Isotropic Analysis of Line Vector Forces and its Application in the Type Synthesis of Redundantly Actuated 3-DOF Translational Parallel Mechanisms

Abstract

The load-carrying capacity of a mechanism is closely related to its line vector force. This article presents a thorough isotropic analysis of line vector forces. The results show that the isotropic condition can be satisfied when the line vector forces are evenly distributed on a conical surface with a cone-top angle of 109.472 degrees. By combining the isotropic line vector forces, a method for the type synthesis of 3-DOF, redundantly actuated translational parallel mechanisms (PMs) is proposed, in which the arrangement of the active joints is taken into account in advance. Using this method, a kinematic chain with a twist system reciprocal to both the constraint and actuation wrenches is constructed firstly, and then the active joint reciprocal to the constraint wrenches but not to the actuation wrench is constructed. Thus, a series of typical redundantly actuated PMs with isotropic actuation forces are obtained. Finally, the 4-PRRR PM is analyzed as an example, and the results show that the isotropy of the load-carrying capacity can always be satisfied during its movement.