The slides are for the Master's Thesis: Dynamics and Modelling for a 3-PRR Parallel Manipulator using Transfer Matrix Method. In my slides, the simulations of the serial multi-flexible manipulator as well as the parallel flexible manipulator are given.

1. Modeling and Dynamics of Planar
Serial/Parallel Manipulators Using Finite
Segment Transfer Matrix Method
HAIJIE LI
SUPERVISOR: PROF. XUPING ZHANG

2. OUTLINE
• Concepts of Finite Segment TMM
• Parallel Manipulator Systems
• Serial Manipulator Systems

3. Concepts of Finite Segment TMM
Equivalent Stiffness:
Equivalent Stiffness (simplified):

4. • State vector:
• Transfer equation:
Concepts of Finite Segment TMM
• Linearization:

5. Solution Procedure
• Decompose a system into
separate components
• Define the state vectors and
transfer matrix for each element
• Obtain the overall transfer
equation for the system
• Apply boundary conditions and solve
the overall equation
• Compute the state vector for each
element
Repeat

6. Transfer Matrices for Components
Rigid body Rigid body Smooth pin hinge
Motor Torsion spring Linear spring

7. Serial Manipulator Systems

8. Serial Manipulator Systems
State vectors:
Transfer equations:

9. Single Link Manipulator

10. Single Link Manipulator(Uniform)
State vectors:
Transfer equations:

11. Single Link Manipulator(Uniform)

12. Single Link Manipulator(Non-uniform)
State vectors:
Transfer equations:

13. Single Link Manipulator(Non-uniform)

14. Single Link Manipulator

15. Multi-link Manipulator with Flexible Joints
State vectors:
Transfer equations:

16. Multi-link Manipulator with Flexible Joints

17. Multi-link Manipulator with Flexible Joints

18. Multi-link Manipulator with Flexible Joints
‣ Easily to model a complex chain system
with joint and link flexibility
• Finite Segment-TMM
‣ No need of the boundary conditions for
each intermediate link
‣ No need of the floating frame
‣ Larger end-effector position error
‣ Joint flexibility play significant role in dynamic
behaviour
• Simulation results
‣ Lower system stiffness
‣ System natural frequencies change
dramatically with configurations

19. Modeling of a 3-PRR Parallel Manipulator

20. Transfer equations:
State vectors:
Modeling of a 3-PRR Parallel Manipulator

21. Modeling of a 3-PRR Parallel Manipulator

22. Modeling of a 3-PRR Parallel Manipulator

23. Modeling of a 3-PRR Parallel Manipulator

24. Modeling of a 3-PRR Parallel Manipulator

25. Modeling of a 3-PRR Parallel Manipulator

26. ‣ Position error at the tip end of links
‣ Deformations at the midpoint of links
‣ Position error and angle error of the platform
‣ Actuated forces of sliders
‣ Elastic motions of intermediate links have
significant influences on actuated forces of sliders
‣ The intermediate links show pinned-pinned
vibration characteristics
Modeling of a 3-PRR Parallel Manipulator

27. Conclusions
‣ No need of the boundary conditions for
intermediate elements
‣ No need of the floating frames
‣ Manipulator with non-uniform links
‣ Easy to describe a system by assembling
corresponding transfer matrices
‣ High computational efficiency(system matrices
keep low orders, pre-defined elements)
Finite Segment TMM

28. Thanks for your time!