Grassmann line geometry based configuration synthesis of equivalent UU parallel mechanisms with two virtual center-of-motion

Abstract

This paper investigates a class of equivalent UU parallel mechanisms with two virtual center-of-motions (VCMs) in terms of the geometric characteristics of the equivalent UU model, and proposes a configuration synthesis method based on the Grassmann line geometry and constraint screw multiset. First, the equivalent UU model is proposed concerning the analysis of ankle rehabilitation and the ankle UU model. Three geometric characteristics and four classes of motion and constraint characteristics of the equivalent UU model are given. Second, the motion principle of equivalent UU parallel mechanism is proposed for the characteristics of motion and constraint, which provides a theoretical method for configurable synthesis. Third, a series of constraint limbs satisfying the motion and constraint characteristics of equivalent UU parallel mechanisms are synthesized by using the constraint screw synthesis method in terms of the screw theory and Grassmann line geometry principle. Finally, the concept of multiset is introduced into mechanism synthesis, and a series of equivalent UU parallel mechanisms are synthesized based on the method of constraint screw multiset.