Numerical Methods for Mechanism and Manipulator Workspace Analysis

Numerical algorithms for mapping boundaries of mechanism and manipulator workspaces are developed and illustrated. Analytical criteria derived are applicable for both manipulators having the same number of input and output coordinates and redundantly controlled manipulators with a larger number of inputs than outputs. A numerical method is presented for finding an initial point on the boundary, from which a continuation method that accounts for simple and multiple bifurcation of one-dimensional solution curves is used. Planar and spatial manipulators are analyzed, determining both the exterior boundaries of workspaces and interior curves that represent local impediments to motion control.

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