Workspace branches for the planar three-degree-of-freedom parallel manipulator

摘要

This study investigates a systematic method for distinguishing the individual workspace branches from the entire reachable space of a planar three-degree-of-freedom parallel manipulator. The closed form solutions for the direct kinematics implied by a sixth-order polynomial are distributed into eight branches with different branch IDs. The workspace boundary for each branch is identified from the characteristics of the polynomial solutions, seeking that each individual workspace is free of singularities. Different workspace branches can cross each other only through the singularities. Every branch may contain a maximum of eight sub-branches, also separated by singularities. Following the identification of workspace branches, a workspace suitable for motion control is defined. Finally the study includes some examples of the branch-crossing conditions.