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.
A general approach to numerical analysis of the kinematic dexterity of mechanisms is presented. Dextrous workspace problems are first defined and illustrated with examples. Composite workspaces are introduced to characterize both positioning and orienting capabilities of mechanisms. A numerical formulation and computer implementation that incorporates computer graphics and a numerical algorithm for solving systems of nonlinear equations are presented. Using the composite workspace formulation and the computer implementation, numerical techniques for dextrous workspace analysis are presented. Examples are given to illustrate the techniques developed.
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