-scale image 2–1. . . . . . . . . . . . . . . . . . . . . . . 2.1 Inspection results data handling without MATH–PAK formulas 2–22.2 Inspection results data handling when using a MATH–PAK

formula 2–3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Accessing the MATH-PAK features 2–4. . . . . . . . . . . . . . . . . . . . . 2.4 Copy and Paste functions 2–5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Results Page displaying formula results 2–5. . . . . . . . . . . . . . . . . . 3.1 Inserting the MATH-PAK installation card 3–2. . . . . . . . . . . . . . . . 3.2 Title banner indicating the presence of the MATH-PAK option 3–34.1 Selecting the formula number 4–2. . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Using the Jump box and calculator pad 4–4. . . . . . . . . . . . . . . . . . . 4.3 Accessing the formula entry keyboard pad 4–5. . . . . . . . . . . . . . . . 4.4 Switching between the two key sets of the formula entry keyboard 4–64.5 Edit/control keys 4–10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Operand keys 4–12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Operator keys (initial key set) 4–17. . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Example application, using the subtraction operator 4–22. . . . . . . . . 4.9 Example of using the DST function 4–25. . . . . . . . . . . . . . . . . . . . . 4.10 Arcsine and arctangent operation results 4–26. . . . . . . . . . . . . . . . . . 4.11 Arccosine operation results 4–27. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Example application: Using the arctangent to calculate

an angle � 4–27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.13 Example application: Using operands GAGE2 and GAGE2.3 4–284.14 Example application: Finding angular results greater than 90° 4–28. 4.15 Example application: Finding angular results greater than 270° 4–294.16 Example application, using three gages to find an

average measurement 4–30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.17 Example application, using windows and the mode operator 4–32. . 4.18 Example application, using gages and the variance operator 4–33. . 4.19 Using the keyboard to set the formula name 4–37. . . . . . . . . . . . . . . 4.20 Enabling a formula 4–38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.21 Copying a formula 4–40. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Assigning range limits 4–43. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.23 Example: Range limits for linear gaging 4–45. . . . . . . . . . . . . . . . . 4.24 Example: Formula with conditional operation for comparing gage

results 4–46. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Table of Contents

iv

Figures (continued)4.25 Selecting output lines for range limits 4–47. . . . . . . . . . . . . . . . . . . . 4.26 Enabling the range limits and outputs for tools 4–48. . . . . . . . . . . . . 5.1 Selecting the Tool Display menu 5–1. . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Range Fail box 5–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Runtime Display menu – setup mode 5–3. . . . . . . . . . . . . . . . . . . . 5.4 Display menu – run mode 5–3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Formulas displayed in Failed Tools display during run mode

operation 5–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Formulas displayed on I/O Page display during run mode

operation 5–5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Calculator pad for entering number of displayed

formula/tool results 5–6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Typical help message for the Disp. Windows option 5–7. . . . . . . . .

A–B 1Chapter

1–1

Using This Manual

ContentsChapter Objectives 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manual Contents 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intended Audience 1–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cautions 1–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Related Publications 1–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Trademarks 1–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The objective of this chapter is to provide an overview of the contents andorganization of this manual, to describe the intended audience, and to listrelated publications.

The contents of this manual are briefly described in Table 1.A below.

Table 1.AChapter Descriptions

Chapter/Appendix Title Description

1 Using This Manual Provides an overview of the manual.

2 Introduction to theMATH-PAK Option

Previews the main features and capabilities ofthe MATH–PAK option.

3 Installation Describes how to install the MATH-PAK optioninto the Color CVIM module.

4 Defining Formulas

Describes how to access the MATH-PAKformula keyboard, lists and describes theformula operators and operands, discussesselecting and enabling/disabling formulas,discusses the Copy and Paste functions, anddiscusses setting range limits and assigningoutputs.

5 Analysis and RuntimeDisplays

Desribes the use of analysis functions andruntime displays with MATH-PAK installed.

AColor CVIM

Communications withMATH-PAK Installed

Lists the effects that MATH-PAK formulashave on the results and configuration blocksavailable through the serial and parallel ports.

Before using this manual, you should be familiar with the Color CVIMmodule features and the procedures used in configuring the Color CVIMmodule for operation.

• For information regarding the Color CVIM module, refer to the ColorCVIM User’s Manual, Cat. No. 5370–ND009 (Series A).

Chapter Objectives

Manual Contents

Intended Audience

Chapter 1Using This Manual

1–2

• If you plan to use Color CVIM communications, refer also to the ColorCVIM Communications Manual, Cat. No. 5370–ND0010 (Series A).

• If you plan to use other software option packages along with theMATH-PAK option, refer to the user’s manuals for the respectivesoftware package as necessary.

Notices of attention are included when the COLOR CVIM module orperipheral equipment could be damaged if the listed procedure is notfollowed. The following format is used:

!ATTENTION: Identifies information about practices orcircumstances that can lead to personal injury or death, propertydamage, or economic loss.

Attentions help you:

• identify a hazard• avoid the hazard• recognize the consequences

Important: Identifies information that is especially important for successfulapplication and understanding of the product.

The following manuals are cited for reference in this manual:

• User’s Reference Manual, Bulletin 5370–CVIMC, Cat. No. 5370–ND009(Series A), also referred to as the Color CVIM User’s Manual in thispublication.

• Communications Manual, Bulletin 5370–CVIMC, Cat. No. 5370–ND010(Series A), also referred to as the Color CVIM Communications Manualin this publication.

The following trademarks apply to products mentioned in this manual:

Color CVIM Module – Allen–Bradley Cat. No. 5370–CVIMC

MATH–PAK Option – Allen–Bradley Cat. No. 5370–CMPK

Notice of Attention

Related Publications

Trademarks

A–B 2Chapter

2–1

Introduction to the MATH–PAK Option

ContentsChapter Objectives 2–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MATH-PAK Preview 2–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This chapter briefly describes the features and capabilities available with theMATH–PAK option package installed in the Color CVIM module.

The MATH–PAK option enables your Color CVIM module to automaticallyperform a variety of mathematical and/or logical operations, using formulasthat you define, on inspection data from any of the module’s analysis tools.

The MATH-PAK option is designed to give you much greater flexibility inthe use and application of the Color CVIM module’s inspection capabilities,allowing you to quickly perform complex data manipulation on the fly. Also,because these calculations are handled within the Color CVIM module itself,the MATH-PAK option can help simplify the programming of, or helpeliminate the need for, an external system host computer or controller.

Definition of a Formula

A MATH-PAK formula is defined by the user. A formula consists of one ormore mathematical or logical operators, and one or more operands, whichcombine to provide a mathematical or a logical (1 or 0) result.

Note: The term operator refers to the mathematical, logical, or otheroperation performed, such as add, multiply, square root, cosine, AND, etc.The term operand refers to the initial data value upon which the operationsare performed, such as a gage result, or a constant.

You can define up to 56 different formulas, each consisting of a number ofdifferent components (operators and operands).

MATH-PAK formulas can perform a variety of operations, from simplearithmetic to more complex trigonometric functions, square roots or statisticsvalues, and a number of other mathematical or logical operations. Operatorscan be used alone in a formula, or in combination.

MATH-PAK formulas can perform operations on a variety of operands,including the numerical results from a tool, tool pass/fail status, objectcontour analysis results, statistics based on a tool’s results, and even theresults from other formulas.

Formula results can be logical (1 or 0), integer, or fixed point (decimal).

Chapter Objectives

MATH-PAK Preview

Chapter 2Introduction to the MATH-PAK Option

2–2

Example formulas: This simple formula scales a window’s results by aconstant multiplier (using the multiply operator (*) and 2 operands –window 4 and the constant, 0.75):

WINDOW4 * 0.75

The formula below averages the results from gages 1, 2, and 3 (using the addoperator (+) and the 3 gage operands, then using the divide operator ( / ) andthe constant, 3):

(GAGE1 + GAGE2 + GAGE3) / 3

How Formula Results Are Applied

Figure 2.1 illustrates how the inspection tool results are range-checked andapplied to discrete outputs, without MATH-PAK installed.

Figure 2.1 Inspection results data handling without MATH–PAK formulas

Color CVIM Inspection

Yes

No Range limits exceeded ortool failed?

WithoutMATH-PAKformulas, toolresults data andpass/warn/faultstatus areavailable for usedirectly – as is.

Bit(s) sent toassigned output(s)

Inspection results datafrom one or more tools

Appropriatefault/warning bit(s)

cleared

Appropriatefault/warning bit(s) set

Results data storedin Color CVIM memory

To: Chassis backplane

To: 1771 Remote I/O port

To: RS-232 port

Upon completion of each inspection cycle, the Color CVIM module storesthe resulting inspection data from each analysis tool used in the inspection.This information is accessible to host devices connected to the Color CVIMthrough the backplane, 1771 Remote I/O port, or RS-232 port.


2–3

When the MATH-PAK option is installed, the results information for eachinspection is also available for use in MATH-PAK formulas. You can defineformulas to combine or manipulate, in any number of ways, the inspectiondata gained from one or more tools used in the inspection.

Figure 2.2 illustrates how the inspection results can be manipulated byformulas with MATH-PAK installed.

Figure 2.2 Inspection results data handling when using a MATH–PAK formula

Using MATH-PAKformulas, tool resultscan be combined ormanipulated.

Formula manipulatesdata from tool(s)

Results from formula1

Inspection results from one or more tools

Range limits exceeded ortool failed?

Bit(s) sent toassigned output(s)

Appropriatefault/warning bit(s)

cleared

Appropriatefault/warning bit(s) set

Results data stored inColor CVIM memory 2

To: Chassis backplane

To: 1771 Remote I/O port

To: RS-232 port

Color CVIM Inspection

1: Formula results can berange-checked instead of, oralong with, tool results.

Yes

To: MATH–PAK formula(s)(if applicable)

2: Formula results canreplace, or be provided alongwith, tool results.

No

Range limits and output assignment: For each formula you define, as withthe inspection tools, you can set warning and fault range limits for theresults, and assign the range limits to discrete outputs (see Figure 2.2).


2–4

Depending on your requirements, you can configure the Color CVIM moduleso that it range-checks formula results instead of, or in addition to, the initialtool results.

Data communication: The formula results information is, as withinspection tool results, also accessible to devices connected to the ColorCVIM module through the backplane, 1771 Remote I/O port, or RS-232 port.Depending on your requirements, you can configure the Color CVIM moduleso that formula results are accessible instead of, or in addition to, the initialtool results.

Accessing the MATH-PAK Features

With the MATH-PAK option installed, the MATH-PAK features are accessedthrough the added Config. Results box on the Archival menu. To accessthe Config. Results (MATH-PAK) menu, you would:

• Pick Misc → Archival to access the Archival menu (see Figure 2.3).

• Pick Config. Results on the Archival menu.

To define a formula, you would pick Set Formula on the Archival menu.When you do, the formula entry keyboard appears (see Figure 2.3). You thenenter a formula by picking the appropriate boxes on the formula keyboard.

Figure 2.3 Accessing the MATH-PAK features

Formulaentrykeyboard


2–5

Copy and Paste Functions

You can copy the definition of one formula to another using the Copy andPaste menu items which are part of the new MATH–PAK menus (seeFigure 2.4). After you copy one formula to another, for example, you canmake changes to the formula as necessary. This can save time and effortduring setup, especially when you want to try out different variations of aformula you have defined, or if two or more formulas will be very similar.

Figure 2.4 Copy and Paste functions

Config. Results menu

Copy and Paste boxes

Runtime Displays

With the MATH-PAK option installed, the runtime displays canaccommodate the MATH-PAK formulas. For example, the Results page canlist the formula results along with other tool results (see Figure 2.5).

Figure 2.5 Results Page displaying formula results

A–B 3Chapter

3–1

Installation

ContentsChapter Objectives 3–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Installing the MATH-PAK Option 3–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This chapter describes how to install the MATH-PAK option in theAllen–Bradley 5370–CVIMC Color CVIM module.

The MATH-PAK option is provided on the supplied memory card. Thissection describes how to install the MATH-PAK option. Please note thefollowing considerations:

Required Firmware: The Color CVIM module must have the RevisionA02 (or higher) firmware before the MATH-PAK option can be installed(the firmware revision is listed on the title banner on the monitor screenfollowing powerup).

One–Time Installation: You need only install the MATH-PAK optiononce; once installed, the MATH-PAK option remains installed for allsubsequent powerups.

To install the MATH-PAK option in your Color CVIM module:

• Remove DC power from the Color CVIM module.

• Insert the MATH-PAK installation card into the Archive Memory slot onthe Color CVIM module. Insert the end with the metal strip facing right(see Figure 3.1, page 3–2).

• Restore DC power to the Color CVIM module – this starts the loadingsequence.

!ATTENTION: Do not remove power to the Color CVIMmodule during loading of the MATH-PAK option. Doing so maydamage the Color CVIM module.

Chapter Objectives

Installing the MATH-PAKOption

Chapter 3Installation

3–2

Figure 3.1 Inserting the MATH-PAK installation cardÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇÇ

MATH-PAK installationcard

Color CVIMmodule

ArchiveMemory slot

Card Label Metal Strip

The loading process requires about 45 seconds. The LEDs near the top ofthe face of the Color CVIM module indicate the progress of thethree–phase loading process (with each phase taking about 15 seconds):

LEDsMATH-PAK Loading Phase

LEDs1 2 3

Pass/Fail Red–to–yellow–to–green

Green Red–to–yellow–to–green

Trigger 1 Green Green Off

Trigger 2 Off Green Green

When the loading process is complete, the Color CVIM module initiatesits normal powerup sequence.

