cad cam3 unit neelima

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C. Neelima Devi



UNIT - IComputers in industrial Manufacturing, Product cycle, CAD / CAM hardware, basic structure

CPU, Memory types, input devices, display devices, hard copy devices, storage devices.

UNIT ±II

Computer Graphics: R asterscan graphics coordinate system, database structure for graphics

modeling, transformation of geometry, 3D transformations, mathematics of projections, clipping,

hidden surface removal.

UNIT-III

Geometric Modeling: R equirements, geometric models, geometric construction models, curve

representation methods, surface representation methods, modeling facilities desired.

UNIT-IVDrafting and modeling systems: Basic geometric commands, layers, disply control commands,

editing, dimensioning, solid modeling, constraint based modeling

UNIT ± V

Numerical Control: NC, NC modes, NC elements, NC machine tools, structure of C NC machine

tools, features of Machining center, turning center, C NC part programming : fundamentals, part

programming methods, computer aided part programming.

UNIT ± VIGroup Tech: Part family, coding and classification, production flow analysis, advantages and

limitations, Computer Aided Processes planning, retrieval type and generative type.

UNIT ± VIIMaterial requirement planning, manufacturing resources planning, D NC, AGV, ASR S, Flexible

manufacturing systems ± FMS equipment, system layouts, FMS control.

UNIT ± VIIICIM: Integration, CIM implementation, major function in CIM, Benefits of CIM lean

manufacturing Just-in-time.

JNTU SYLLABUS:



Geometric Modeling: Requirements, geometric models,

geometric construction models, curve representation methods,

surface representation methods, modeling facilities desired.

JNTU SYLLABUS: UNIT- 3



LECTURE PLAN ± UNIT-3Lecture

NoTopic Slide No¶S

FROM ----TO

Lecture 1 INTRODUCTION TO GM,REQUIREMENTSOF GM, FUNCTIONS OF GM 6-14

Lecture 2 GEOMETRIC MODELS ± 2D, 2.5D, 3D, WIRE FRAME MODELING 15-22

Lecture 3 SURFACEMODLEING 23-32

Lecture 4 SOLID MODELING 33-41

Lecture 5 GEOMETRIC CONSTRUCTION METHODS 42-48

Lecture 6 GEOMETRIC MODELING APPLIC ATON 49-77

Lecture 7 CURVE REPRESENT ATION METHODS 78-88

Lecture 8 SURFACE REPRESENT ATION MTHODS, MODELING FACILITIESDESIRED.

89-96

SUBJECT TITLE:

UNIT -1



Introduction to Geometric Modeling

Requirements of Geometric Modeling

Functions of Geometric Modeling



Geometric modelling refers to a set of techniques

concerned mainly with developing efficient representations of geometric aspects of a design. Therefore, geometric modelling

is a fundamental part of all C AD tools.

Geometric modelling

Geometric modeling is the basic of many applicationssuch as:

Mass property calculations.

Mechanism analysis.

Finite-element modelling.

NC programming.



R equirements of geometric modelling include:

Completeness of the part representation.

The modelling method should be easy to use by designers.

R endering capabilities (which means how fast the entities

can be accessed and displayed by the computer).



Total product cycle in a manufacturing environment



Functions of Geometric Modelling

Design analysis:

± Evaluation of areas and volumes.

± Evaluation of mass and inertia properties.

± Interference checking in assemblies. ± Analysis of tolerance build-up in

assemblies.

± Analysis of kinematics ² mechanics,

robotics. ± Automatic mesh generation for finite element

analysis.



geometric models.



3D geometric representation techniques



Wire-frame ModelingWire-frame modelling uses points and curves (i.e. lines,

circles, arcs), and so forth to define objects.

The user uses edges and vertices of the part to form a

3-D object

Wire-frame model part



Surface Modeling



Surface Modeling

Surface modeling is more sophisticated than wireframe modeling

in that it defines not only the edges of a 3D object, but also its

surfaces.

In surface modeling, objects are defined by their bounding faces.



SURFACE ENTITIES

Similar to wireframe entities, existing CAD/CAM

systems provide designers with both analytic andsynthetic surface entities.

Analytic entities include :

Plane surface,

R uled surface,Surface of revolution, and

Tabulated cylinder.

