Parallel manipulator dynamics embedded in singularity free domains of functionality

Abstract

Ordinary differential equations of motion for a broad spectrum of parallel manipulators are derived and implemented in manipulator input coordinates for system simulation and controller design. Equations of motion are systematically embedded in singularity free domains of manipulator configuration space, assuring controllability and existence of a unique solution of the equations of motion. The kinematic foundation for the formulation is a mechanics-based model of the underlying mechanism with forward and inverse kinematic mappings that are evaluated on singularity free domains of manipulator configuration space. The kinetic foundation is d’Alembert’s variational formulation of multibody dynamics that, with forward kinematic mappings, yields explicit ordinary differential equations of motion. No ad-hoc derivations of Lagrange’s equations, Newton–Euler equations, or Lagrange multiplier-based differential-algebraic equations are required. Differential equations of motion for a planar front-end loader and a spatial Stewart platform manipulator are implemented to illustrate the formulation.