Mobility of the Myard 5R Linkage Involved in “Gogu Problem”

Abstract

Since the traditional Grbler-Kutzbach criterion fails in many overconstrained mechanisms, developing a general mobility formula is a hot topic lasting for more than 150 years in mechanisms. GOGU systematically investigated various mobility methods, and pointed that the methods were not fit for two kinds of paradoxical overconstrained mechanisms. The mobility on the two kinds of mechanisms is regarded as "Gogu problem" . The Modified Grbler-Kutzbach criterion has solved the mobility of the second kind of mechanisms in "Gogu problem" , and has developed into a systematic mobility methodology. Myard 5R linkage is one of the single-loop mechanisms involved in "Gogu problem" , its joint axes are distributed in space with special geometric conditions, which increases the difficulty of mobility analysis. The study is to calculate the global mobility of the Myard 5R linkage using the mobility methodology. Firstly, the mobility methodology based on screw theory is briefly introduced. Secondly, some homogeneous transforms are performed according to the D-H parameters and the invariance of the linkage plane symmetry is revealed, which provides an idea to judge a plane-symmetric loop. The special geometric features of the axes distribution are discussed as well. Finally, the global mobility of the Myard 5R linkage is determined by the Modified Grbler-Kutzbach criterion. The results show that the methodology can be applied to more paradoxical mechanisms.