DEXTEROUS WORKSPACES OF MANIPULATORS .1. ANALYTICAL CRITERIA

A formulation for analysis of dextrous workspaces of manipulators is presented, including mobility-limited joints, full-range dexterity requirements, full-range input requirements, and planar and spatial closed-loop kinematic structures. A terminology for mechanism and manipulator models that permits specification of input, output, and dexterity requirements is proposed and demonstrated to yield broadly applicable conditions necessary for boundaries of dextrous workspaces. Row-rank deficiency of constraint sub-Jacobian matrices is shown to yield necessary conditions for boundaries of accessible output sets and dextrous accessible output sets that characterize the workspace and dextrous workspace, respectively, of both planar and spatial manipulators. Three closed-loop planar manipulators are analyzed in detail and a three-dimensional, closed-loop Stewart platform is formulated to illustrate applicability of necessary conditions derived for spatial manipulators. Analytical solutions of planar examples presented in this paper illustrate use of the formulations and necessary conditions and suggest that the computational methods presented in Part 2 of the paper are essential for analysis of dextrous workspaces of more realistic manipulators.