Kinematic Synthesis of Planar Multi-limb Mechanisms for Multi-directional Interaction with Bodies in the Environment

The paper considers the synthesis of planar mechanisms to manipulate a body in multiple desired directions in the vicinity of a contact pose, a critical focus not fully captured in existing design methodologies. The mechanism consists of multiple planar Revolute-Prismatic-Revolute (RPR) limbs in contact with the body. Under equilibrium grasp, each of the desired directions impose normal forces and curvature constraints in the vicinity of the limb-body contact. We discuss how to transform these constraints into velocity and acceleration requirements of the body, and formulate the synthesis equations of planar RPR serial chains to achieve each desired manipulation task. The simultaneous design of two planar RPR limbs able to manipulate an object in two different directions in the vicinity of a contact pose illustrates the feasibility of the proposed design approach.