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.