Dextrous Workspaces of Manipulators, Part 2: Computational Methods

In Part 1 of this paper, analytical criteria for dextrous workspaces were presented and analytical solutions of planar examples were used to illustrate the formulation and necessary conditions to determine boundaries of accessible and dextrous accessible output sets. Not all dexterity problems can be solved analytically, however, especially for large-scale systems. Computational methods developed in this part of the paper are needed to successfully analyze dextrous workspaces of spatial manipulators. In order to map one- or two-dimensional regular solution sets of nonlinear algebraic equations, well-developed numerical analysis packages are adopted in this research. A new approach that combines a condition for the null space of the constraint Jacobian matrix with second-order Taylor expansion of the constraint equations to switch solution branches near simple bifurcation points is developed. To determine the existence of an impending void inside candidate regions of the dextrous accessible output set, a numerical method is presented to determine whether necessary conditions presented in Part I of the paper are satisfied. With these capabilities, an algorithm for determining dextrous accessible output sets is developed. Computational methods developed for dextrous workspace analysis are shown to be effective in solving dexterity problems for a variety of manipulators.