Determination of overconstraint and mobility analysis for planar mechanisms

The mobility(or degree of freedom) analysis of planar mechanisms is traditionally calculated using the Grubler–Kutzbach formula. However, this method often fails in practice due to overconstraint, which is a core problem in all mobility analysis. Analyzing the cause of overconstraint, it is presented that overconstraint in closed-loop mechanisms can be recognized by analyzing the relative movements of the two elements in a rigidity re-closure. A solution to determine the overconstraint in multiloop mechanisms is also proposed. In this method, each loop is opened and the overconstraint can be calculated when the loop is reclosed. A mobility analysis must begin by determining the overconstraint. However, given that most planar mechanisms do not have any overconstraint, it is important to identify rapidly whether overconstraint exists in a mechanism. This paper proposes a concise technique to determine the existence of overconstraint based on the concept of “Assur groups”. To simplify the process of mobility...