Numerical Analysis of the Kinematic Working Capability of Mechanisms

A broadly applicable approach for numerical analysis of the kinematic working capability of mechanisms is presented. Composite workspaces are introduced to represent position and orientation capabilities of mechanisms, both individually and together. Numerical methods for solving systems of kinematic constraint equations, using a moving-frame algorithm and equations that characterize the workspace boundary are developed. Two analytic methodologies, comparison and incorporation methods, are presented to determine whether the workspace of a mechanism satisfies design requirements. An experimental computer program for workspace analysis that incorporates a numerical solver and computer graphics for visualization on a high speed graphics workstation is outlined. The feasible positioning space of a Stewart platform that is subject to orientation constraints is computed, to illustrate the use of this approach.