Modeling and Dynamics of a Planar Parallel Manipulator Using
Discrete Time Transfer Matrix Method
Modeling and Dynamics of Planar Serial/Parallel Manipulators
Using Finite Segment Transfer Matrix MethodHaijie LiSupervisor:
Prof. Xuping Zhang
OUTLINE Concepts of Finite Segment TMM Parallel Manipulator
Systems
Serial Manipulator Systems
Concepts of Finite Segment TMM
Equivalent Stiffness:
Equivalent Stiffness (simplified):
State vector:Transfer equation: Concepts of Finite Segment
TMMLinearization:
Solution Procedure
Decompose a system into separate componentsDefine the state
vectors and transfer matrix for each elementObtain the overall
transfer equation for the systemApply boundary conditions and solve
the overall equationCompute the state vector for each
elementRepeat
Transfer Matrices for ComponentsRigid bodyRigid bodySmooth pin
hingeMotorTorsion springLinear spring
Serial Manipulator Systems
Serial Manipulator Systems
State vectors:Transfer equations:
Single Link Manipulator
Single Link Manipulator(Uniform)State vectors:
Transfer equations:
Single Link Manipulator(Uniform)
Single Link Manipulator(Non-uniform)State vectors:
Transfer equations:
Single Link Manipulator(Non-uniform)
Single Link Manipulator
Multi-link Manipulator with Flexible JointsState vectors:
Transfer equations:
Multi-link Manipulator with Flexible Joints
Multi-link Manipulator with Flexible Joints
Multi-link Manipulator with Flexible Joints
Easily to model a complex chain system with joint and link
flexibility Finite Segment-TMMNo need of the boundary conditions
for each intermediate linkNo need of the floating frame
Larger end-effector position errorJoint flexibility play
significant role in dynamic behaviour Simulation resultsLower
system stiffness System natural frequencies change dramatically
with configurations
Modeling of a 3-PRR Parallel Manipulator
Transfer equations:State vectors:
Modeling of a 3-PRR Parallel Manipulator
Modeling of a 3-PRR Parallel Manipulator
Modeling of a 3-PRR Parallel Manipulator
Modeling of a 3-PRR Parallel Manipulator
Modeling of a 3-PRR Parallel Manipulator
Modeling of a 3-PRR Parallel Manipulator
Position error at the tip end of linksDeformations at the
midpoint of linksPosition error and angle error of the
platformActuated forces of slidersElastic motions of intermediate
links have significant influences on actuated forces of slidersThe
intermediate links show pinned-pinned vibration characteristics
Modeling of a 3-PRR Parallel Manipulator
ConclusionsNo need of the boundary conditions for intermediate
elementsNo need of the floating framesManipulator with non-uniform
links
Easy to describe a system by assembling corresponding transfer
matricesHigh computational efficiency(system matrices keep low
orders, pre-defined elements)Finite Segment TMM
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