The Optimum Kinematic Design of a Planar Three-Degree-of-Freedom Parallel Manipulator

TLDR

The study designs a planar three‑degree‑of‑freedom parallel manipulator from a kinematic perspective. Four optimization criteria—symmetry, full‑orientation workspace, maximal global workspace, and Jacobian isotropy—are formulated and solved, with two problems requiring numerical methods for nonlinear algebraic systems. The resulting optimum designs are presented.

Abstract

In this paper, the design of a planar three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Four different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) the existence of a nonvanishing workspace for every orientation of the gripper (c) the maximization of the global workspace, and (d) the isotropy of the Jacobian of the manipulator. The four associated problems are formulated and their solutions are derived. Two of these require to resort to numerical methods for nonlinear algebraic systems. Results of optimum designs are also included.