• Once the powerup sequence is complete, you can verify that theMATH-PAK option is installed by checking for the MATH-PAKindication on the powerup title banner on the monitor; if the MATH-PAKoption is installed, it is listed as on of the “Packages” on the title banner,along with other installed options, if any.

• Remove the MATH-PAK installation card from the Archive Memory slot.

At this point, the MATH-PAK option has been successfully installed, and canbe used as required in your Color CVIM module configurations.

A–B 4Chapter

4–1

Defining Formulas

ContentsChapter Objectives 4–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formula Definition: Basic Steps 4–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selecting a Formula 4–2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Defining a Formula 4–4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Naming a Formula 4–37. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Enabling/Disabling a Formula 4–38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Copy and Paste 4–39. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Setting Range Limits and Assigning Outputs 4–41. . . . . . . . . . . . . . . . . . . .

This chapter describes how to configure MATH-PAK formulas, includinghow to select formulas, how to access and use the formula entry keyboard todefine a formula, and how to copy formulas.

The MATH–PAK option enables your Color CVIM module to automaticallyperform a variety of mathematical and/or logical operations, using formulasthat you define, on inspection data from any of the module’s analysis tools.

A MATH-PAK formula is defined by the user. A formula consists of one ormore mathematical or logical operators, and one or more operands, whichcombine to provide a mathematical or a logical (1 or 0) result.

The result of the formula can be assigned range limits, and the range limitscan be assigned to outputs.

You can define up to 56 different MATH-PAK formulas.

Listed below are the basic steps involved in initially defining a formula:

1. Select formula – Select the number of the formula to define, taking intoconsideration that results from enabled formulas can replace output fromcorresponding tools.

2. Define and save formula – Define the formula by selecting and placing,in logical sequence, the appropriate components (operands andoperators) using the formula entry keyboard, accessed through the SetFormula box.

3. Name formula – Enter a descriptive name for the formula, if desired, bypicking the Set Name box and using the character entry keyboard.

4. Enable formula – Enable the formula, if appropriate, by picking theFormula #: Disabled box.

5. Set range limits and assign outputs – Set range limits and assignoutputs for the formula, as required, by picking the Range/Outputs box.

Chapter Objectives

Formula Definition: Basic Steps

Chapter 4Defining Formulas

4–2

The first step in defining a formula is to select, by number (from 1–56), theformula you want to define. The current formula number is listed in theFormula #: box on the Config. Results menu (see Figure 4.1).

Figure 4.1 Selecting the formula number

Formula # box

Previous / Next boxes

In selecting the formula(s) you want to define, and also when selectingwindows and gages to define, consider the following points:

• Formulas are evaluated in numerical order: If you define formulaswhich require results information from some other formula(s) from thecurrent inspection, make sure the formulas providing the required resultsprecede (in terms of numerical order) the formula requiring those results.

• Formulas prevent the use of corresponding gage and windowoutputs: Any formula you select and enable will disable the use ofresults outputs from a corresponding gage or window, as listed inTable 4.A, page 4–3. Note that gages 33–64 and windows 25–48 arenot listed in Table 4.A; they are not affected by the use of formulas.

Warning message: Whenever you enable a formula, a warning messageappears, identifying the corresponding tool that is being prevented fromdriving an output (see “Enabling / Disabling a Formula” on page 4–38).

• Formula results replace the results of the corresponding gage andwindow in the results blocks: When you enable a formula, itsinspection results are listed in the results block, in place of thecorresponding gage or window results (as listed in Table 4.A, page 4–3).Results blocks contain the comprehensive inspection results available bytransfer through the Color CVIM backplane, or through one of the ColorCVIM serial ports (see Appendix A for communications information).

When any formula is enabled, the Color CVIM module disables theRange/Outputs box on the Range/Reference menu for the correspondingtool (see “Setting Range Limits and Assigning Outputs” on page 4–41).

Selecting a Formula


4–3

To avoid losing the use of particular window or gage outputs or results,when defining formulas, select formula numbers which do not correspond toany gages or windows you have previously defined (see Table 4.A, page4–3), or that you intend to define. Or, define a formula to provide the resultvalue for a tool for which there is a conflict (see “Operands” in this chapter).

Otherwise, during setup of gages and windows, select gage and windownumbers that will not conflict with the formulas you intend use. One way todo this is to select only gages numbered from 33–64, or windows numberedfrom 25–48, which are not affected by the use of formulas.

Use Copy and Paste functions: If you define a formula that turns out tocorrespond to a gage or window whose output or results block informationyou wish to use, you can copy that formula to another formula number thatdoes not conflict (see “Using Copy and Paste” on page 4–39).

See Appendix A for communications information: Appendix A providesmore information on the specific effects that using formulas has on theresults blocks, on the configuration blocks, and on the discrete input bits.

Table 4.AFormula numbers and corresponding gage/window numbers

Formula Tool Formula Tool Formula Tool Formula Tool

1 Window 1 15 Gage 7 29 Gage 13 43 Gage 19


3 Window 3 17 Window 9 31 Gage 15 45 Gage 21


5 Window 5 19 Window 11 33 Window 17 47 Gage 23




9 Gage 1 23 Window 15 37 Window 21 51 Gage 27


11 Gage 3 25 Gage 9 39 Window 23 53 Gage 29


13 Gage 5 27 Gage 11 41 Gage 17 55 Gage 31


Selecting the Formula Number(s)

There are two ways to select the formula number:

• Use the Previous / Next boxes to decrement / increment the formulanumber, until the desired number appears (see Figure 4.1, page 4–2).

• Use the Jump box to enter the desired formula number directly (seeFigure 4.2, page 4–4).


4–4

To use the Jump box to select the formula number:

• Pick Misc → Config. Results to access the Config. Results menu.

• Pick the Jump box on the Config. Results menu. The calculator padappears (see Figure 4.2).

• Pick the appropriate numeric key boxes on the calculator pad to select thedesired formula number.

• When the desired formula number appears in the calculator pad display,pick Enter on the calculator pad. This changes the selected formula tothe number on the calculator pad display.

Figure 4.2 Using the Jump box and calculator pad

Jump box

Calculator pad

Formulas can be defined in a variety of ways to perform a variety ofcalculations.

Multiple operators, of different types, can be combined in different wayswithin a formula. “Nesting” of operations within a formula can be employedthrough the use of the parentheses. Or, a formula can consist of a singleoperand, with no operators.

A first step in formula definition is to review the available operators andoperands – this information is listed in the sections “Entering Operands” and“Entering Operators” in this chapter.

The next step in formula definition is to decide on the formula content, andresults desired from the formula – that is, determine what you want theformula to do, based on your application requirements.

Once you have decided on the formula requirements, to define a formula, usethe formula entry keyboard, which is described in the following two sections.

Defining a Formula


4–5

Accessing the Formula Entry Keyboard

In order to define a formula you have selected, access the formula entrykeyboard by selecting the Set Formula box. To do this:

• Pick Misc → Config. Results to access the Config. Results menu.(see Figure 4.3).

• Pick Set Formula on the Config. Results menu. The formula entrykeyboard appears.

Figure 4.3 Accessing the formula entry keyboard

Set Formula box Formula entry fieldFormula name field

Keyboard display area

Key Area

The formula entry keyboard enables you to select the various operands,operators, and other elements that will make up the formula you are defining.The keyboard has two main areas – the key area, and the display area (seeFigure 4.3).

Display area: The display area lists the formula name (which can beuser-assigned), and lists the formula components as you select them.

Key area: You pick the keys in the key area in order to select components(operators and operands) to define the formula. The keys fall into severalgeneral categories – operand keys, operator keys, numeric keys, edit keys,and miscellaneous other keys.

Accessing the two key sets: The formula entry keyboard actually has twodifferent key sets, in order to accommodate all of the formula elements. Youcan easily switch between the two key sets as necessary (see Figure 4.4).


4–6

Figure 4.4 Switching between the two key sets of the formula entry keyboard

Picking the up or downarrow key switchesbetween the two keysets

Initial key set

Secondarykey set

To switch between key sets, use the ↑ and ↓ arrow keys (see Figure 4.4):

• Pick the up (↑ ) arrow key to switch from the initial key set to thesecondary key set.

• Pick the down (↓ ) arrow key to switch back to the initial key set.

The initial key set contains all of the available operand keys, along withvarious operator keys, the numeric keys, and the edit/control keys. Each ofthese key types is discussed in later sections in this chapter.

The secondary key set offers additional operator types, replacing the initialoperands and some of the operators. It retains some of the initial keys,including the numeric keys, the arithmetic keys, and the edit/control keys.


4–7

Using the Formula Entry Keyboard

To define a formula, you would generally follow the steps listed below:

• Pick Set Formula on the Config. Results menu to access the formulaentry keyboard (see Figure 4.3, page 4–5).

• Enter your formula – Pick the keys on the keyboard which correspond tothe operators, operands, and other items (decimal points, commas,parentheses) you are using in the formula. As you pick your formulaentries, they appear in the keyboard display:

Formula is displayed

A cursor indicates the point at which the next component entered willappear.

• You can edit the formula as you enter it, using these edit keys:

← → Pick the arrows keys (← or→) to move the cursor to the left or rightalong the formula, in order to insert a component at a particular point in aformula, or to prepare to delete a particular component.

Del Pick the Del(ete) key to erase the entry to the left of the cursor.

Clr Pick the Clr (clear) key to erase the entire formula.

• When finished, you can pick the Ret key to save a formula, or pick theEsc key, to restore the formula content to what it was when last saved.

When you pick the Ret key, the formula is saved, and a message appears:

You can continue to edit the formula after picking the Ret key – however,to save the changed formula, you must pick the Ret key when finished.

Saving the formula also enables the Set Name and Formula #:Disabled boxes on the Config. Results menu, which allow you toenable and name the formula.


4–8

Results Display: When you pick the Ret key, and the formula is saved,the current result of the formula is listed in the keyboard display area:

The result format is either integer, or fixed decimal point, depending onthe requirements of the operator(s) and/or operand(s) in the formula.

Question mark (?) – incorrect syntax: The question mark (?) in thedisplay, when present during formula entry, indicates that the formula isincomplete as entered, and/or that the syntax for one or more of theformula components is incorrect:

If you pick the Ret key while a (?) appears in the display, this warningmessage appears at the top of the screen:

To avoid losing your current formula entry, pick any key besides the Retkey (other than Clr or Esc). Otherwise, picking the Ret key at this pointwill clear the formula entry.

• Using parentheses in formulas: Parentheses can be used when enteringformulas, in two different ways –

Prioritizing operations – You can place parentheses around an operatorand its operands in order to prioritize that operation – that is, theoperation in parentheses can be used as an operand by another operator.“Nesting” of operations within a formula can be employed, where aparenthetical portion is itself contained within another parentheticalportion of the formula.

Listing operands – Some operators require that you enter one or moreoperands in a parenthetical list following the operator. In these cases,when you pick the operator, the “open” parenthesis is displayed. Afteryou list the operand or operands (separated by commas), you then enterthe “close” parenthesis.


4–9

Example Formula Entry

To enter this formula: AVG (GAGE1,GAGE2) * 0.250

• Select an undefined formula (see “Selecting a Formula” in this chapter),and pick the Set formula box to access the formula entry keyboard.

• Pick the AVG key on the formula entry keyboard (located on thesecondary key set). The formula keyboard display shows:

= AVG( ?Formula: Cursor

The “?” indicates the formula is incomplete to this point; the cursorindicates the point at which the next component will be entered.

• Pick G (on the initial key set), to begin to enter the GAGE1 operand:

= AVG( GAGE0 ?Formula:

• Pick 1, to complete the entry of the GAGE1 operand:

= AVG( GAGE1 ?Formula:

• Pick “ , ” (comma) , then G, then 2:

= AVG( GAGE1, GAGE2 ?Formula:

• Pick “ ) ” (close parenthesis) on the secondary key set. The formula isnow correct in syntax at this point; the “?” disappears:

= AVG( GAGE1, GAGE2 )Formula:

• Pick “ * ” , then “.” (decimal point), then 2, then 5:

= AVG( GAGE1, GAGE2 ) * 0.25

Formula:

Pick the Ret key to save the formula; a result is displayed:

= AVG( GAGE1, GAGE2 ) * 0.250Formula: result: 602.000


4–10

Edit / Control Keys

You can edit the contents of a formula, using the edit/control keys, which arelisted and described in Table 4.B.

Table 4.BEdit / Control Keys

Key Name Edit / Control Function

Del Delete Deletes the formula item to the left of the cursor.

Clr Clear Clears the entire formula.

Ret Return Causes the formula to be saved in memory.

Esc Escape Restores the formula to its condition when last saved.

← Left arrow Moves the cursor to the left. Picking and holding the lightpen tip down moves the cursor continuously left.

→ Right arrow Moves the cursor to the right. Picking and holding thelight pen tip down moves the cursor continuously right.

↓ Down arrow Selects the second keyboard from the first keyboard.

↑ Up arrow Selects the first keyboard from the second keyboard.

All of the edit/control keys can be found on either of the two key sets(Figure 4.5 shows key locations).

Figure 4.5 Edit/control keys

Edit/controlkeys

To edit a formula:

← → Pick the arrows keys (← or→) to move the cursor to the left or rightalong the formula, in order to insert a component at a particular point in aformula, or to prepare to delete a particular component.

