Dextrous Workspaces of Manipulators, Part III: Calculation of Continuation Curves at Bifurcation Points

ABSTRACT

An efficient numerical method is presented to obtain all tangent vectors at bifurcation points of continuation curves that define the boundary of manipulator workspaces. The method developed is based on analytical criteria presented in Part I of this paper [1] and computational methods presented in Part II [2]. As observed in the latter paper, difficulties in mapping boundaries of accessible output sets include (1) systematically finding an initial point on the boundary and (2) efficiently calculating tangent vectors at multiple bifurcation points. The first difficulty has been solved by Haug, Luh, Adkins, and Wang [3]. The second difficulty is resolved in this paper.