Workspace Analysis of Closed Loop Mechanisms With Unilateral Constraints

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Abstract
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.

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