Del Pick the Del(ete) key to erase the entry to the left of the cursor.

Clr Pick the Clr (clear) key to erase the entire formula.


4–11

After editing a formula, pick either Ret or Esc:

Ret Pick the Ret key to save the formula as edited.

Esc Pick the Esc key to restore the formula to the way it was when last saved.

Example of Formula Editing

To edit this formula: AVG (GAGE1,GAGE2) * 0.250and change it to: AVG (GAGE1,GAGE3) * 1.250

• Pick the arrows keys (← or→) as necessary to move the cursor to theright of the GAGE2 operand:

= AVG( GAGE1, GAGE2 ) * 0.250

Formula:

• Pick the Del key to erase the GAGE2 operand:

= AVG( GAGE1, ? ) * 0.250

Formula:

• Pick G, then 3:

= AVG( GAGE1, GAGE3 ) * 0.250

Formula:

• Move the cursor to the right of the 0.250 operand:

= AVG( GAGE1, GAGE3 ) * 0.250

Formula:

• Pick the Del key; notice the entire 0.250 operand is erased:

= AVG( GAGE1, GAGE3 ) * ?

Formula:

• Pick 1, then “.” (decimal point), then 2, then 5:

= AVG( GAGE1, GAGE3 ) * 1.25

Formula:

After editing the formula, you can pick either Ret or Esc. Pick the Retkey to save the formula as edited. Pick the Esc key to restore the formulato the way it was when last saved.


4–12

Operands

With respect to MATH-PAK formulas, an operand is a symbol (such asGAGE1 or WINDOW3.2 or 32.45) that represents a mathematical orlogical value. Operands represent such values as tool results, statistics,constants, or formula results (see Table 4.C, starting on page 4–14, foroperand listings and descriptions).

Figure 4.6 Operand keys

Initial key set

Operand keys

To enter a particular operand in a formula:

• Pick the appropriate operand key on the formula entry keyboard – thecorresponding operand symbol appears in the display area of thekeyboard (see Figure 4.6).

• Typically you must then pick additional keys (decimal point and/ornumeric keys) to complete the operand entry.

For example, to enter the operand for gage 5 numerical results (number ofpixels, number of edges, and so on), enter the operand GAGE5, as follows:

• Pick G on the formula entry keyboard – this will initially display theoperand GAGE0 in the formula display area:

= ? GAGE0Formula:

• Pick 5 – this will change the operand to GAGE5.

= GAGE5Formula:


4–13

Using a sub-code: The operands can be defined so as to provide any of anumber of different types of results data. You do this by including asub-code – a decimal point and a number (refer to Table 4.C, page 4–14, forthe definitions of the valid sub-codes).

For example, to specify the pass/fail results from gage 5, in the exampleabove, you would enter the operand GAGE5.2:

• Pick G on the formula entry keyboard – this will initially display theoperand GAGE0 in the formula display area:

= ? GAGE0Formula:

• Pick 5, then “.” (decimal point), then 2 – this will change the operand toGAGE5.2.

= GAGE5.2Formula:

You can see in Table 4.C, page 4–14, that the “.2” sub-code definition is“Pass/fail condition for fault range (1 = pass, 0 = fail).” During inspections, then,if gage 5 were to fail, the value 0 would be entered for the Gage5.2operand. Conversely, if gage 5 passes, the value of 1 is entered.

Listing operands: Some operators require that you enter one or moreoperands in a parenthetical list following the operator. In these cases, whenyou pick the operator, the “open” parenthesis is displayed. After you list theoperands (separated by commas), you then enter the “close” parenthesis.

For example, to average the results from gages 1 and 2, enter the formula:AVG( GAGE1, GAGE2)

• Pick the AVG key on the formula entry keyboard (located on thesecondary key set). The formula keyboard display shows:

= AVG( ?Formula:

• Pick G (on the initial key set), then 1, then “,” (comma), then G, then 2.

= AVG( GAGE1, GAGE2 ?Formula:

• Pick “ ) ” (close parenthesis) on the secondary key set. The formula isnow correct in syntax at this point; the “?” disappears.


4–14

Table 4.C (part 1 of 3)Operand Definitions

Key OperandType

*Operand Symbol *Sub-code (s) Type of Data Returned to Formula

CNT Counter CNT.s(s = 0 to 2)

.0

.1

.2

Total number of triggers.Number of missed triggers.Number of master range faults.

G GageGAGEn.s

(n = 1 to 64)(s = 0 to 9)

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9

Gage measurement value (# of pixels, # of edges, etc.).Pass/fail condition for warning range (1 = pass, 0 = fail).Pass/fail condition for fault range (1 = pass, 0 = fail).Second coordinate value (Y coordinate for X Position gage;X coordinate for Y Position gage).Number of faults detected.Nominal value.Fault range high.Fault range low.Warning range high.Warning range low.

W WindowWINn.s

(n = 1 to 48)(s = 0 to 19)

.0

.1

.2

.3

.4

.5

.6

.7

.8.91,2

.101,2

.111,2

.121,2

.131,2

.141,2

.151,2

.161,2

.171,2

.181,2

.191,2

Window measurement value (# of pixels, # of objects, etc.).Pass/fail condition for warning range (1 = pass, 0 = fail).Pass/fail condition for fault range (1 = pass, 0 = fail).Number of faults detected.Nominal value.Fault range high.Fault range low.Warning range high.Warning range low.Total number of objects counted before target filtering.Perimeter value of first counted object.Area value of first counted object.X center value of first counted object.Y center value of first counted object.Inertial value of first counted object.Theta value of first counted object.Min radius value of first counted object.Max radius value of first counted object.H size value of first counted object.L size value of first counted object.

*The letter n = tool or formula number (as appropriate). The letter s = operand subcode.1Window sub-codes 9-19 pertain to the object–counting operation only. The “first counted object” is the object which, among those that satisfy the filterparameters, is closest to the upper-left corner of the window. 2 If a filter parameter is not enabled for the window, a result of –1000 is returned for that parameter.


4–15


Key OperandType


RL Ref. LineREFLn.s

(n = 1 to 3)(s = 0 to 3)

.0

.1

.2

.3

.4

X coordinate value of edge position on reference line.Y coordinate value of edge position on reference line.Pass/fail condition for reference line (1 = pass, 0 = fail).Theta from a reference line configured for “X–X then Y” or“Y–Y then X” rotation compensation.Number of faults detected.

RW Ref.Window

REFWn.s(n = 1 to 3)(s = 0 to 16)

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9.10.11.12.13.14.15.16

Cumulative position: X coordinate value.Cumulative position: Y coordinate value.Cumulative angle (θ).Cumulative pass/fail condition (1 = pass, 0 = fail).Active feature #1 position: X coordinate value.Active feature #1 position: Y coordinate value.Active feature #1 score value.Active feature #1 pass/fail condition (1 = pass, 0 = fail).Active feature #2 position: X coordinate value.Active feature #2 position: Y coordinate value.Active feature #2 score value.Active feature #2 pass/fail condition (1 = pass, 0 = fail).Active feature #3 position: X coordinate value.Active feature #3 position: Y coordinate value.Active feature #3 score value.Active feature #3 pass/fail condition (1 = pass, 0 = fail).Number of faults detected.

LP LightProbe

LPRB.s(s = 0 to 20)

.0

.1

.2

.3

.4

.5

.6

.7

.8

.9.10.11.12.13.14.15.16.17.18.19.20

Light probe brightness value for red channel.Light probe brightness value for green channel.Light probe brightness value for blue channel.Pass/fail condition for warning range (1 = pass, 0 = fail).Pass/fail condition for fault range (1 = pass, 0 = fail).Number of faults detected.Nominal value for red channel.Fault range high for red channel.Fault range low for red channel.Warning range high for red channel.Warning range low for red channel.Nominal value for green channel.Fault range high for green channel.Fault range low for green channel.Warning range high for green channel.Warning range low for green channel.Nominal value for blue channel.Fault range high for blue channel.Fault range low for blue channel.Warning range high for blue channel.Warning range low for blue channel.

*The letter n = tool or formula number (as appropriate). The letter s = operand sub-code.


4–16


Key OperandType


RES FormulaResult

RSLTn.s(n = 1 to 56)(s = 0 to 2)

.0

.1

.2

Formula (n) results data value.Pass/fail condition for warning range (1 = pass, 0 = fail).Pass/fail condition for fault range (1 = pass, 0 = fail).

STA StatisticsSTATn.s1,2

(n = 1 to 112)(s = 0 to 4)

.0

.1

.2

.3

.4

Formula/tool (n) statistics: Number of samples taken.Formula/tool (n) statistics: Minimum reading value.Formula/tool (n) statistics: Maximum reading value.Formula/tool (n) statistics: Mean value.Formula/tool (n) statistics: Standard deviation value.

*The letter n = tool or formula number (as appropriate). The letter s = operand sub-code.1 The n values 1-56 can refer to either tools or formulas. If the formula corresponding to the selected n number is enabled, the formula statistics are supplied;otherwise, the corresponding tool results are supplied. Refer to Table 4.A, page 4–3, for a listing of the formulas and corresponding tools.2 Statistics are available only if the Color CVIM module is run in “learn” mode.

Entering Constants as Operands

You can, of course, enter constant values, in either integer or fixed point(decimal) format, to act as operands in a formula, if appropriate. To do this,use the numeric keys (0–9), and the decimal point (.) key (for fixed pointnumbers) which are found on both of the two key sets (see Figure 4.4, page4–6).

For example, to enter the constant operand 1.25:• Pick 1, then “.” (decimal point), then 2, then 5:

= 1.25 ?Formula:

Here are some additional considerations when entering constant values:

Integer range: Integer values entered must be within the range –32767 to32767. Values outside this range are not accepted into the formula.

Fixed point (decimal) range: Fixed point decimal values entered must bewithin the range –32767.999 to 32767.999. Values outside this range are notaccepted into the formula.

Fixed point operands are always listed with 3 decimal places – trailing 0’sare added if necessary, or, if more than 3 decimal places are entered, thevalue is truncated to three decimal places.

Negative values: Negative values are created by placing the Unary minus(±) operator to the immediate left of the positive constant entered.


4–17

Operators

With respect to MATH-PAK formulas, an operator is a symbol (such as “+”or “–”) or term (such as “AND” or “AVG”) that represents a mathematical orlogical operation that is to be performed. Table 4.D, starting on page 4–18,lists the operator keys, and describes the corresponding operators.

To enter a particular operator in the formula:

• Pick the appropriate operator key on the formula entry keyboard – whenyou pick an operator key, the corresponding operator symbol appears inthe display area of the keyboard (see Figure 4.7).

Note: Additional operators are located on the secondary key set, which isaccessed by picking the ↑ key on the initial key set.

Figure 4.7 Operator keys (initial key set)

Initial key set

Operator keys

Prioritizing operations: Place parentheses around an operator and itsoperand(s) in order to prioritize that operation – that is, the result of theoperation(s) in parentheses can be used as an operand by another operator.“Nesting” is possible, too – this allows a parenthetical portion of aformula to be contained within another parenthetical portion.

ARC TAN ((GAGE2 – GAGE3) / (GAGE2.3 – GAGE4))

Listing operands: Some operators require that you enter one or moreoperands in a parenthetical list following the operator. In these cases,when you pick the operator, the “open” parenthesis is displayed alongwith the operator. After you list the operands (separated by commas), youthen enter the “close” parenthesis.

AVG( GAGE1, GAGE2 )


4–18

Table 4.D (part 1 of 2)Operator Definitions

Key / Symbol Operator Type *ResultType

Operator UsageFormat

Operator Function

Mathematical

+ Add INT/FP X +Y Adds the right operand to the left operand.

– Subtract INT/FP X – Y Subtracts the right operand from the left operand.

* Multiply INT/FP X * Y Multiplies the left operand by the right operand.

/ Divide INT/FP X / Y Divides the left operand by the right operand.

± Unary minus INT/FP ± XWhen placed to the immediate left of an operand, itnegates the numeric value of the operand.

% Modulo INT/FP X % Y Produces the whole number remainder of the divisionof the left operand by the right operand.

ABS Absolute value INT/FP ABS(X) Produces the absolute value of the listed operand(negates the value if it is negative).

SQ Square INT/FP SQ(X) Computes the square of the listed operand.

SQR Square root FP SQR(X) Computes the square root of the listed operand.

DST Distance FP DST(X1,Y1,X2,Y2)

Computes distance from a point A to a point B – givenfour listed coordinate operands X1, Y1, X2, and Y2 – bycomputing the square root of the sum of the squareddifferences (X2–X1 and Y2–Y1).

SIN Sine FP SIN(X) Computes the sine of a listed operand (angle –assumed in degrees). Returns a fixed point number.

COS Cosine FP COS(X) Computes the cosine of a listed operand (angle –assumed in degrees). Returns a fixed point number.

TAN Tangent FP TAN(X) Computes the tangent of a listed operand (angle –assumed in degrees). Returns a fixed point number.

ARCArc (prefix toSIN, COS, or

TAN)FP

SINARC COS (X)

TAN

ARC combines with SIN, COS, or TAN function, tocreate the respective inverse function – arcsine,arccosine, or arctangent. These inverse functionsproduce an angular result (in degrees).

Logical

AND Logical AND INT/FP X AND Y Produces a “1” result if both the left and right operandsare nonzero; otherwise, produces a “0” result.

OR Logical OR INT/FP X OR Y Produces a “1” result if either the left or right operandis nonzero; otherwise, produces a “0” result.

