From Constraint Counting to Geometry-Informed Frameworks: A Critical Review of Mobility Theory for Overconstrained Mechanisms

Abstract

In mechanisms, there is a growing trend to establish theories, aiming to explain the mobility of mechanism. According to the degree-of-freedom (DOF) theory, multiple mechanism designs have been built, for example, Bennett and Bricard linkages. However, present theories of mobility are insufficient for all mechanisms. To broaden the application scope of the DOF theory, researchers have tried to introduce mathematic theories on DOF calculation to satisfy present mechanism design. This paper is a detailed summary of the historical changes and recent progress of DOF theory. In particular, it focuses on the analysis of overconstrained mechanisms, which is the standard to judge whether various theoretical methods are correct or not. By tracing the changes of existing methods, this review not only shows their development process, but also discusses their inherent limitations in dealing with complex machining.