Reconfiguration of a 3-(rR)PS Metamorphic Parallel Mechanism Based on Complete Workspace and Operation Mode Analysis

This paper focuses on the reconfiguration of a 3-(rR)PS metamorphic parallel mechanism based on complete workspace and operation mode analysis. The mechanism consists of three (rR)PS legs, and each (rR) joint is composed of two perpendicular revolute joints. One of the (rR) joint axes can be reconfigured continuously, which allows the mechanism to exhibit three distinct configurations. Initially, the constraint equations are derived by using algebraic geometry approach, and the primary decomposition is computed for the three configurations. It reveals that the 3-(rR)PS metamorphic parallel mechanism can exhibit one up to two operation modes among three configurations. When the second axes of the three (rR) joints intersect at a finite point and not coplanar, the 3-(rR)PS metamorphic parallel mechanism has only one operation mode. If the second axes of the three (rR) joints are coplanar, the 3-(rR)PS metamorphic parallel mechanism has two operation modes. It is shown that both operation modes have the same motion type, namely, 1T2R motion. However, to realize the same trajectories in both operation modes, the moving platform will have different orientations. Hence, the orientation workspaces of both operation modes are characterized and the axodes are used to compare the instantaneous motion of the moving platform when passing through the same trajectories. Based on these results, an identification approach is introduced to identify which operation mode a given mechanism pose belongs to and this provides a useful method for trajectory planning.