NOT Logical NOT INT/FP NOT XUsed to invert a logical value – Produces a “0” result ifthe operand is nonzero; produces a “1” result ifoperand is 0.

*INT=integer format. FP = fixed point (decimal) format


4–19

Table 4.D (part 2 of 2)Operator Definitions

Key / Symbol Operator Type *ResultType

Operator UsageFormat

Operator Function

Statistical

AVG Average INT/FP AVG(X, Y, ...) Computes the average of a list of operands.

MAX Maximum INT/FP MAX(X, Y, ...) Finds the maximum numeric value among operands.

MED Median INT/FP MED(X, Y, ...)Finds the middle numeric value in a list of operands bysorting the list in ascending order and returning thevalue located at the center position in the sorted list.

MIN Minimum INT/FP MIN(X, Y, ...) Finds the minimum numeric value in a list of operands.

MOD Mode INT/FP MOD(X, Y, ...) Finds the listed value that appears most often. If novalue appears more than once, finds the lowest value.

VAR Variance FP VAR(X, Y, ...)

Computes the variance of a list of operands. Thevariance is the sum of the square of the differencebetween each operand and the average value of theoperands, divided by the number of operands.

Conditional

= Equal INT/FP X = Y Produces a “1” result if the left operand is equal to theright operand; otherwise, produces a “0” result.

⟨ ⟩ Not equal INT/FP X ⟨ ⟩ Y Produces a “1” result if the left operand is not equal tothe right operand; otherwise, produces a “0” result.

> Greater than INT/FP X > Y Produces a “1” result if the left operand is greater thanthe right operand; otherwise, produces a “0” result.

< Less than INT/FP X < Y Produces a “1” result if the left operand is less than theright operand; otherwise, produces a “0” result.

>= Greater than orequal INT/FP X >= Y

Produces a “1” result if the left operand is greater thanor equal to the right operand; otherwise, produces a“0” result.

<= Less than orequal INT/FP X <= Y

Produces a “1” result if the left operand is less than orequal to the right operand; otherwise, produces a “0”result.

Other

. Decimal point –– –– Used when entering a fixed point decimal value. Alsoused in designating an operand sub-code.

, Comma –– –– Used to separate the operands in a list of operands.

( Open –– –– Used with “)” to prioritize operations with a formula.

) Close –– –– Used with “(” to prioritize operations with a formula.Also used to end operand listing for some operators.

*INT=integer format. FP = fixed point (decimal) format


4–20

Operator Execution Hierarchy

The order and priority of execution of the operations defined in a formula,where multiple operators are used, follows that of general mathematicalrules. Operators of higher priority are executed first. In cases of equalpriority, the operators are executed from left to right.

For example, multiplication and division have higher priority than additionor subtraction.

This formula would first divide the results of gage 2 by 3, and then add theresult to the gage 1 result:

GAGE1 + GAGE2 / 3

Add operator Divide operator

Prioritizing operations: You can place parentheses around an operator andits operands in order to prioritize that operation – that is, the result of theoperation in parentheses will be used as an operand by another operator.

This formula would first add the result of gage 1 and gage 2, and then dividesthe result by 2:

(GAGE1 + GAGE2) / 2

Add operator Divide operator

In defining formulas, as in general mathematical practice, it is best to useparentheses in formulas where multiple operators are used, to ensure theformula is executed as expected, rather than relying on priority rules.

Nesting operations within a formula: “Nesting” of operations within aformula can be employed, where a parenthetical portion is itself containedwithin another parenthetical portion of the formula.

The formula below would first add 2 to the result of gage 2, then multiplythis result by the gage 1 result, and then subtract 2 from the product:

(GAGE1 * (GAGE2 + 2)) – 2

Nested operation


4–21

Operator Usage

The MATH-PAK operators generally fall into one of four categories –mathematical, statistical, logical, and conditional (refer to Table 4.D,beginning on page 4–18, for a brief description of the operator types, whichare listed according to category). The operators are discussed in thefollowing sections, according to category.

Mathematical Operators

This section discusses the mathematical operators, which include thearithmetic operators, trigonometric operators, inverse trigonometricoperators, and other operators.

Arithmetic operators: + – / *

+ (addition) – Adds the two operands on either side of the “+”

– (subtraction) – Subtracts the operand on the right of the “–” from the operand on the left.

/ (division) – Divides the operand on the left of the “/” by the operand on the right.

* (multiplication) – Multiplies the two operands on either side of the “*”

Format / Usage: In general, enter and use the arithmetic operators informulas just as you would in writing an arithmetic equation – use twooperands with an operator, placing the arithmetic operator in the formulabetween the two operands, as shown in the example below:

GAGE1 * GAGE2

Multiply operator placed between two operands

Arithmetic hierarchy of execution: In general, arithmetic operations areexecuted from left to right, with multiplication and division operatorsevaluated before either addition or subtraction, as in general practice.

Example usage: This formula averages the results from gages 1 and 2. Theformula first uses the add operator (+) to add the 2 gage operands (becausethe parentheses prioritize the add operation), then uses the divide operator ( / ) to divide the result of the add operation by the constant, 2:

(GAGE1 + GAGE2) / 2


4–22

Subtraction example: The following formula uses the subtraction operator tofind the difference between two gage measurements:

GAGE2 – GAGE1

In this example, each of two gages is set to measure the X position of thecenter of an object (see Figure 4.8). Two gages are used, because the objectsbeing measured are of different colors, so each of the two gages is assignedthe appropriate color. The above formula subtracts the gage 1 result from thegage 2 result, yielding the horizontal distance between the two objects.

Figure 4.8 Example application, using the subtraction operator

Gage 1

XX

Gage 2

Unary minus operator: �

Format/Usage: The unary minus operator (� ) negates the value to itsimmediate right in the formula. The unary minus operator can be used with1) operands, including parenthetical expressions, and 2) operator/operandportions of the formula – that is, operators of the type that are followed by aparenthetical listing of operands.

Formula symbol: When you pick the � key to enter the unary minus into aformula, the “–” (minus) symbol is entered. Take care not to confuse thiswith the subtraction operator, which looks the same when entered.

Example usage: Use the � operator to negate the value of an operand:

– GAGE2 * GAGE3

Use the � operator to negate the value of an operator/operand:

1.250 * – AVG (GAGE2, GAGE3, GAGE4)


4–23

Modulo operator: %

Format/Usage: The modulo operator (%) performs the “long division”operation on one operand by a second operand, and yields the whole numberremainder of that division operation. In general, use two operands, placingthe modulo operator in the formula between the two operands. The leftoperand is the dividend, the right operand is the divisor.

The modulo operator can be applied in formulas, for example, to producebinary values from decimal-based integer values.

Example usage: Use the modulo operator to calculate a 5-place “binary”result from a gage 1 object-counting result (for values 0–31 decimal), using aseries of 10 formulas:

Formula 1: GAGE1 % 2

Formula 2: GAGE1 / 2

Formula 3: RSLT2 % 2

Formula 4: RSLT2 / 2






Formula 10: RSLT9 * 10000 + RSLT7 * 1000 + RSLT5

* 100 + RSLT3 * 10 + RSLT1

For example, if the gage 1 result were 19:

Formula 1: 19 % 2 (RSLT1=1)

Formula 2: 19 / 2 (RSLT2=9)








Formula 10: 1 * 10000 + 0 * 1000 + 0 * 100 + 1 *10 + 1 (RSLT 10=10011)

In the above example, the result of formula 10 is 10011, which, if interpretedas a binary value, would equal 19 (decimal).


4–24

Absolute value operator: ABS

Format/Usage: The absolute value operator (ABS) provides the absolutevalue of the operand or expression enclosed in the following parentheses. Touse the absolute value operator, enter the ABS operator – which includes theopen parenthesis “(” – then enter the operand or expression, and then enterthe close parenthesis “).”

The absolute value operator can be used with 1) single operands, 2) operator/operand expressions, such as arithmetic expressions, 3) operator/operandportions of the formula – that is, operators of the type that are followed by aparenthetical listing of operands.

Example usage: Use the absolute value operator with a parentheticalsubtraction operation, to ensure a positive result value:

ABS (GAGE2 – GAGE1)

Square operator: SQ

Format/Usage: The square operator (SQR) computes the square (anoperand multiplied by its own value) of an operand or expression enclosed inthe following parentheses. To use the square operator, enter the SQ operator– which includes the open parenthesis “(” – then enter the operand orexpression, and then enter the close parenthesis “).”

The square operator can be used with 1) single operands, 2) operator/operand expressions, such as arithmetic expressions, 3) parentheticaloperator/operand expressions, and 4) operator/operand portions of theformula – that is, operators of the type that are followed by a parentheticallisting of operands.

Example usage: Use the square operator with a linear gaging measurement tocalculate the area of a square object.

SQ (GAGE2) – WINDOW1.11

Square root operator: SQR

Format/Usage: The square root operator (SQR) computes the square root ofthe operand or expression enclosed in the following parentheses. To use,enter the SQR operator – which includes the open parenthesis “(” – thenenter the operand or expression, and then enter the close parenthesis “).”

Negative operand value: If the operand used returns a negative value, thesquare root operator result is zero (0).

The square root operator can be used with 1) single operands, 2) operator/operand expressions, such as arithmetic expressions, 3) parenthetical


4–25

operator/operand expressions, and 4) operator/operand portions of theformula – that is, operators of the type that are followed by a parentheticallisting of operands.

Example usage: Use the square root operator with a parenthetical expressionwhich adds the squares of gage 2 and gage 3, possibly to calculate a distance(by the Pythagorean theorem):

SQR (SQ (GAGE2) + SQ (GAGE3))

Distance operator: DST

Format/Usage: The distance operator (DST) computes the distance betweentwo points, given the x- and y-coordinates of the two points.

The format for the DST operator: DST (X1, Y1, X2, Y2), where X1 and Y1are assumed to be the x- and y-coordinates of the first point, and X2 and Y2are assumed to be the x- and y-coordinates of the second point.

To use the distance operator, enter the DST operator – which includes theopen parenthesis “(” – then enter four operands or expressions, separated bycommas, and then enter the close parenthesis “).”

Example usage: Use the distance operator to find the distance between twoobjects identified and located by two different windows:

DST (WIN1.12, WIN1.13, WIN2.12, WIN2.13)

Operands WIN1.12 and WIN1.13 indicate the x- and y-coordinates,respectively, of the center of gravity of the object identified by color inwindow 1 (see Figure 4.9). Similarly, operands WIN2.12 andWIN2.13 indicate the x- and y-coordinates, respectively, of the center ofgravity of the object identified by color in window 2.

Figure 4.9 Example of using the DST function

Window 1

Window 2

Distance fromwindow 1 objectto window 2objectObject

identified bycolor inWindow 1

Objectidentified bycolor inWindow 2


4–26

Trigonometric operators: SIN COS TAN

SIN – Calculates the sine value of the listed operand. Assumes the operand to be a value (�) stated in degrees.

COS – Calculates the cosine value of the listed operand. Assumes the operand to be a value (�) stated in degrees.

TAN – Calculates the tangent value of the listed operand.Assumes the operand to be a value (�) stated in degrees.The tangent (�) = sine (�) � cosine (�).

Format / Usage: In general, enter and use the trigonometric operators informulas just as you would in writing an equation – place the trigonometricoperator in the formula – which provides the open parenthesis “(” – followedby the operand, and then close the expression with the parenthesis “).”

Example usage: This formula yields the sine for the gage 2 result (GAGE2):

SIN(GAGE2)

Inverse trigonometric operators: ARC SIN ARC COS ARC TAN

ARC SIN – (arcsine) Calculates the angle (�) value (in degrees) of theoperand. Assumes the operand to be a sine value.

ARC COS – (arccosine) Calculates the angle (�) value (in degrees) of the operand. Assumes the operand to be a cosine value.

ARC TAN – (arctangent) Calculates the angle (�) value (in degrees) of the operand. Assumes the operand to be a tangent value.

Format / Usage: To enter an inverse trigonometric function, place the ARCoperator in the formula immediately followed by the respective trigonometricoperator. Then enter the operand, followed by the “)” (close parenthesis).

Valid range: Operand values for arcsine and arccosine operators must bebetween –1 and 1. Values beyond this range will provide a result of 0, andthe formula will fail.

Figure 4.10 Arcsine and arctangent operation results

–90�

90� 45�

–45�

0�Result (implied angle) isalways given as a valuebetween –90° and 90°

(0 to –90� if sine < 0 )

(0 to 90� if sine > 0 )


4–27

Results: Inverse trigonometric function results imply an angle or angularmeasurement. The result of an arcsine or arctangent operation is alwaysgiven as being between –90° and 90° (see Figure 4.10, page 4–26).

The result of an arccosine operation is always given as being between 0° and180° (see Figure 4.11).Figure 4.11 Arccosine operation results

90� 45�

0� Result (implied angle) isalways given as a valuebetween 0° and 180°

180�

135�

( 0 to 90� if cosine > 0 )( 90 to 180� if cosine < 0 )

Example arctangent usage: One objective of an inspection is to measure theangle, clockwise, of an object on a workpiece, relative to an imaginaryhorizontal line through the workpiece center (see Figure 4.12).

In this case, gage 2, a circular gage, is set to the Y Position operation, withthe feature offset defined to locate of the center of the object (seeFigure 4.12) on a circular workpiece. The Y Position operation for acircular gage finds directional vertical distance from the defined feature tothe implied center of the gage. It is assumed here that the implied center ofthe gage is aligned with the center of the workpiece.

