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TABLE OF CONTENTS
Acknowledgments iii
1 Introduction ........................................................................................................................... 3
1.1 Motivation ...................................................................................................................... 3
1.2 Software and Hardware used in Thesis .......................................................................... 3
1.3 Notations ........................................................................................................................ 3
1.3.1 Acronyms ................................................................................................................ 3
1.3.2 Variables and parameters ........................................................................................ 3
2 Background ............................................................................................................................ 6
2.1 Robotics .......................................................................................................................... 6
2.2 ELAU GmbH ................................................................................................................. 7
2.2.1 PacDrive automation system – ELAU GmbH ........................................................ 7
2.2.2 Software – ELAU GmbH ........................................................................................ 8
2.2.3 SERCOS bus ........................................................................................................... 8
2.2.4 Delta-3 Robot – ELAU GmbH ............................................................................... 9
3 Kinematics – Serial Robot ................................................................................................... 10
3.1 Forward Kinematics ..................................................................................................... 10
3.2 Inverse Kinematics ....................................................................................................... 12
3.3 Velocity Kinematics ..................................................................................................... 13
4 Kinematics & Kinetics – Delta-3 Robot .............................................................................. 14
4.1 Model assumptions ....................................................................................................... 14
4.2 Geometric Parameters .................................................................................................. 15
4.3 Forward Kinematics ..................................................................................................... 16
4.4 Inverse Kinematics ....................................................................................................... 17
4.5 Velocity Kinematics ..................................................................................................... 19
4.6 Acceleration Kinematics .............................................................................................. 21
4.7 Actuator Dynamics ....................................................................................................... 22
4.8 Inverse Dynamic model ............................................................................................... 22
4.8.1 Dynamic Parameters ............................................................................................. 23
4.8.2 Virtual work principle ........................................................................................... 24
4.8.3 Calculation of dynamic model based on virtual work principle ........................... 25
4.9 System Dynamics ......................................................................................................... 26
5 Trajectory............................................................................................................................. 28
5.1 Trajectory with desired start and end velocity ............................................................. 28
6 Trajectory – ELAU GmbH .................................................................................................. 30
6.1 Linear interpolation ...................................................................................................... 31
6.2 Circular interpolation ................................................................................................... 32
6.3 Cubic spline .................................................................................................................. 32
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Public Report ELAU GmbH, Marktheidenfeld
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