Dynamics of Parallel Robots

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.