Mobility Analysis of Robotic Mechanisms Based on Computer Algebra

Abstract

The Chebychev-Kutzbach-Gru¨bler criterion (CKG Criterion) is useful in evaluating the mobility of robotic mechanisms. However, it cannot correctly evaluate the mobility of some mechanisms (e.g., overconstrained mechanisms, mechanisms with Passive DOF, etc.). In this paper, we propose a more general method for automatically evaluating mobility, based on computer algebra. In this method, the constraints caused by links and joints are expressed as simultaneous algebraic equations (SAE), which is converted into a type of canonical form, constructed from special polynomials called the Gro¨bner Bases. The mobility can be then determined by checking the appearance sequence of the variables in the Gro¨bner Bases. The results are reliable because the method consists only of symbolic calculations and are free of numerical error problems. Moreover, the method is automatically applicable to spatial mechanisms containing various types of joints as no heuristics are required. We show the mobility analysis of three robotic mechanisms for which the CKG Criterion is not applicable, and show that the proposed method can correctly evaluate their mobility.