Geometric design of planar mechanisms based on virtual guides for manipulation

This paper presents recent results and applications of our planar kinematic synthesis of serial and parallel linkages to guide a rigid body, such that it does not violate normal direction and curvature constraints imposed by contact with objects in the environment. The paper briefly reviews the recently developed theory on transforming contact direction and curvature constraints into conditions on velocity and acceleration of certain points in the moving body to obtain synthesis equations which can, subsequently be solved to find the dimensions of a mechanical linkage. The main contribution of the paper is in demonstrating the applicability of the proposed theory to the kinematic synthesis of both open and closed-loop kinematic linkages. We provide preliminary results on the synthesis of kinematic chains based on novel task specifications that incorporate curvature constraints with a variety of applications, such as passive suspensions for small rovers, assistive technologies, as well as grasping.

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