A formulation for automatic generation of workspace boundary of N-R manipulators

Abstract

In this paper, a numerical algorithm has been developed for an automatic procedure to compute and determine the workspace boundary of open chain manipulators with unlimited revolute joints. The formulation is based on the geometry of the envelope surface of revolving ring volumes and on a numerical evaluation of recursive terms to simplify the computations. The automatic procedure has been developed by using the fact that the internal workspace boundary delimits a ring void, which can be generated only when the generating workspace has a hole. This means that a workspace boundary is generated by the external branch of the envelope boundary of a generating workspace only. The numerical procedure has been developed as based on an algebraic formulation and it has been specified for a numerical automatic determination and evaluation of manipulator workspace, which can be performed easily on a common PC computer by using no particular requirement in computational programming.