Configuration Design of Single-Loop Non-overconstrained Mechanism with Inactive Joints

Abstract

In order to weaken the strict geometric constraint relationship between the axes of joints so as to reduce manufacturing/assembling errors of overconstrained mechanism, a configuration design methodology for single-loop non-overconstrained mechanism with inactive joints is proposed in this paper based on the screw theory. After completing analysis of degrees of freedom, the design principle and corresponding process of single-loop non-overconstrained mechanism with inactive joints are presented. By introducing two inactive R (R: single-degree-of-freedom revolute joint) joints to an active R joint of Goldberg overconstrained mechanism, the corresponding Goldberg non-overconstrained mechanism is obtained. It is verified that the velocities of two inactive joints in the Goldberg non-overconstrained mechanism are zero via investigating motion screws of branches. By further solving input and output kinematic parameters of Goldberg non-overconstrained mechanism, it is discovered that the overconstrained mechanism and corresponding non-overconstrained mechanism have the identical input–output relationship. Above results confirm that the overconstrained mechanism and its non-overconstrained counterpart with inactive joints are completely equivalent kinematically, which thereby demonstrate fully correctness of the configuration design principle and method of single-loop non-overconstrained mechanism proposed in this paper.