Figure 4.12 Example application: Using the arctangent to calculate an angle �

X

Gage 2 (circular) finds the position ofthe center of theobject on theworkpiece

Workpiece

Implied center ofcircular gage,aligned withworkpiece center

Object

Formula finds the angle ofthe object, relative to ahorizontal line drawnthrough workpiece center

Horizontal line drawnthrough workpiece center

This formula provides the required angular measure:

ARC TAN (GAGE2 / GAGE2.3) + 180 * (GAGE2.3 < 0)


4–28

Here is how the example formula works: First, the formula calculates thearctangent value of the ratio GAGE2 / GAGE2.3, which is the verticaldistance between the object and the workpiece center divided by thecorresponding horizontal distance (see Figure 4.13). Note that if the operandGAGE2.3 equals 0 (zero), the formula fails (you cannot divide by 0).

Figure 4.13 Example application: Using operands GAGE2 and GAGE2.3

X

Object

Vertical distance(operand GAGE2)from workpiece centerto object center

Horizontal distance(operand GAGE2.3)from workpiece centerto object center

Then the formula conditionally adds 180 to the measure ( + 180 *(GAGE2.3 < 0) ), to provide for angular measurements greater than90° when necessary (remember that the arctangent operator result is alwaysgiven as between –90° and 90° – see Figure 4.10, page 4–26).

If, for example, the value of GAGE2.3 is negative, it means the object issomewhere to the left of the workpiece center, which implies an angle greaterthan 90° (see Figure 4.14). In this case, the conditional expression(GAGE2.3 < 0) is then true, which yields the value 1 for the conditionalexpression. The value 1 is multiplied by 180 in the formula and added to thearctangent result. As shown in Figure 4.14, the arctangent value of theratio(GAGE2 / GAGE2.3) is –55. However, since the operandGAGE2.3 is negative (since the object is to the left of the workpiececenter), 180 is added to the value –55, for a result of 125.

Figure 4.14 Example application: Finding angular results greater than 90°

X

�

� = –55° (arctangentmeasure of theobject relative to theworkpiece center)

Angle of object, relative toworkpiece center (125°)


4–29

When the value of GAGE2.3 is positive, the conditional expression(GAGE2.3 < 0) equals 0, so that 0 is added to the arctangent value.

Note that the previous example formula does not provide positive angularmeasurements for arctangent values between 0° and –90° (see Figure 4.15),which would correspond to positive angular measurements from 270° to360°. In order to supply values from 270° to 360° rather than values 0° to–90° , you could redefine the formula to also conditionally add 360:

ARC TAN(GAGE2 / GAGE2.3) + 180 *(GAGE2.3 < 0) + 360 * (GAGE2.3>0 AND GAGE2 < 0)

If the value of GAGE2.3 is positive (meaning the object is to the right ofthe workpiece center), and the value of GAGE2 is negative (meaning theobject is above the workpiece center), the conditional / logical expression(GAGE2.3>0 AND GAGE2 < 0) equals 1. The value 1 is multiplied by360 and added to the arctangent value. As shown in Figure 4.15, the operandGAGE2.3 would be a positive value, and the value of GAGE2 is negative,so that 360 would be added to the arctangent value –55, for a formula resultof 305.

Figure 4.15 Example application: Finding angular results greater than 270°

X

�

� = –55° (arctangentmeasure of theobject relative to theworkpiece center)

Angle of object, relative toworkpiece center (305°)

Statistical Operators

This section discusses the statistical operators, which include AVG (average),MAX (maximum), MED (median), MIN (minimum), MOD (mode), and VAR(variance).

Format/Usage: To use any of the statistical operators, enter the respectiveoperator (AVG, MED, etc.) – which includes the open parenthesis “(” – thenenter the operand or expression, and then enter the close parenthesis “).”

The statistical operators can be used with 1) single operands, 2) operator/operand expressions, such as arithmetic expressions, 3) parenthetical


4–30

operator/operand expressions, and 4) operator/operand portions of theformula – that is, operators of the type that are followed by a parentheticallisting of operands.

Average operator: AVG

The average operator computes the average value of the operands and/orexpressions that are listed in parentheses following the operator.

Example usage: The formula below averages the results from 3 gages:

AVG(GAGE1,GAGE2,GAGE3)

In this example, each of three gages is set for linear gaging, in order tomeasure the distance between the center of two objects (see Figure 4.16).The formula above provides the average measurement of the three gages. Inthis example, if the average value is beyond an acceptable range, the part isrejected.

Figure 4.16 Example application, using three gages to find an average measurement

Gages 1-3, each measuringdistance betweenthe two objects ofthe same color

X XX

X XX

Maximum operator: MAX

The maximum operator returns the maximum value among the operandsand/or expressions listed in parentheses following the operator.

Example usage: The formula below finds the maximum value among theresults of 3 gages:

MAX(GAGE1,GAGE2,GAGE3)

In this example, each of three gages is set for linear gaging, in order tomeasure the distance between the center of two objects (see Figure 4.16).The formula above yields the maximum value among the measurements ofthe three gages. In this example, if the maximum value is above a certainlevel, the part is rejected.


4–31

Median operator: MED

The maximum operator returns the median value among the operands and/orexpressions listed in parentheses following the operator. The median value isthe value for which there are an equal number of values in the list above andbelow the value. For example, for the list (2, 5, 7, 4, 3), the median is 4.

Note: If there is an even number of operands in the list, there cannot be anequal number of values below and above the median value. In this case, themedian value returned is the value with one less value above than below inthe list. For example, for the list (2, 5, 4, 7), the median is 5.

Example usage: The formula below finds the median value among theresults of 3 gages:

MED(GAGE1,GAGE2,GAGE3)

In this example, each of three gages is set for linear gaging, in order tomeasure the distance between the center of two objects (see Figure 4.16,page 4–30). The formula above yields the median value among themeasurements of the three gages. For example, if the three gages returnedthe values 1.250, 1.291, and 1.242, the median value would be 1.250, sinceone value is above (1.291) and one value is below (1.242).

Minimum operator: MIN

The minimum operator returns the minimum value among the operandsand/or expressions listed in parentheses following the operator.

Example usage: The formula below finds the minimum value among theresults of 3 gages:

MIN(GAGE1,GAGE2,GAGE3)

In this example, each of three gages is set for linear gaging, in order tomeasure the distance between the center of two objects (see Figure 4.16,page 4–30). The formula above yields the minimum value among themeasurements of the three gages. In this example, if the minimum value isbelow a certain level, the part is rejected.

Mode operator: MOD

The mode operator returns the value among the listed operands and/orexpressions which occurs most often. If more than one value occurs mostoften, the lower of these values is returned.


4–32

For example, from the list (1, 2, 2, 3, 3), the value 2 and the value 3 bothappear twice. In this case, the value 2 is returned.

Example usage: The formula below finds the mode value among the resultsof four object-counting windows:

MOD(WIN1,WIN2,WIN3,WIN4)

In this example, each of four windows is set for object-counting, in order toidentify parts by the number of objects counted (see Figure 4.17). The partscan rotate from inspection to inspection, so the exact number of objects to befound in each window is uncertain. Each window identifies object by color,and by object shape. In this example, if the mode value (most commonly-occurring value) is not 3, the part is rejected.

Figure 4.17 Example application, using windows and the mode operator

Windows 1-4each countobjects

Objectidentified bycolor andshape

Variance operator: VAR

The variance operator computes the variance value of the operands and/orexpressions that are listed in parentheses following the operator.

The variance operator computes the variance by:

1) Taking the average of the listed values;

2) Subtracting each listed value from the average, to obtain the difference from average for each value, then squaring each difference;

3) Adding up all the values obtained in step 2) to obtain the sum of the squares of the differences;

4) Dividing the sum obtained in step 3) by the number of listed operands.

The variance operator can be used as a means of evaluating variations amongmeasurements in an inspection.


4–33

Example usage: The formula below finds the variance of the results from 6gages:

VAR(GAGE1,GAGE2,GAGE3,GAGE4,GAGE5,GAGE6)

In this example, each of six gages is set for linear gaging, in order to measurethe distance between the center of two objects (see Figure 4.18). Theformula above provides the variance of the measurements of the six gages.In this example, if the variance value is beyond an acceptable range, the partis rejected.

Figure 4.18 Example application, using gages and the variance operator

Gages 1-6, each measuringdistance betweenthe two objects ofthe same color

X XX

X XX

X XX

X XX

Logical Operators

The logical operators, AND, OR, and NOT, perform the indicated logicalfunction, and return a logical (1 or 0) result. Generally, it makes sense to useoperands which are logical values (1 or 0), such as conditional operationresults, or tool pass/fail results. Nonetheless, you can use operands of anyvalue.

AND operator

The AND operator evaluates two operands as to whether or not each equals 0(zero), and then provides either a 1 or 0 result, as follows:

1 result – Only if both operands are non-zero.

0 result – If either or both of the operands equals zero.

Format / Usage: In general, use two operands with the operator, placing theAND operator in the formula between the two operands.

Example usage: This formula ANDs the pass/fail results from gages 1 and 2.A pass condition yields a 1 result, a fail yields a 0 (zero) result. The formula


4–34

yields a 1 result if both gages pass, and a 0 (zero) result if either or bothgages fail.

(GAGE1.2 AND GAGE2.2)

OR operator

The OR operator evaluates two operands as to whether or not each equals 0(zero), and then provides either a 1 or 0 result, as follows:

1 result – If either or both operands are non-zero.

0 result – Only if both of the operands equal zero.

Format / Usage: In general, use two operands with the operator, placing theOR operator in the formula between the two operands.

Example usage: This formula ORs the pass/fail results from gages 1 and 2.A pass condition yields a 1 result, a fail yields a 0 (zero) result. The formulayields a 1 result if either or both gages pass, and a 0 (zero) result only if bothgages fail.

(GAGE1.2 OR GAGE2.2)

NOT operator

The NOT operator inverts the logical evaluation (1 or 0) of an operand orexpression in a formula, assigning a logical value as follows:

0 – If the operand is non-zero.

1 – If the operand equals 0 (zero).

Format / Usage: Place the NOT operator to the immediate left of the operandin the formula.

Example usage: This formula first ANDs the pass/fail results from gages 1and 2. A pass condition yields a 1 result, a fail yields a 0 (zero) result.

(GAGE1.2 AND GAGE2.2) AND NOT GAGE3.2

Then, the formula takes the result of the first AND operation, and ANDs itwith the inverse (NOT) of the pass/fail result of gage 3. In this case, theresult of the formula is 1, only if both gage 1 and gage 2 pass, and gage 3fails. Otherwise, the result is 0.


4–35

Conditional Operators

A conditional operator compares two operands, and returns a true (1) or false(0) value for the indicated condition. The conditional operators include = (equal to), <> (not equal to), <= (less than or equal to), => (greater than orequal to), < (less than) , and > (greater than).

Format / Usage: Use two operands or parenthetical expressions with theoperator, placing the conditional operator in the formula between the twooperands.

Example conditional operators: This formula compares the numerical resultof gage 1 to gage 2 to see if the two are equal, and also compares thenumerical result of gage 2 to that of gage 3, to see if they are not equal.

(GAGE1 = GAGE2) AND (GAGE2 <> GAGE3)

In this case, the result of the formula is 1 (true), if the gage 1 result equals thegage 2 result, and if the gage 2 result does not equal the gage 3 result.Otherwise, the result is 0 (false).

Additional Formula Examples

This section presents additional formula examples, to illustrate some of theadditional functionality and flexibility possible through the use of formulas.

Flagging Consecutive Rejects

This example requires the use of two formulas, the result of which is toprovide an output signalling the occurrence of 10 consecutive rejects.

Assume that the example application requires the use of gages 1 and 2, andof windows 1 and 2.

Formula 1 would be as follows:

GAGE1.2 AND GAGE2.2 AND WIN1.2 AND WIN1.2

The result of formula 1 will be 1 if all tools pass, otherwise, the result will be0 (zero).

Formula 2 would be as follows:

(RSLT2 + NOT RSLT1) * NOT RSLT1


4–36

For each inspection, if any tool fails, the value RSLT1 =0. Therefore thevalue NOT RSLT1 =1. Thus, for any inspection that fails, the value 1 isadded to RSLT2 by the portion of the formula(RSLT2 + NOT RSLT1).Thus, if consecutive failures occur, the value of RSLT2 is incremented byone for each failure. This is because the RSLT2 value (the result of formula2) is retained from inspection to inspection.

As soon as an inspection passes, however, the value RSLT2 is reset to 0.This is because when an inspection passes the value RSLT1 =1. Thereforethe value NOT RSLT1 =0. Thus, in the formula, when an inspection passes,the quantity (RSLT2 + NOT RSLT1) is multiplied by 0.

The fault range limit for formula 2, in this example, is set to 10. Thus when10 consecutive failures occur, Formula 2 fails. The output of the formula 2range limits can be assigned to a results output and used to trigger a signalthe event of 10 consecutive failures.

Creating a Shift Register

This example requires the use of four formulas, the result of which is toprovide a shift register effect, which produces a pass/fail output that isdelayed by four triggers.

Assume that the example application requires the use of window 3.

Formula 4 would be set to yield the numerical result of window 3:

WIN3

Formula 3 would be set to yield the result of formula 4:

RSLT4


RSLT3


RSLT2

The formulas are evaluated in numerical order for each inspection. Thus, foreach inspection, formula 1 is first set to the formula 2 result value, thenformula 2 is set to the formula 3 result value, then formula 3 is set to the


4–37

current value of formula 4, then formula 4 is set to the current value ofwindow 3. The result of this shifting of window 3 results is that the formula1 result equals the window 3 result from four inspections ago.

