Analogy Between Bifurcations in Stability of Structures and Kinematics of Mechanisms

摘要

This article discusses singularities occurring in compatibility paths of planar bar-and-joint mechanisms with 1 degree-of-freedom. Bifurcation of branches of compatibility paths are examined and simple examples are given for several bifurcation modes. Effects of geometric imperfections on the kinematic behavior are also considered. The behavior and properties of kinematic bifurcations are paralleled to those of equilibrium bifurcations known in stability theory. An analogy is presented between the two areas incorporating the different types of bifurcation, effects of imperfections, and detection of singularities. A formulation of potential energy for mechanisms is also proposed in analogy with the potential energy function used in structural analysis.