Kinematic Analysis of a Novel Actuation Redundant 3-DOF Parallel Manipulator Based on Parallelogram-Linkage

The passive joints occurring in the parallel robots require additional steps to be calculated, which may lead to complicated analytical kinematic and dynamic models, become burdens to derive these mathematical solutions or demand extra efforts to measure their motions. This research presents a special planar parallel manipulator with actuation redundancy based on parallelogram linkage. Every moving linkage excluding the mobile platform is parallel to one of the actuation rods within the reachable workspace and all these passive joint angles can be conveniently resolved from the active joint angles through simple arithmetic operations. The constant linkage dimension relationships are utilized to formulate the inverse kinematic solution with the assistance of two additional virtual points. The vector loop equations are employed to compute the forward kinematic results. The Jacobian matrix is established from the forward kinematic model. The spatial searching methodology is utilized to obtain the reachable workspace and the kinematic performance distributions are explored.