The fault range limit for formula 1, in this example, is set to the appropriateparameters for window 3. The output of formula 2 can be assigned to aresults output and used to trigger a signal the event window 3 failure.

This application example is particularly useful where indexing of partsoccurs, and where the action taken on a part failure occurs further down theline (in this example “further down” means “four triggers down”).

Once you have defined a formula’s contents, you can name the formula usingthe Set Name box on the Config. Results menu. Entering descriptivenames for formulas can be useful – during run mode, for example, formulascan be displayed according to their pass/fail status. It may be easier, when aformula is displayed, to identify a formula’s function if it has a name relatingto its content or functionality.

Default name: In case you do not name a formula, a default name is enteredautomatically, when you define the formula. The default name for a formulais F#, where # is the formula number.

Define formula first: The Set Name box for a selected formula is disableduntil the formula has been defined. Thus you cannot enter a formula nameuntil you enter a valid definition (see “Defining a Formula” in this chapter).

Figure 4.19 Using the keyboard to set the formula name

To enter a formula name:

• Pick Set Name on the Config. Results menu. The keyboard appears(see Figure 4.19).

Naming a Formula


4–38

• Enter the desired formula name, by picking the appropriate keys on thekeyboard (see Chapter 5 in the Color CVIM User’s Manual for morekeyboard usage information). Pick Ret when the name is entered asdesired. When you do, this message appears:

Name restrictions: Names can contain up to seven characters, includingspaces. Any additional characters entered are truncated from the right.

Once you have defined a formula’s contents, you must then enable theformula, in order for the formula to function as part of the configuration, andin order to set range limits and assign outputs for the formula.

Define formula first: The Formula #: Disabled box for a selected formulais itself disabled until the formula has been defined. Thus you cannot enablea formula until you first define it (see “Defining a Formula” in this chapter).

To enable a formula:• Pick the Formula #: Disabled box on the Config. Results menu (see

Figure 4.20).Figure 4.20 Enabling a formula

Formula #: Disabled box

A warning message appears, listing the corresponding gage or windowwhich is affected.

Enabling / Disabling aFormula


4–39

• Pick the Formula #: Disabled box again to confirm. The box toggles toEnabled, and the Range/Outputs box for the formula is enabled.

To disable a formula:

• Pick the Formula #: Enabled box on the Config. Results menu. Awarning message appears, stating that a corresponding gage or windowcan now be range checked (when its range checking is also enabled):

• Pick the Formula #: Enabled box again to confirm. The box toggles toDisabled, and the Range/Outputs box for the formula is disabled.

Here are some additional considerations for enabling formulas:

Formulas prevent the use of associated gage and window outputs: Anyformula you select and enable will disable the use of results outputs from acorresponding gage or window (as listed in Table 4.A, page 4–3).

Formula results replace the results of the corresponding gage andwindow in the results blocks: When you enable a formula, its inspectionresults are listed in the results block, in place of the corresponding gage orwindow results (as listed in Table 4.A, page 4–3). Results blocks containthe comprehensive inspection results available by transfer through the ColorCVIM backplane, or through one of the Color CVIM serial ports.

For more information: See “Selecting a Formula” in this chapter, and seealso Appendix A, for more information on the effects of using formulas.

The Copy and Paste features, which are found on the Config. Resultsmenu, allow you to copy all the contents a selected formula, along with theformula name, to one or more other formula numbers.

Using Copy and Paste can save you time and effort in creating yourformulas, especially when you intend to use a number of similar formulas, orif you want to investigate a number of variations of a formula.

You can also use Copy and Paste when you have defined a formula whoseformula number is such that it conflicts with a tool whose results you want toaccess (see “Selecting a Formula” in this chapter). You could resolve theconflict by copying the formula to a non-conflicting formula number (onewhose corresponding tool is either disabled or whose results are notrequired), and then disable the original formula (see Figure 4.21, page 4–40).

Using Copy and Paste


4–40

To use the Copy and Paste features, follow this general procedure:

• Select the source formula – Pick the Next or Previous box, or use theJump box, to set the formula number to the formula you wish to copy.

• Pick the Copy box. This marks the current formula selection as thesource. The Paste box will then designate the number of the source.

• Select the destination – Pick the Next or Previous box, or use the Jumpbox, to set the number to the destination – the formula which will receivecontents from the source.

• Pick the Paste box. The formula contents are automatically copied fromthe previously selected source formula to the currently selecteddestination formula.

Figure 4.21 Copying a formula

Copy / Paste boxes

Previous / Next boxes

Note these additional considerations regarding the Copy/Paste features:

Previous contents overwritten: When you copy the contents of the sourceformula into the destination formula, the previous contents of the destination,if any, are overwritten.

Source formula remains selected: The source formula selection remains asselected until a different source formula is selected. This means that you cancopy the source formula contents to a number of different formulas.

Copied formula contents pasted: When you pick the Paste box, thecopied contents of the selected source are pasted. For example, suppose thatyou select formula 1 and pick the Copy box, then change some of thecontents of formula 1 before picking the Paste box. When you do pick thePaste box, the copied former version, not the current version, of formula 1would be pasted to the destination formula.


4–41

Formula name copied: The formula name is copied as well as the formulacontents. When you copy a formula, you may want to change the name ofthe formula at the destination, or at the source, as appropriate.

Name and contents copied: Only the formula contents and formula nameare copied; the range limits and output assignment(s) are not copied.

Copying an undefined formula: If you copy an undefined formula (onewhich has no contents currently entered), when you paste the formula to aformula which has already been defined, you will delete the destinationformula, and this message will be displayed:

Example Copy and Paste

To copy the contents of formula 1 to formula 2, you would do the following:

• Pick the Previous or Next boxes, or use the Jump box, as required toselect formula 1.

• Pick the Copy box to select formula 1 as the source. The Paste box willdisplay the number of the source formula – in this case, the box readsPaste 1, for formula 1 (see Figure 4.21, page 4–40).

• Pick the Next box to select the destination formula – formula 2.

• Pick the Paste box to place the source formula contents into thedestination formula.

The Paste box retains the source formula listing (1, in this case) until youuse the copy box to select another source formula. The source formuladesignation is updated if and when you select a different source formula.

Once you have defined a formula’s contents, and have enabled the formula,you can set range limits and assign outputs for the formula. The usage andfunction of range limits and output line assignment for a formula areidentical to that of inspection gages and windows (see also the chapter onrange limits and output lines in the Color CVIM User’s Manual).

The term range limit refers to the tolerance limits you set for the formularesults. You can specify High and Low FAULT RANGE limits, and/or theHigh and Low WARNING RANGE limits, for the formula results.

Setting Range Limits andAssigning Outputs


4–42

The two sets of range limits have this relationship:

LF <= LW <= REFERENCE <= UW <= UF, where:

LF = Low FAULT RANGE limit

LW = Low WARNING RANGE limit

UW = High WARNING RANGE limit

UF = High FAULT RANGE limit

The REFERENCE value could be based, for example, on the “mean”formula result from a trial series of inspections conducted with the ColorCVIM module running in learn mode.

Once you have set the High and Low WARNING RANGE and/or FAULTRANGE limits for a formula, you can assign the limits to output lines, whichwould then be activated whenever the respective range limits were exceeded.

Formula status: If a formula inspection result lies within both the FAULTRANGE and WARNING RANGE limits, a “pass” condition exists for thatformula. If the result lies outside a WARNING RANGE limit, but withinthe FAULT RANGE limits, a WARNING condition exists for the formula.In addition, if the formula result also lies outside the FAULT RANGE limits,a FAULT condition also exists for that formula.

Formula result format/conversion: The result for a particular formula isexpressed in either fixed decimal point, or integer value, as appropriate forthe operands and operators in use. When you set the range limits, either theinteger format or fixed decimal point format is used by the Color CVIMautomatically, as appropriate for the type of result.

If the formula is changed after the range limits are set, so that the requiredresult format changes, the format of the range limit is convertedautomatically. If a fixed point range limit is converted to integer format, therange limit value is rounded to the nearest integer value.

Result Restrictions: Integer results for a formula are restricted to the rangeof �2,147,483,647. Fixed point (decimal) results for a formula arerestricted to the range of �32767.000. If a formula result goes beyond theallowable range, a result of 0 is returned, and the formula fails.

Master range status: The FAULT status for each formula has an effect onan output called the Master Range. For each inspection, if any user-definedFAULT RANGE limit is exceeded, the Master Range status is activated; ifMaster Range is assigned to one of the output lines, the output line isactivated accordingly (see Chapter 11 in the Color CVIM User’s Manual forinformation on the Master Range and output line assignment).

Multiple range limit assignment to a single output: You can assign morethan one range limit to a single Results output line. For example, you canassign both the High and Low WARNING RANGE limits to one Results


4–43

output line, and assign both the High and Low FAULT RANGE limits toanother Results output line.

Formulas prevent the use of associated gage and window outputs: Anyformula you select and enable will disable the use of results outputs from acorresponding gage or window (as listed in Table 4.A, page 4–3).

Entering Range Limits for Formulas

After you determine the appropriate FAULT RANGE and/or WARNINGRANGE limit values for a formula, you can enter these values using therange/output setup table.

Define and enable formula first: A formula must be both defined andenabled before you can enter range limits.

To access the range/output setup table for a formula:• Pick Range/Outputs on the Config. Results menu to display the

range/output table (see Figure 4.22).

Figure 4.22 Assigning range limits

Calculator pad

Inspectionstatistics

table

Range/output table

If all range limits are currently set to zero as shown in Figure 4.22, enter theappropriate High and Low FAULT RANGE and/or WARNING RANGElimits in the following order:

1. Pick the High box under FAULT RANGE. When you do, the calculatorpad appears, as shown in Figure 4.22.


4–44

2. Enter the desired value (positive or negative) for the FAULT RANGEHigh limit.

3. Repeat steps 1. and 2. for the Low box under FAULT RANGE, enteringthe Low limit for the FAULT RANGE.

4. Repeat steps 1. and 2. for the High box under WARNING RANGE.

5. Repeat steps 1. and 2. for the Low box under WARNING RANGE.

If the range limits are not currently zero, the following rules apply:

• If you change a FAULT RANGE limit to a smaller value than thecorresponding WARNING RANGE limit, the WARNING RANGE limitwill change to the new FAULT RANGE limit, and this message appears:

• If you attempt to change the High WARNING RANGE limit to a largervalue than the High FAULT RANGE limit . . .

• Or, if you attempt to change the Low WARNING RANGE limit to asmaller value than the Low FAULT RANGE limit . . .

• Or, if you attempt to change an High range limit to a smaller value thanthe associated Low range limit . . .

• Or, if you attempt to change an Low range limit to a larger value than theassociated High range limit . . .

the following message will flash briefly in the calculator pad window . . .

WARNING OUT OF RANGE

. . . and the previous value will be retained.

Inspection Statistics Table

This table can contain data from a series of inspections with the Color CVIMmodule running in the learn mode (see Chapter 20, Runtime options, in theColor CVIM User’s Manual, for more information).

The Nominal value in the table is not available for formulas.

The remaining values in the statistics table are the number of inspectionsperformed (Samples) and the statistical results based on a series ofinspections performed in learn mode. If no inspections have been performedwith the Mode set to Learn, these values will be all zeros (as shown inFigure 4.22, page 4–43).


4–45

Using the learn mode statistics: You can run a series of trial inspections,using a representative sample of workpieces, with the Color CVIM modulein Learn mode, in order to accumulate a statistical basis for setting theFAULT RANGE and WARNING RANGE limits. For more information onthe learn mode, refer to the Chapter 20 in the Color CVIM User’s Manual.

Example Range Limit Setting

Here is an example of setting the range limit values for a formula:

AVG(GAGE1, GAGE2, GAGE3)

which averages the values of three gages (see Figure 4.23), in relation to theREFERENCE value:

• The REFERENCE (ideal or nominal) value is 15.000.

• WARNING RANGE – Low 14.800. High 15.200.

• FAULT RANGE – Low 14.600. High 15.400.

With the range limits set as shown above, if a formula result is outside eitherWARNING RANGE limit (above 15.200 or below 14.800), but within theFAULT RANGE limits, the formula will have a WARNING condition only.If an inspection result is outside either FAULT RANGE limit (above 15.400or below 14.6), the formula will have both a WARNING and a FAULTcondition.

Figure 4.23 Example: Range limits for linear gaging

A B

15 cm (Ideal)

Gages measure distancefrom feature A to feature B

A B

A B

Gage 1Gage 2

Gage 3

Here is an example of setting the range limit values for a conditionaloperation by a formula (see Figure 4.24, page 4–46), where theREFERENCE value, 1, is the only acceptable value:


4–46

• The REFERENCE (ideal or nominal) value is 1.

• WARNING RANGE – Low 0. High 2.

• FAULT RANGE – Low 0. High 2.

With the range limits set as shown above, the only acceptable formula resultis 1. If the formula result is not 1, the formula fails. Note that in this caseWARNING RANGE limits are the same as the FAULT RANGE limits.

Figure 4.24 Example: Formula with conditional operation for comparing gage results

GAGE1 > GAGE2

Assigning Range Limits to Results Output Lines

As with range limits for gages and windows, you can assign outputs to therange limits you set for formulas. To assign a formula range limit to aResult output line:

• Pick the Output box under the FAULT RANGE or WARNING RANGEheading, as appropriate. The USAGE menu appears (see Figure 4.25,4–47).

