DEVELOPMENT OF A CAD/CAE TOOL – ROBOKINE

(ROBOtic KINEmatics)–FOR WORKSPACE, INVERSE KINEMATICS

AND TRAJECTORY PLANNING

BY

MUKUND V. NARASIMHAN

MASTER THESIS

SUPERVISING PROFESSOR: Dr. T.C. YIH

COMMITTEE MEMBERS : Dr. K. L. LAWRENCE

Dr. B. P. WANG

MECHANICAL ENGINEERING DEPARTMENTTHE UNIVERSITY OF TEXAS AT ARLINGTON

November 19th 2002

A reprogrammable, multifunctional manipulator designed to move material, parts or tools through various programmed motions for the performance of a variety of tasks.

Robots were used mostly in the automobile industry but now a days they can be seen in hospitals, laboratories, energy plants, warehouses etc.

By 2003 there will be nearly 900,000 multi-purpose robots in use worldwide compared with 750,000 that are currently available. According to “World Robotics 2000”, a survey published by the united nations economic commission for Europe in co-operation with the international federation of robotics.

ROBOT

REVIEW OF C-B NOTATION

This notation is based on the homogeneous cylindrical coordinates and bryant angles transformations matrices and hence termed c-b notation.

The homogeneous transformation matrix is given by

Ti (i, hi, ri, i, i) =Tci(i, hi, ri) Tbi(i, i)

Oi-1

Oi Xi

i i

ex(i-1)

i

hi

ri

Zi

Zi-1

Zi+1

Xi+1

exi

ezi

Oi+1

i

i-1

Tc(, h, r)= Tr(Z, ) Tt(Z, h) Tt(X, r) =

1000

h100

rsθ0cθsθ

rcθ0sθcθ

CYLINDRICAL COORDINATES

Tr(Z, ) represents rotation about Z-axis

Tt(Z, h) represents translation h along Z-axis

Tt(X, r) represents translation r along X-axis

Tb(, , ) = Tr(X, ) Tr(Y, ) Tr(Z, ) =

BRYANT ANGLES CONVENTION

1000

0cαcβcαsβsγsαcγcαsβcγsαsγ

0sαcβsαsβsγcαcγsαsβcγcαsγ

0sβcβsγcβcγ

Tr(X, ) represents rotation about X-axis

Tr(Y, ) represents rotation about Y-axis

Tr(Z, ) represents rotation about Z-axis

Y

Z

X

Y

Z

X

Y

Z XY

Z Xl

h = l

r = 0

= 90

= 0

l

1000

hccssc

rscscssccssccs

rccsssccsssscc

T(, h, r, , ) = Tc(, h, r) Tb(, , 0) =

HOMOGENEOUS SHAPE MATRIX

h = 0 r = l = 90 = 0

Written in java and java3d.

Java used for generating the homogeneous matrices

Java3d for generating 3-dimensional features and simulations.

Contains 18 classes, 350+ methods and numerous variables

Advanced features include Automatic C-B notation table generation (24 X 24 X 2)

Workspace generation (solid and wire frame modes)

Dynamic slice of the workspace in real time

Single slice of the workspace

Solving inverse kinematic problems

Trajectory planning

ROBOKINE

DISPLACEMENT ANALYSIS AND WORKSPACE GENERATION

Generate workspace profiles for even 3-dimensional robots and also for robots which does not have adjacent axes parallel or perpendicular to each other.

Can validate the generated profiles with the use of “Dials”.

Kinematic analysis consists of position or displacement, velocity and acceleration analyses.

The workspace / work volume of a robotic manipulator is defined as the set of all 3-dimensional points that can be accessed by the manipulator.

One of the design criteria for design of robots.

Study of robotic workspaces is important in arranging the associated flexible manufacturing cell of a robot and assessing its efficiency in a manufacturing line.

FEATURE 1

DISPLACEMENT ANALYSIS

The general homogeneous characteristic matrix, ti, for different kinematic lower pairs are given by

1000

hccssc

srcscssccssccs

crcsssccsssscc

iiiiii

iiiiiiiiiiiiii

iiiiiiiiiiiiii

Ti =

The position analysis of the end effector or manipulator can be obtained from this resultant matrix h given below

H =

n

1iiT

1000

PD ii

Where D is direction cosine matrix and P is position vector and these specify the orientation and position respectively.

VISUALIZATION BASED INVERSE KINEMATICS SOLVER

The difficulty in solving inverse kinematic problems is because of its non-linear nature. the difficulties associated with this non-linearity are

Multiple to infinite solutions

No solutions because of divergence

The convergent set of solutions obtained may not be a desirable solution to the problem

A graphical, visualization based technique is developed to solve inverse kinematic problems without resorting to the numerical procedures.

FEATURE 2

Given the target point, finding the values of the joint parameters to reach that desired point.

VISUALIZATION BASED TRAJECTORY PLANNER

A visualization based trajectory planner is developed to accomplish this task.

Drastic reduction in time for planning trajectories and ease of use.

Obstacle avoidance.

Robots can be pre-programmed in either point-to-point mode or continuous path mode.

Point-to-point mode is used for tasks such as spot welding, inspection and moving parts.

Continuous path mode is used for tasks such as spray painting and arc welding.

FEATURE 3

ROBOKINE

USER INPUTS NUMBER OF JOINTS AND MAXIMUM CO-ORDINATE

VALUES OF SKETCHING

USER INPUTS FOR GENERATING THE HOMOGENEOUS SHAPE

MATRICES FOR EACH OF THE JOINTS

DATA SAVED INTO AN

OUTPUT FILE

EXIT

ALGORITHM GENERATES SHAPE MATRICES FROM C-B NOTATION

TABLE, FOR EACH OF THE JOINTS IN THE CONFIGURATION

2- SLICE OPTION 3- REAL TIME OPTION1- PLOT OPTION

UNIMATE 2000 SPHERICAL ROBOT

UPJ ROBOT

NUMERICAL EXAMPLES

CINCINNATI MILACRON T3 ROBOT

BENEDIX AA/CNC INDUSTRIAL ROBOT

UNIMATE 2000 SPHERICAL ROBOT

KR 60 P/2 ROBOT

UPJ ROBOT

CINCINNATI MILACRON T3 ROBOT (RRR/RRR)

C-B NOTATION TABLE

WORKSPACE

INVERSE KINEMATICS

BENDIX AA/CNC INDUSTRIAL ROBOT (RRP/RRR)

C-B NOTATION TABLE

WORKSPACE

INVERSE KINEMATICS

UNIMATE 2000 SPHERICAL ROBOT (SP/RRR)

C-B NOTATION TABLE

WORKSPACE

INVERSE KINEMATICS

KR 60 P/2 (6R)

C-B NOTATION TABLE

WORKSPACE

INVERSE KINEMATICS

UPJ ROBOT

C-B NOTATION TABLE WORKSPACE INVERSE KINEMATICS

LIMITATIONS

The dials take in integer values

The orientations of the links have to be either horizontal and vertical while sketching the links at home position

Range of the input parameters of the joints should pass through zero or contain zero

If one of the joints in the configuration is helical other than the base then the workspace is not generated

Workspaces generated in certain cases may not be 100% accurate because of the following reasons

1) Joints with no range of motion

2) Algorithm considers maximum reach position when all the links are set to zero which may not be the case in certain configurations

Workspace generated is based on the projection of the profile on the sagittal plane

The results and plots generated can be saved nor printed

The inputs have to be provided each time the application is started

Software limitations

Hardware limitations

FUTURE WORK

Velocity and acceleration spaces

Dynamic analysis

Closed chain and combined open and closed chain analyses