Manipulability and static stability of parallel manipulators (Q1855333)

In earlier papers, P. Maisser developed a systematic analytical approach for the derivation of kinematic relationships of holonomic (geometric) constrained mechanical systems (CMS) [\textit{P. Maisser}, Z, Angew. Math. Mech. 71, No. 4, 116--119 (1991); Nonlinear Anal., Theory Methods Appl. 30, No. 8, 5127--5133 (1997; Zbl 0908.70007)]. Parallel manipulators (PM) are modelled as CMSs, where the holonomic constraints describe the closure conditions of selected joints. All the kinematic loops can be cut open to get a kinematic tree structure, from which both the forward and inverse kinematic relationships can be derived. Points on the CMS manifold, where one or both of Jacobians become singular, are local singularities of the manipulator, as previously defined by the author and \textit{P. Maisser} [Multibody Syst. Dyn. 5, No. 3, 223--249 (2001; Zbl 0989.70004)]. Here these results are extended, and global manipulability measures are introduced. The static stability of PMs is investigated, including the transformation of driving to platform forces. The elastic stiffness of PMs is incorporated in a stability analysis of the PM dynamics. The paper focuses on PMs consisting of a platform rigidly connected to the end-effector, and of a set of arms flexibly connected with the base so that each arm is part of a kinematic chain. The procedures are illustrated using a hexapod as an example.