Kinematics and Singularity Analysis of 2 DOF Planar Parallel Manipulators with Symmetrical Parallelogram Chains

Abstract

This paper presented the kinematic and singularity analysis of two degree of freedom planar parallel manipulator or 2DOF PPM, in short, with symmetrical parallelogram chains. There were two configurations of 2DOF PPM that analyzed in this paper, that were 2-ΠΠΠ and 2-ΠΠ. Both PPM were represented on a topology diagram using graphs, respectively. Before conducting a kinematic analysis, 2-ΠΠΠ dan 2-ΠΠ were simplified to an equivalent kinematic chain, which was a well-known 5R kinematic chain. Then, the closed-form solutions for the inverse kinematic and the direct kinematic of the PPM were obtained by using the equivalent kinematic chain. Afterward, the velocity analysis was carried out to acquire Jacobians of the PPM. Hence, the singularity analysis can be performed to investigate singularity conditions that existed on the manipulator using these Jacobians. The singularity analysis showed that three singularity conditions existed on the manipulator, i.e. inverse, direct, and combined kinematic singularity. An insightful schematic was provided to illustrate each singularity condition.