• Pick the appropriate �� box in the USAGE menu.

You can select outputs lines only if have been previously assigned to results.For example, as shown in Figure 4.25, only output lines #1 and #2 areenabled and available; they are the only lines with a Results assignment, inthis case. The other output lines are either assigned other functions or are notused; thus, they are not available for range limit use. For information onassigning functions to output lines, see Chapter 11, Discrete I/O LineConfiguration in the Color CVIM User’s Manual.

Remember, you can assign more than one range limit to a single Resultsoutput line. For example, you might assign both the High and LowWARNING RANGE limits to one Results output line, and assign both theHigh and Low FAULT RANGE limits to a different Results output line.

Or, for example, you might assign the FAULT RANGE limits for severaldifferent formulas to a single Results output, if this meets your applicationrequirements. In this case, the Results output would be activated if any oneof the assigned FAULT RANGE limits for any of the formulas wereexceeded.


4–47

Figure 4.25 Selecting output lines for range limits

USAGEmenu

Enabling Results and Range Limits for Corresponding Tools

Any formula you select and enable will disable the use of results outputsfrom a corresponding gage or window, as listed in Table 4.A, page 4–3. Inorder to use the results from a tool which corresponds to a formula in use,you must disable the formula, then enable the tool results, as describedbelow:

• Disable the formula (see “Enabling / Disabling a Formula” in thischapter) which corresponds to the tool (as listed in Table 4.A, page 4–3).

• Pick the Range/Reference box on the corresponding gage or window(see Figure 4.26, page 4–48).

• Pick the Range box to toggle the setting to Enabled. This enables theRange/Outputs box.

• Pick Range/Outputs to display the range/output setup table.

• Set the range limits and assign outputs as necessary (for moreinformation, refer to Chapter 13 in the Color CVIM User’s Manual).

Clearing of Range Limits and Output Assignments for Tools: If youdefine range limits and assign outputs for a tool, and you then enable aformula corresponding to that tool (as listed in Table 4.A, page 4–3), therange limits and output assignments for the tool are reset to default values(no output assignments, and range limits set to 0).


4–48

Pass status for tools whose results are disabled by a correspondingwindow: Any formula you select and enable will disable the use of resultsoutputs from a corresponding gage or window, as listed in Table 4.A, page4–3. Any tool whose results are thus disabled will always be assigned apass status by the Color CVIM module. This means, for example, thatduring runtime, any tool whose results are thus disabled will appear in greenwhen the All Tools display is selected.

Figure 4.26 Enabling the range limits and outputs for tools

Range: box

Range/Reference: box

A–B 5Chapter

5–1

Analysis Functions and Runtime Displays

ContentsChapter Objectives 5–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis Functions 5–1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Statistics (Learn Mode) for Failed Tools 5–2. . . . . . . . . . . . . . . . . . . . . . . . Runtime Displays 5–3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This chapter describes the use of Analysis functions and runtime displayswith MATH-PAK installed.

The Color CVIM module’s Analysis functions allow you to obtain theinspection processing time required for your current configuration. WithMATH-PAK installed, the analysis function calculations can also include theformulas you have enabled and defined.

You can determine which tools are included in analyzing the processing time,including formulas, by using the Tool Display menu.

Figure 5.1 Selecting the Tool Display menu

Tool Displaymenu

To access the Tool Display menu (see Figure 5.1):

• Pick Misc → Analysis to access the Analysis menu.

• Pick Tool Display to access the Tool Display menu.

With the Tool Display menu selected, you can see that the Formulas boxallows you to specifically analyze the formulas for processing time (seeFigure 5.1). If you pick the All Tools box, all tools are included in theanalysis, including formulas.

Chapter Objectives

Analysis Functions

Chapter 5Analysis Functions and Runtime Displays

5–2

With MATH-PAK installed, the Color CVIM module allows you to selectwhether you will include or exclude data from failed tools when collectingstatistics (when running the Color CVIM in learn mode).

You determine whether data from failed tools is included in the statisticsthrough the use of the Range Fail box on the Runtime Init. menu (seeFigure 5.2):

• Pick Exit → Runtime Init. to access the Runtime Init. menu.

• Pick the Range Fail: box to toggle the setting between No Stats andStats.

The effects of the Range Fail selection are as follows:

Stats: Statistics collected will include results from failed tools as well asfrom tools which pass.

No Stats: Statistics collected will include results only from tools whichpass.

Figure 5.2 The Range Fail box

Range Fail box

Statistics (Learn Mode) forFailed Tools


5–3

The Color CVIM module’s runtime displays allow you to observe updatedinspection results during run mode, as the inspections occur. WithMATH-PAK installed, the various runtime displays can also include theformulas you have enabled and defined. These runtime displays include:

• Runtime tools displays (All Tools or Failed Tools)

• I/O Page

• Results Page

• Stat. Page 1

Selecting runtime display – setup mode: During setup mode, you canselect the initial runtime display using the Runtime Display menu, accessedthrough the Exit box on the main menu (see Figure 5.3):

• Pick Exit → Runtime Display to access the Runtime Display menu.

• Pick the desired Runtime Display option.

Figure 5.3 Runtime Display menu – setup mode

Runtime Displaymenu

Selecting runtime display – run mode: You can select the runtime displayduring run mode, using the Display menu (see Figure 5.4):

• Pick the Display box to access the Display menu.

• Pick the desired Display option.

Figure 5.4 Display menu – run mode

Displaymenu

Runtime Displays


5–4

Runtime Tools Displays

With MATH-PAK installed, the tools displays, All Tools and Failed Tools,will include the enabled formulas. Formulas are displayed by formula name,in numerical order, in the top left corner of the screen (see Figure 5.5).

Figure 5.5 Formulas displayed in Failed Tools display during run mode operation

Formulaslisted in red (oryellow)

Tools displayedin red (oryellow)

During runtime, any enabled formulas are listed according to the runtimeDisplay menu selection (see Figure 5.5):

All Tools – Displays all enabled tools and formulas. The displays arecolor-coded – failed tools and formulas are displayed in red; tools whichare within fault range limits, but not within warning range are displayedin yellow; tools which are within all range limits are green.

Failed tools – Displays only the tools and formulas whose results arebeyond the fault (red) and/or warning range (yellow).

I/O Page

Formula output status is displayed on the I/O Page during run mode –formula results are found on the third page of the I/O Page display.

As with other tool output status, formula output status is color-coded – green(pass), yellow (warning), or red (fault).


5–5

To display the formula result on the I/O Page during run mode:

• Pick Display → I/O Page to access the I/O Page display.

• Pick the Page ↓ button twice, to page down to the formula page.

Figure 5.6 Formulas displayed on I/O Page display during run mode operation

Formula statusshown on I/O Display

Results and Stat1 Page Displays

Formula results can be displayed on the Result Page during run mode –along with gage and window results – provided a number of formulasdisplayed is selected, during setup, using the Disp. Formulas box on theRuntime Init. menu.

Similarly, formula statistics can be displayed on the Stat1 Page during runmode – along with gage and window statistics.

The Disp. Formulas, Disp. Windows, and Disp. Gages parameters on theRuntime Init. menu determine the mix of formulas,windows, and gageswhose corresponding data appear on each individual page of the ResultPage (and Stat1 Page) display panels during the run mode (these displaypanels each include several “pages” of data).

To enter a value for number of formulas (or gages or windows) displayed:

• Pick Exit → Runtime Init. to access the Runtime Init. menu.


5–6

• Pick the Disp. Formulas box (or Disp. Windows or Disp. Gages box,as appropriate); when you do, the “calculator pad” appears on the screenas shown in Figure 5.7.

• Enter the value using the calculator pad number keys, then pick the Enterkey; the new value will appear in the Disp. Formulas box (or Disp.Windows or Disp. Gages menu box).

Figure 5.7 Calculator pad for entering number of displayed formula/tool results

Calculator pad

Disp. Formulas box

Results Display Limitations: Since the Stat1 Page and Result Pagedisplay panels are of a fixed size, the mix of window, gage, and light proberesults that can fit on one page of these panels must be traded off.

The maximum number of gages and/or windows you can indicate for display(per display page) depends on whether the Disp. Probe (light probe data) isenabled or disabled, and whether you are displaying only one kind of data(that is, only formula, or window, or only gage data), or you are displaying acombination of formula, window, and/or gage data.

With Disp. Probe (light probe data) disabled – If you display only one typeof data, you can display up to 12 of the the single type – that is, 12 formulasonly or 12 windows only or 12 gages only. Or you can combine two types oftools – so that the total number of the two types is l0 or less. Or you cancombine three types of tools – so that the total of the three types is 8 or less.

With Disp. Probe (light probe data) enabled – If you display only one typeof data, you can display up to 9 of the the single type – that is, 9 formulasonly or 8 windows only or 9 gages only. Or you can combine two types oftools – so that the total number of the two types is 7 or less. Or you cancombine three types of tools – so that the total of the three types is 5 or less.


5–7

For example, assume no light probe results are displayed (that is, Disp.Probe: set to Disabled). If you set Disp. Formulas to 4, you can set Disp.Windows to a value from 0–6. If you then set Disp. Windows to 3, you canthen set you can set Disp. Gages to a value from 0–1. If you then set Disp.Gages to 1, this would display the data from formulas 1–4, windows 1–3,and gage 1 on the first page of the Stat1 Page and Result Page displaypanels, formulas 5–8, windows 4–6, and gage 2 on the second page, and soon.

Help message: If you pick the “help” symbol with the Disp.Formulas, Disp. Windows or Disp. Gages box selected, the help messagebox . . .

Figure 5.8 Typical help message for the Disp. Windows option

. . . will show you the current maximum number of formulas, windows orgages that you can select, given the number of tools currently selected, andthe enabled/disabled status of the light probe results display.

To display the formula/tool results on the Result Page during run mode:

• Pick Display → Result Page to access the Result Page display.

• Pick the Page ↓ and Page ↑ buttons to page up or down through theformula and tool results.

To display the formula/tool statistics on the Stat1 Page during run mode:

• Pick Display → Stat1 Page to access the Stat1 Page display.

• Pick the Page ↓ and Page ↑ buttons to page up or down through theformula and tool statistics.

A–B AAppendix

A–1

Color CVIM Communications with MATH-PAK Installed

This appendix discusses and lists the configuration, result, and discrete bitoutput information for MATH-PAK formulas, which is accessible throughthe communication ports of the Color CVIM module. This informationincludes:

• Location and format of formula results blocks.

• Accessing formula results and statistics.

• Location and format of formula configuration blocks.

• Location and format of discrete bit outputs for formulas.

The Color CVIM communications manual (Cat. No. 5370-ND010) describeshow to access the configuration, results, and discrete bit output informationthrough the various communication ports – the backplane, remote I/O port,and the RS-232 port. That information also applies with MATH–PAKinstalled, except when any formulas are enabled. When a formula is enabledin the Color CVIM configuration, the results, discrete bit, and configurationinformation for all enabled formulas will replace the results, discrete bit, andconfiguration information for the corresponding gages or windows.Table A.1 provides a listing of formula numbers and the corresponding tools.

Table A.1Formula numbers and corresponding gage/window numbers

Formula Tool Formula Tool Formula Tool Formula Tool















Objective

Formula Data ReplacesTool Data

Appendix AColor CVIM Communications with MATH-PAK Installed

A–2

The Color CVIM communications manual lists and describes all of theaccessible results blocks. The results information for an enabled formulawill replace the results information for a corresponding gage or window inthe results blocks, as shown in the following tables:

• Table 4.C, page 4–14, shows the locations of the formula results in resultsblock 1.

• Table 4.D, page 4–18, shows the locations of the formula results in resultsblock 2.

• Table 4.B, page 4–10, shows the locations of the formula results in resultsblock 3.

Configurable results block: Results block 6 is a configurable results block(refer to the Color CVIM communications manual for more information). Ifneed be, you can configure results block 6 to supply tool results informationthat has been replaced by formula information in results blocks 1–3. Youcannot configure the results block 6 to provide formula results information.

When attempting to use results block 6 to obtain gage or window statisticsinformation, the gage or window statistics will be replaced by formulastatistics, if the corresponding formula is enabled (refer to Table A.1, pageA–1, for a listing of the formula numbers and the corresponding tools).

Data types for formula results:

• If the results are for a formula which includes any items that require fixedpoint values, then the result will be conveyed in fixed point values(16.16).

• If the results are for a formula which has only items that require integervalues, then the result will be conveyed in integer values (32.0).

Results Blocks


A–3

Table A.2Results Block 1 – Formula/Tool Results

Word #

PIBackplane

RS–232and

RemoteI/O

Bit # Enabled Formula(Formula Not Enabled) Usage Notes

56–57 24–25 0–15 Formula #1 Result(Window #1 Value)








72–73 40–41 0–15 Formula #9 Result(Gage #1 Value)









A–4

Table A.3 (part 1 of 2)Results Block 2 – Formula/Tool Results

Word #

PIBackplane

RS–232and

RemoteI/O























A–5

Table A.3 (part 2 of 2)Results Block 2 – Formula/Tool Results

Word #

PIBackplane

RS–232and

RemoteI/O













A–6

Table A.4 Results Block 3 – Formula/Tool Results

Word #

PIBackplane

RS–232and

RemoteI/O












The Color CVIM communications manual lists and describes all of theaccessible configuration blocks. The configuration information for anenabled formula (fault and warning range information only) will replace theconfiguration information for a corresponding gage or window in theconfiguration blocks, as shown in the following tables:

• Table A.5, page A–7, shows a summary cross-listing of the configurationblock numbers for corresponding formulas and tools.

