# development of a cad/cae tool – robokine (robotic kinematics)–for workspace, inverse kinematics

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MASTER THESIS. DEVELOPMENT OF A CAD/CAE TOOL ROBOKINE (ROBOtic KINEmatics)FOR WORKSPACE, INVERSE KINEMATICS AND TRAJECTORY PLANNING. BY MUKUND V. NARASIMHAN. SUPERVISING PROFESSOR : Dr. T.C. YIH COMMITTEE MEMBERS : Dr. K. L. LAWRENCE - PowerPoint PPT PresentationTRANSCRIPT

DEVELOPMENT OF A CAD/CAE TOOL ROBOKINE(ROBOtic KINEmatics)FOR WORKSPACE, INVERSE KINEMATICS AND TRAJECTORY PLANNINGBYMUKUND V. NARASIMHANMASTER THESISSUPERVISING PROFESSOR: Dr. T.C. YIHCOMMITTEE MEMBERS : Dr. K. L. LAWRENCE Dr. B. P. WANGMECHANICAL ENGINEERING DEPARTMENTTHE UNIVERSITY OF TEXAS AT ARLINGTONNovember 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)

Tc(, h, r)= Tr(Z, ) Tt(Z, h) Tt(X, r) = CYLINDRICAL COORDINATESTr(Z, ) represents rotation about Z-axisTt(Z, h) represents translation h along Z-axisTt(X, r) represents translation r along X-axis

Tb(, , ) = Tr(X, ) Tr(Y, ) Tr(Z, ) =BRYANT ANGLES CONVENTIONTr(X, ) represents rotation about X-axisTr(Y, ) represents rotation about Y-axisTr(Z, ) represents rotation about Z-axis

YZXYZXYZXYZXlh = l r = 0 = 90 = 0lT(, h, r, , ) = Tc(, h, r) Tb(, , 0) =HOMOGENEOUS SHAPE MATRIXh = 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 planningROBOKINE

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 ANALYSISThe general homogeneous characteristic matrix, ti, for different kinematic lower pairs are given by Ti =The position analysis of the end effector or manipulator can be obtained from this resultant matrix h given belowH =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 JOINTSDATA SAVED INTO AN OUTPUT FILEEXIT

ALGORITHM GENERATES SHAPE MATRICES FROM C-B NOTATION TABLE, FOR EACH OF THE JOINTS IN THE CONFIGURATION

2- SLICE OPTION

3- REAL TIME OPTION

1- PLOT OPTIONUNIMATE 2000 SPHERICAL ROBOTUPJ ROBOT

The required inputs are as follows1 ) Type of joints The various options are R, P, C, H, and S2) Joint local axis There are twenty-four options to choose from3) Link length and orientation These details are provided after sketching the links4) Range of motion of the joints

Optional inputs1) The value of the interval2) Size of the tracker

INPUT

1 PLOT OPTIONCONDITION AMANUAL REMOVAL OF EXTRA CURVESGENERATING THE WORKSPACES WITH THESE CURVESDOES ALL THE JOINTS IN THE CONFIGURATION MOVE IN THE SAME PLANE?FEATURES4CUTTING PLANESDISPLAY MODESURFACE REMOVALEXITCONDITION A IF THE RANGE OF THE PARAMETER(S) OF THE JOINT DOES NOT PASS THROUGH ZERO OR ANY OF THE JOINTS OTHER THAN THE BASE JOINT IS A HELICAL JOINT. MESSAGE POPS UP THE INFORMATION THAT WORKSPACE GENERATION IS NOT POSSIBLEALGORITHM GENERATES THE INITIAL CURVESYN

4 DRAG THE DIALS

DISPLAY DISPLACEMENT DATAEXTRA CURVES

EXIT

ANIMATION FEATUREANIMATIONS OF THE LINK MOTIONS TO TRACE THE PRE-DEFINED TRAJECTORY

PRECISION MODE

MANUAL REMOVAL OF THE EXTRA CURVES

FILE 1

5-TRAJECTORY PLANNING

5 TRAJECTORY PLANNING

RECORD

FILE 1

STOP

DISPLAY

OUTPUT

FILE 2

EXIT

2 SLICE OPTION

ALGORITHM GENERATES THE INITIAL CURVESEXIT

4

CONDITION BMESSAGE POPS UP THE INFORMATION THAT WORKSPACE GENERATION IS NOT POSSIBLECONDITION B All the joints in the configuration move in the same plane or if the range of the parameter(s) of the joint does not pass through zero or any of the joints other than the base joint is a helical joint. YN

4 DRAG THE DIALS

DISPLAY DISPLACEMENT DATAEXTRA CURVES

EXIT

ANIMATION FEATUREANIMATIONS OF THE LINK MOTIONS TO TRACE THE PRE-DEFINED TRAJECTORY

PRECISION MODE

MANUAL REMOVAL OF THE EXTRA CURVES

FILE 1

5-TRAJECTORY PLANNING

5 TRAJECTORY PLANNING

RECORD

FILE 1

STOP

DISPLAY

OUTPUT

FILE 2

EXIT

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 TABLEWORKSPACEINVERSE KINEMATICS

C-B NOTATION TABLE FOR CINCINNATI T3 ROBOT

JOINT (deg)h (m) r (deg) (deg) (deg)1 (R)-120, 1201.5090002 (R)0, 9001.0670003 (R)-150, 001.0670004 (R)-90, 9000.205-90005 (R)-90, 9000.36909006 (R)-135, 13500000

BENDIX AA/CNC INDUSTRIAL ROBOT (RRP/RRR)C-B NOTATION TABLEWORKSPACEINVERSE KINEMATICS

C-B NOTATION TABLE FOR BENDIX AA/CNC ROBOT

JOINT (deg)h (m) r (deg) (deg) (deg)1 (R)-95, 951.067090002 (R)-45, 22500.65909003 (P)00, 0.6100004 (R)-95, 950.10900-9005 (R)-20, 20000.14609006 (R)0, 36000000

UNIMATE 2000 SPHERICAL ROBOT (SP/RRR)C-B NOTATION TABLEWORKSPACEINVERSE KINEMATICS

C-B NOTATION TABLE FOR UNIMATE 2000 ROBOT (SP/RRR)For a spherical joint the parameters h and r are dependent on the relative length a and also with angle , h = a cos(), r = a sin(), and ranges between 26 and 30.

JOINT (deg)h (m) r (m) (deg) (deg) (deg)1 (S)-104, 104**09002 (P)900.75, 2.2500-9003 (R)-110, 11000.2-90004 (R)-100, 10000.209005 (R)0, 36000000

KR 60 P/2 (6R)C-B NOTATION TABLEWORKSPACEINVERSE KINEMATICS

C-B NOTATION TABLE FOR KR 60 P/2 ROBOT

JOINT (deg)h (m) r (deg) (deg) (deg)1 (R)-185, 1850.99090002 (R)0, 000.700903 (R)-110, 4001.400-904 (R)-60, 21000.507-909005 (R)-350, 3500.8930900906 (R)-120, 12000.21-909007 (R) -350, 35000000

UPJ ROBOTC-B NOTATION TABLEWORKSPACEINVERSE KINEMATICS

C-B NOTATION TABLE FOR UPJ ROBOT (6R)

JOINT (deg)h (m) r (deg) (deg) (deg)1 (R)-160, 1600.290900902 (R)-90, 8500.260003 (R)-55, 17500.0300-904 (R)0, 000.05-909005 (R)-170, 1700.220900906 (R)-120, 12000.09-909007 (R) -360, 36000000

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 limitati

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