Quaternion method for the kinematics analysis of parallel metamorphic mechanisms

Abstract

The parallel metamorphic mechanism is a novel metamorphic mechanism. Its kinematics analysis is not only a new research field, but also a difficult problem. In this paper, with the origin of coordinates on the moving platform describing its position and Euler angles describing its orientation, we present the quaternion expression of an arbitrary point’s location on the moving platform in the fixed coordinate system. Then a method to establish the unified mathematical model for kinematics analysis of the parallel metamorphic mechanism is presented. Based on this unified mathematical model, forward and inverse kinematics analysis of the parallel metamorphic mechanism in different configurations can be conducted. Using kinematics analysis of a novel 4-URU parallel metamorphic mechanism, the proposed kinematics analysis method is further elaborated, and the resultant elimination method is presented to solve the kinematics equations. Finally, a numerical example is given to verify that the proposed method is correct and effective.