• Table A.6, page A–8, shows the configuration block information (blocks46–77) for formulas 9–16, 25–32, 41–56 (gages 1–32).

• Table A.7, page A–9, shows the configuration block information (evennumbered blocks, 110–156) – for formulas 1–8, 17–24, 33–40 (windows1–24).

Configuration Blocks


A–7

Table A.5 Configurations block numbering for formulas 1–56 (and corresponding tools)

Formula Tool Config.Block Formula Tool Config.

Block

1 Win. 1 110 29 Gage 13 58

2 Win. 2 112 30 Gage 14 59

3 Win. 3 114 31 Gage 15 60

4 Win. 4 116 32 Gage 16 61

5 Win. 5 118 33 Win. 17 142

6 Win. 6 120 34 Win. 18 144

7 Win. 7 122 35 Win. 19 146

8 Win. 8 124 36 Win. 20 148

9 Gage 1 46 37 Win. 21 150

10 Gage 2 47 38 Win. 22 152

11 Gage 3 48 39 Win. 23 154

12 Gage 4 49 40 Win. 24 156

13 Gage 5 50 41 Gage 17 62

14 Gage 6 51 42 Gage 18 63

15 Gage 7 52 43 Gage 19 64

16 Gage 8 53 44 Gage 20 65

17 Win. 9 126 45 Gage 21 66

18 Win. 10 128 46 Gage 22 67

19 Win. 11 130 47 Gage 23 68

20 Win. 12 132 48 Gage 24 69

21 Win. 13 134 49 Gage 25 70

22 Win. 14 136 50 Gage 26 71

23 Win. 15 138 51 Gage 27 72

24 Win. 16 140 52 Gage 28 73

25 Gage 9 54 53 Gage 29 74

26 Gage 10 55 54 Gage 30 75

27 Gage 11 56 55 Gage 31 76

28 Gage 12 57 56 Gage 32 77


A–8

Table A.6 Configuration blocks 46–77 – for formulas 9–16, 25–32, 41–56 (gages 1–32) – fault andwarning ranges

Remote I/O& RS–232Word #*

Bit # Definition Usage Notes

17 0–15 Fault Range High (Integer) Words 17 and 18 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer R

18 0–15 Fault Range High (Fraction)

19 0–15 Fault Range Low (Integer) Words 19 and 20 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer.

20 0–15 Fault Range Low (Fraction)

21 0–15 Warning Range High (Integer) Words 21 and 22 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer.

22 0–15 Warning Range High (Fraction)

23 0–15 Warning Range Low(Integer)

Words 23 and 24 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer.

24 0–15 Warning Range Low (Fraction)

25–27 0–15 Reserved

* Refer to Color CVIM Communications Manual, Chapter 6, for Pyramid Integrator long word descriptions.

Configuration blocks 46–77 provide the fault and warning range informationfor gages 1–32, respectively, if no corresponding formulas are enabled. Ifformulas are enabled, the fault and warning ranges for the enabled formulaswill replace the ranges for corresponding gages in the configuration blocks.For a listing of configuration blocks for corresponding formulas and tools,refer to Table A.5, page A–7.


A–9

Table A.7 Configuration blocks (even numbered, 110–156) for formulas 1–8, 17–24, 33–40(windows 1–24) – fault and warning ranges

Remote I/O& RS–232

Word #Bit # Definition Usage Notes

15 0–15 Fault Range High (Integer) Words 15 and 16 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer.

16 0–15 Fault Range High (Fraction)

17 0–15 Fault Range Low (Integer) Words 17 and 18 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer.

18 0–15 Fault Range Low (Fraction)

19 0–15 Warning Range High (Integer)

Words 19 and 20 represent a 16 (bit). 16 (bit)fixed point decimal value or 32 bit integer.

20 0–15 Warning Range High(Fraction)

21 0–15 Warning Range Low(Integer)

Words 21 and 22 represent a 16 (bit).16 (bit)fixed point decimal value or 32 bit integer.

22 0–15 Warning Range Low(Fraction)

23 0–15 Reserved

Configuration blocks 110-156 (even-numbered) provide the fault andwarning range information for windows 1–24, respectively, if nocorresponding formulas are enabled. If formulas are enabled, the fault andwarning ranges for the enabled formulas will replace the ranges forcorresponding windows in the configuration blocks. For a listing ofconfiguration blocks for corresponding formulas and tools, refer toTable A.5, page A–7.

Formula contents: The contents of the defined formulas are stored inblocks in a portion of Color CVIM memory referred to in the Color CVIMCommunications Manual as “template” memory. In order to transfer theformula content information, you must set the discrete bits for template blocktransfer (refer to, in the Color CVIM Communications Manual, Table 4.C,Word 23, Block Transfer Type bits).

The Color CVIM communications manual lists and describes all of theaccessible discrete bits. The discrete bit information for an enabled formula(fault and warning range flags) will replace the discrete bit information for acorresponding gage or window, as shown in Table A.8, beginning on pageA–10.

Discrete Bits


A–10

Table A.8 (part 1 of 6)Discrete Input Bits for formulas and corresponding tools

PI Backplane Remote I/O RS–232 ASCII RS–232 DF1

Word # Bit # Word # Bit #* Hex # Bit # Byte # Bit #Definition Usage

17 0 1 0 4 0 11 0 Formula 1 / Window 1Warning Flag

0 = Pass1 = Fail

17 1 1 1 4 1 11 1 Formula 1 / Window 1Fault Flag

0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail

*Remote I/O bit numbers are octal-based.


A–11





0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail

19 0 3 0 8 0 15 0Formula 33 / Window 17

Warning Flag0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail



A–12





0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail

20 0 4 0 10 0 17 0 Formula 9 / Gage 1Warning Flag

0 = Pass1 = Fail

20 1 4 1 10 1 17 1 Formula 9 / Gage 1Fault Flag

0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail

20 6 4 6 10 6 17 6 Formula 12 / Gage 4Warnig Flag

0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail



A–13





0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail



A–14





0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail



A–15





0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


0 = Pass1 = Fail


Index

Index – 1

A

Absolute value operator, 4–24

Analysis function, 5–1, 5–2

AND operator, 4–33

Arccosine operator, 4–26

Arcsine operator, 4–26

Arctangent operator, 4–26

Arithmetic operators, 4–21

Arrow keys, 4–6

Attention, notices of, 1–2

Audience, intended, 1–1

Average operator, 4–30

B

Bits, discrete, A–9(table), A–10

C

Chapter descriptions (table), 1–1

Conditional operators, 4–35

Config. Results box, 4–5

Configurable results block, A–2

Configuration blocks, A–6(table), A–7Formula contents, A–9

Constants, entering as operands, 4–16

Contents, Manual, 1–1

Copy and pasteIntroduction, 2–5Using, 4–39

Additional considerations, 4–40Example, 4–41

Corresponding tools/formulas, 4–3

Cosine operator, 4–26

D

Data typesConstants, 4–16Formula results, A–2

Default name, 4–37

Defining a formula, 4–4See also Formula

D (cont.’d)

Disabling a formula, 4–38

Discrete bits, A–9(table), A–10

Distance operator, 4–25

E

Edit/control keys, 4–10

Enabling a formula, 4–38

F

Firmware, required for installing MATH–PAK, 3–1

Fixed pointConstant operand, 4–16Formula results, A–2

FormulaAccessing MATH–PAK features, 2–4Configuration blocks, A–6

(table), A–7Formula content, A–9

Copy and paste, 4–39Defining, 4–4

Basic steps, 4–1Introduction, 2–1

Enabling / disabling, 4–38Entry keyboard, 4–5

Using, 4–7Example

Additional, 4–35Editing, 4–11Entry, 4–9

How results are applied, 2–2Naming, 4–37Operands, 4–12

Definitions (table), 4–14Operators, 4–17

Definitions (table), 4–18Execution hierarchy, 4–20Usage, 4–21

ResultsBlocks, A–2Conversion, 4–42Data types, A–2Restrictions, 4–42

Runtime displays, 5–4Selecting, 4–2

Index

Index – 2

I

I/O page display, 5–4

Installing the MATH–PAK option, 3–1Required firmware, 3–1

IntegerConstant operand, 4–16Formula results, A–2

Intended audience, 1–1

Inverse trigonometric operators, 4–26

J

Jump box, 4–4

K

Keyboard, Formula entry, 4–5Question mark (?), 4–8Results display, 4–8Using, 4–7

KeysEdit/control, 4–10Operand, 4–12Operator, 4–17Switching between initial and secondary sets, 4–6

L

Loading process, MATH–PAK installation, 3–2

Logical operators, 4–33

M

Manual contents, 1–1

MATH–PAKAccessing features, 2–4Installing, 3–1

Required firmware, 3–1Preview, 2–1

Mathematical operators, 4–21

Maximum operator, 4–30

Median operator, 4–31

Minimum operator, 4–31

Mode operator, 4–31

Modulo operator, 4–23

N

Naming a formula, 4–37

Nesting of operations, 4–20

NOT operator, 4–34

O

Operand, 4–12Definitions (table), 4–14Entering constants, 4–16Sub–code, using, 4–13

Operator, 4–17Definitions (table), 4–18Execution hierarchy, 4–20Usage, 4–21

Arithmetic, 4–21Conditional, 4–35Inverse trigonometric, 4–26Logical, 4–33Mathematical, 4–21Statistical, 4–29Trigonometric, 4–26

OR operator, 4–34

Outputs, assigning, 4–41, 4–46

P

Parentheses, using, 4–8Listing operands, 4–8, 4–13, 4–17Prioritizing operations, 4–8, 4–17

Paste, copy andIntroduction, 2–5Using, 4–39

Preview, MATH–PAK, 2–1

Publications, related, 1–2

R

Range Fail box, 5–2

Range limits, setting, 4–41Entering for corresponding tools, 4–47Entering for formulas, 4–43

Statistics table, 4–44Example, 4–45

Index

Index – 3

R (cont.’d)

Rejects, flagging consecutive (formula example),4–35

Related publications, 1–2

RestrictionsConstant values, 4–16Naming, 4–38Results page display, 5–6

ResultsBlocks, A–2

(table), A–3Configurable, A–2

Conversion, 4–42Display

Formula entry keyboard, 4–8Runtime, 5–5

Restrictions for formulas, 4–42Tool

(Operands table), 4–14Enabling, 4–47

Runtime displays, 2–5, 5–3

Runtime tools display, 5–4I/O page, 5–4Results page, 5–5

Help message for, 5–7Limitations, 5–6

Stat1 page, 5–5

S

Selecting a formula, 4–2, 4–3

Set Formula box, 4–5

Set Name box, 4–37

Shift register, creating (formula example), 4–36

S (cont.’d)

Sine operator, 4–26

Square operator, 4–24

Square root operator, 4–24

Statistical operators, 4–29

StatisticsFor failed tools, 5–2Runtime display (Stat1 page), 5–5Table for range limits, 4–44

T

Tangent operator, 4–26

ToolsConfiguration blocks, A–6

Formula contents, A–9Corresponding to formulas, 4–3, A–1Display

Analysis function, 5–1Runtime, 5–4

Failed, statistics for, 5–2Results

(Operand table), 4–14Blocks, A–2

Trademarks, 1–2

Trigonometric operators, 4–26

U

Unary minus operator, 4–22

V

Variance operator, 4–32

1993 Allen-Bradley Company

ALLEN-BRADLEY

With offices in major cities worldwide.WORLD HEADQUARTERSAllen-Bradley1201 South Second StreetMilwaukee, WI 53204 USATel:(414) 382–2000Telex:43 11 016FAX:(414)382–4444

A subsidiary of Rockwell International, one of the world’s largest technology companies,Allen-Bradley meets today’s automation challenges with over 85 years of practical plant floorexperience. More than 13,000 employees throughout the world design, manufacture andapply a wide range of control and automation products and supporting services to help ourcustomers continuously improve quality, productivity and time to market. These products andservices not only control individual machines, but also integrate the manufacturing processwhile providing access to vital plant floor data that can be used to support decision–makingthroughout the enterprise.

A ROCKWELL INTERNATIONAL COMPANY

EUROPE/MIDDLE EAST/AFRICA HEADQUARTERSAllen–Bradley Europe B.V.Amsterdamseweg 151422 AC UithoornThe NetherlandsTel:(31) 2975/43500Telex:(844) 18042FAX:(31) 2975/60222

ASIA/PACIFIC HEADQUARTERSAllen–Bradley (Hong Kong) LimitedRoom 1006, Block B, Sea View Estate2-8 Watson RoadHong KongTel:(852)887-4788Telex:(780) 64347FAX:(852)510-9436

CANADA HEADQUARTERSAllen–Bradley Canada Limited135 Dundas StreetCambridge, Ontario N1R 5X1CanadaTel:(519)623–1810FAX:(519)623–8930

LATIN AMERICAHEADQUARTERSAllen-Bradley1201 South Second StreetMilwaukee, WI 53204 USATel:(414)382–2000Telex:43 11 016FAX:(414)382–2400

Catalog No. 5370–ND016 (Series A)Printed in USA

40064–005–01 (A)

5370-nd016, bulletin 5370 color cvim module math-pak option … · 2014-07-18 · analysis and...

Documents