Synthetic entities include

The bicubic Hermite spline surface,B-spline surface,

R ectangular and triangular Bezier patches,

R ectangular and triangular Coons patches, and

Gordon surface.



Plane surface. This is the simplest surface. It requires

three noncoincident points to define an infinite plane.



Ruled (lofted) surface. This is a linear surface. It interpolates

linearly between two boundary curves that define the surface

(rails). R ails can be any wireframe entity. This entity is ideal torepresent surfaces that do not have any twists or kinks.



S urface of revolution. This is an axisymmetric surface

that can model axisymmetric objects. It is generated by

rotating a planar wireframe entity in space about the axis

of symmetry a certain angle.



T abulated cylinder . This is a surface generated by

translating a planar curve a certain distance along a

specified direction (axis of the cylinder).



Bezier surface. This is a surface that approximates given

input data. It is different from the previous surfaces in

that it is a synthetic surface. Similarly to the Bezier curve,it does not pass through all given data points. It is a

general surface that permits, twists, and kinks . The

Bezier surface allows only global control of the surface.



B-spline surface. This is a surface that can approximate

or interpolate given input data (Fig. 6-9). It is a synthetic

surface. It is a general surface like the Bezier surface but

with the advantage of permitting local control of the

surface.



Solid Modeling



Solid Modeling

Solid models give designers a completedescriptions of constructs, shape, surface, volume,

and density.



In CAD systems there are a number of representation schemes for solid modeling

include:

Primitive creation functions.Constructive Solid Geometry (CSG)

Sweeping

Boundary R epresentation (BREP)



Primitive creation functions:

These functions retrieve a

solid of a simple shape from

among the primitive solidsstored in the program in

advance and create a solid of

the same shape but of the

size specified by the user.



Constructive Solid Geometry (CSG)

CSG uses primitive shapesas building blocks and

Boolean set operators (U

union, difference, and intersection) to constructan object.



Sweeping

Sweeping Sweeping isa modeling function in

which a planar closed

domain is translated or

revolved to form a

solid. When the planar domain is translated,

the modeling activity is

called translational

sweeping; when the

planar region isrevolved, it is called

swinging, or rotational

sweeping .



Boundary R epresentation

Objects are represented by their bounded faces.



B-R ep Data Structure



Component model produced using translational (linear) sweep

(extrusion)



Component model produced using translational (linear) sweep with taper in

sweep direction



Component model produced using linear sweep with the sweep

direction along a 3D cur ve



Component model produced using translational (linear) sweep with an

overhanging edge



Component produced by the rotational sweep technique



geometric construction models, curve

representation methods, surface

representation methods, modeling facilities

desired



Rendering:



Rendering: Rasterization



Rendering: Raycasting



Rendering: Radiosity



Rendering: Raytracing



Reverse Engineering of a computer mouse



Reverse Engineering of a computer mouse

Step 1: Point Cloud Data in Sub Regions



Step 2: Point Cloud Data after applying Maximum Error Method



Step 3: Surface fitting to Point Cloud Data



Step 4: Surface after Cleaning



Step 5: Computer mouse after Prototyping



Curve Representation

P t i C R t ti



Parametric Curve Representation

The x, y, and z coordinate of a point on the

curve are represented respectively as a

single valued function of a same parameter u

of real value:

I = [u0, u1] is called the domain interval of

P(u).



Examples of Parametric Curves

x = 3u2

y = u3 ±u + 1

z = 2u + 3

f C



Examples of Parametric Curves

Diff i l G f C



Differential Geometry of Curves

Scalar and vector functions

- Scalar function: A single valued real

number function of a real number parameter, e.g.

f(u) = u3 ±u + 1 + sin(u)

- Vector function: A vector or a point in 3Dwhose x, y, and z coordinates are scalar

functions of a same parameter, e.g.

Diff ti l G t f C




Functions of class Cm

- A scalar function f(u) belongs to class Cm

on an

interval I if the mth order derivative of f exists and is

continuous on I. (³Exist´ means the mth order derivativeis defined and not a constantly zero.)

- A vector function f (u) belongs to class Cm

on an

interval I if the mth order derivative of f exists and iscontinuous on I. (³Exist´ means the mth order derivative

is defined and not a constantly zero vector.)

- Examples

Y

Diff ti l G t f C




Regular curves

- f (u) (uI) is a regular curve if

1. f (u) is of class C1 in I

2. f ¶(u) { 0 for all u in I.

