Redundant non-serial compound manipulator kinematics and dynamics

Abstract

Redundant non-serial compound manipulators with closed kinematic and actuator loops that enhance precision control and load carrying capacity are treated. Generalized coordinates and associated holonomic constraints that account for kinematic and actuator closed loops and singularity free representation of orientation of spatial manipulator bodies augment input and output coordinates in the kinematic formulation. Disjoint assembly components and path connected singularity free assembly components of manipulator configuration space are defined, in which manipulator kinematics and dynamics can be reliably carried out. A set-valued inverse kinematic configuration mapping is derived, with which compound redundant manipulators are shown to be locally cyclic. A new system of manipulator operational coordinates comprised of output and self-motion coordinates are defined and shown to be equivalent to input coordinates in representation of manipulator kinematics and dynamics. Well-posed ordinary differential equations of manipulator dynamics in both input and operational coordinates are presented that require no ad-hoc derivation. Five model manipulators illustrate applications involved and theoretical methods presented.