Synthesis of Planar Parallel Mechanism

Abstract

Parallel mechanisms are found as positioning platforms in several applications in robotics and production engineering. Today there are various types of these mechanisms based on the strcture, type of joints and degree of freedom. An important and basic planar mechanism providing three degree of freedom at the end-effector (movable platform) is a 3-RPR linkage. Here the underscore below P indicates the presence of actuated prismatic joints and 3 indicates the number of legs used to carry the mobile platform. A lot of work has been done on this mechanism since 1988. In the present work, the kinematics of 3-RPR linkage is specifically studied to understand the synthesis procedure. The forward kinematics in parallel mechanisms is a multi-solution problem and involves cumbersome calculations compared to inverse kinematics. In inverse kinematics, we design the actuator input kinematic parameters for a known table center coordinates. In other words it is a transformation of platform pose vector to the actuator degrees of freedom. In 3-RPR mechanism considered in present task, the actuators are sliders and hence the slider displacements reflect the input degrees of freedom. On the other hand, for a known posture (available slider displacement status), the table center coordinates are predicted in forward kinematics. In present work, forward kinematics solutions are obtained by defining error function and optimizing it using genetic algorithms programs. Also, the workspace and Jacobian matrices are computed at corresponding solution and singularity analysis is briefly highlighted.