Singularity Analysis Method of Multi-Loop Coupling Mechanism Using Geometric Algebra

Abstract

Multi-loop coupling mechanisms (MCMs) have been widely used in aerospace engineering, architectural design, and outdoor activities. This paper proposes a general method for analyzing the singularities of MCMs using geometric algebra. The limbs of MCM can be divided into basic limbs and coupling limbs. For independent basic limbs, constraint space can be obtained directly by outer product and dual operator. For basic limbs coupled with closed-loops in an MCM, the modified constraint space can be obtained by analyzing each coupled single closed-loop. The singular polynomial of the MCM is obtained from the join of all the basic limb constraint space, which can be calculated by the outer operator. The singular polynomial is analyzed to obtain all singular configurations in the global coordinate system. The proposed method has the advantages of simple computation and clear physical significance. Furthermore, three MCM examples of different couple types are used to demonstrate the correctness of this method.