Part I Prerequisites
1 Generalities on parallel robots
1.1 Introduction
1.2 General definitions
1.3 Types of PKM architectures
1.4 Why a book dedicated to the dynamics of parallel robots?
2 Homogeneous transformation matrix
2.1 Homogeneous coordinates and homogeneous transformation matrix
2.2 Elementary transformation matrices
2.3 Properties of homogeneous transformation matrices
2.4 Parameterization of the general matrices of rotation
3 Representation of velocities and forces / acceleration of a body
3.1 Definition of a screw
3.2 Kinematic screw (or twist)
3.3 Representation of forces and moments (wrench)
3.4 Condition of reciprocity
3.5 Transformation matrix between twists
3.6 Transformation matrix between wrenches
3.7 Acceleration of a body
4 Kinematic parameterizing of multibody systems
4.1 Kinematic pairs and joint variables
4.2 Modified Denavit-Hartenberg parameters
5 Geometric, velocity and acceleration analysis of open kinematic chains
5.1 Geometric analysis of open kinematic chains
5.2 Velocity analysis of open kinematic chains
5.3 Acceleration analysis of open kinematic chains
6 Dynamics principles
6.1 The Lagrange formulation
6.2 The Newton-Euler equations
6.3 The principle of virtual powers
6.4 Computation of actuator input efforts under a wrench exerted on the end-effector
Part II Dynamics of rigid parallel robots
7 Kinematics of parallel robots
7.1 Inverse geometric model
7.2 Forward geometric model
7.3 Velocity analysis
7.4 Acceleration analysis
7.5 Singularity analysis
8 Dynamic modeling of parallel robots
8.1 Introduction
8.2 Dynamics of tree-structure robots
8.3 Dynamic model of the free moving platform
8.4 Inverse and direct dynamic models of non-redundant parallel robots
8.5 Inverse and direct dynamic models of parallel robots with actuation redundancy
8.6 Other models
8.7 Computation of the base dynamic parameters
9 Analysis of the degeneracy conditions for the dynamic model of parallel robots
9.1 Introduction
9.2 Analysis of the degeneracy conditions of the IDM of PKM
9.3 Avoiding infinite input efforts while crossing Type 2 or LPJTS singularities thanks to an optimal trajectory planning
9.4 Example 1: the five-bar mechanism crossing a Type 2 singularity
9.5 Example 2: the Tripterion crossing a LPJTS singularity
9.6 Discussion
Part III Dynamics of flexible parallel robots
10 Elastodynamic modeling of parallel robots
10.1 Introduction
10.2 Generalized Newton-Euler equations of a flexible link
10.2.3 Matrix form of the generalized Newton-Euler model for a flexible clamped-free body
10.3 Dynamic model of virtual flexible systems
10.4 Dynamic model of a flexible parallel robot
10.5 Including the actuator elasticity
10.6 Practical implementation of the algorithm
10.7 Case Study: the DualEMPS
11 Computation of natural frequencies
11.1 Introduction
11.2 Stiffness and inertia matrices of the virtual system
11.3 Stiffness and inertia matrices of the PKM
11.4 Including the actuator elasticity
11.5 Practical implementation of the algorithm
11.6 Case Studies
11.7 Conclusion
Appendices
A Calculation of the number of degrees of freedom of robots with closed chains
A.1 Introduction
A.2 Moroskine's Method
A.3 Gogu's Method
A.4 Examples
B Lagrange equations with multipliers
C Computation of wrenches reciprocal to a system of twists
C.1 Definitions
C.2 Condition of reciprocity
C.3 Computation of wrenches reciprocal to a system of twists constrained in a plane
C.4 Computation of wrenches reciprocal to other types of twist systems
D Point-to-point trajectory generation
E Calculation of the terms facc1 , facc2 and facc3 in Chapter 10
E.1 Calculation of the term facc1
E.2 Calculation of the term facc2
E.3 Calculation of the term facc3
F Dynamics equations for a clamped-free flexible beam
F.1 Shape functions for a free flexible beam
F.2 Stiffness matrix for a free flexible beam
F.3 Evaluation of the inertia matrix of a free flexible 3D Bernoulli beam for qe j = 0
References
Index.