Forward and inverse acceleration analyses of in-parallel manipulators

Simple expressions for the forward and inverse acceleration analyses of a s ix degree of freedom in-parallel manipulator are derived. The expressions a re obtained by firstly computing the "accelerator" for a single Hooke-Prism atic-Spheric, HPS for short. connector chain in terms of the joint velociti es and accelerations. The accelerator is a function of the line coordinates of the joint axes and of a sequence of Lie products of the same line coord inates. A simple expression for the acceleration of the prismatic actuator is obtained by forming the Klein form, or reciprocal product, with the acce lerator and the coordinates of the line of the connector chain. Since the K lein form is invariant, the resulting expression can be applied directly to the six HPS connector chains of an in-parallel manipulator. As a required intermediate step, this contribution also derives the corresponding solutio ns for the forward and inverse velocity analyses. The authors believe that this simple method has applications in the dynamics and control of these in -parallel manipulators where the computing rime must be minimized to improv e the behavior of parallel manipulators. [S1050-0472(00)01303-9].