- Example (the circular helix curve)

f (u) = [x(u), y(u), z(u)] = [acos(u), asin(u), bu]

f ¶(u) = [-asin(u), acos(u), b] is a non-zero

vector in -g<u<+g.

Diff ti l G t f C




What¶s so special with regular curves?- A cusp (³kink´) on a curve

- If f (u) is of class C1, can it have a ³kink´?

- Impossible if it is regular

f·(u)

x

y

f(u)x

y

Diff ti l G t f C




Definition of arc lengthLet f (u) be defined on interval a e u e b.

a = u0 < u1 < « < un

= b

f 0=f (u0), f 1=f (u1), «,

f n=f (un)

s(Pn) = §|f i ± f i-1|f 0

f 1

f 2 f n-1

f n

Diff ti l G t f C




How to calculate arc length

- If f (u)=[x(u), y(u), z(u)] is a regular curve on interval

aeueb, its arc length between a and b is:

- Example

f (u) = [x(u), y(u), z(u)] = [acos(u), asin(u), bu],

0eue2T

Diff ti l G t f C




Arc length as a parameter

- Let f = f (u) be a regular curve on interval aeueb

Define:

Note:

Same curve f, but defined as a function of its arc

length s:

f = g(s).



Surface Representation

Parametric Surface Representation



Parametric Surface Representation

The x, y, and z coordinate of a point on the

surface are represented respectively as a

single valued continuous function of two

parameters u and w in a range and.

P(u, w): also called a patch.

[u0, u1]v[w0, w1]: the parameter domain of

P(u, w).

10 uuu ee

10 wuw ee

±±À

±±¿

¾

±±°

±±¯

®

!

),(

),(

),(

,P

wu z

wu y

wu x

wu )(

Component Parametric Patches



Component Parametric Patches

[u0, u1]v[w0, w1] = [0,1]v[0, 1]

Each of x(u,w), y(u,w),

and

z(u,w) is a continuoussingle-

value function of u and w,

a

component parametric

patch.

They together form a

continuous patch in the

3D

Euclidean space.

Terms of Parametric Patches



Terms of Parametric Patches

Four corners:

p00=P(0,0), p01=P(0,1), p10=P(1,0), p11=P(1,1)

Four parametric boundary curves:

P(u,0), P(u,1), P(0,w), P(1,w)

Isoparametric curves:

u-constant curve: P(ui,w)

w-constant curve: P(u,w j)

Partial derivatives:

Pu(u, w) = ; Pw(u, w) =

Normal vector:

(u, v) = Pu(u, w) v P

w(u, w)

u

wu

xx ),P(

w

wu

xx ),P(

nÖ

Example of Parametric Patches




A planar patch

x = (c ± a)u + a y = (d ± b)w + b z = 2u + w

Four corners:

p00 = (a,b,0), p01=(a,d,1), p10=(c,b,2), p11=(c,d,3)

Four boundary curves:

P(0,w ) = (a, (d-b)w + b, w ); P(1,w ) = (c, (d-b)w + b, 2 + w );

P(u,0) = ((c ± a)u + a, b, 2u); P(u,1) = ((c ± a)u + a, d, 2u +1) Isoparametric curves:

u-constant curve: ((c ± a)ui + a, (d ± b)w + b, 2ui + w )

w-constant curve: ((c ± a)u + a, (d ± b)w j+ b, 2u + w j)

Normal vector at (u, w ):

(u, w ) = Pu(u, w) v P

w(u, w) = (c-a, 0, 2) v (0, d-b, 1)

nÖ





A sphere

nÖ

,, ¼½»¬-

«22TTu ? AT 20,w

x = a + r cosu cosw

y = b + r cosu sinw

z = c + r sinu

(u, w) = ???

(T/2, w) = ???nÖ





An ellipsoid

nÖ

,, ¼½»¬-

«22TTu ? AT 20,w

x = x0 + a cosu cosw

y = y0 + b cosu sinw

z = z0 + c sinu

(u, w) = ???

(T/2, w) = ???nÖ





A revolution

? A,,10u ? AT 20,w

x = x(u) cosw

y = x(u) sinw

z = z(u)

u = constant curve?

v = constant curve?

(u, w) = ???

(, w) = ???z

nÖ

nÖ(x(u), 0, z(u))

cad cam3 unit neelima

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