Workspace Analysis of Closed Loop Mechanisms With Unilateral Constraints Available to Purchase

Kinematics of mechanisms that contain elements with unilateral constraints such as stops are characterized by systems of equalities and inequalities. A slack variable formulation is introduced to convert inequality constraints to equalities, in a higher dimensional space of variables. The slack variable formulation permits use of manifold based theoretical and numerical methods for analysis of the boundaries of workspaces. The workspace of a simplified Stewart platform is analyzed, including rotatability of the top platform. Sets of reachable points of the top platform of a three dimensional Stewart platform, with fixed platform orientation, are analyzed.