Kinematic path analysis of kinematically indeterminate systems

Kinematically indeterminate systems are geometrically unstable. Considering that there is only tiny elastic deformation in the process of the mechanism motion, the method to simulate kinematic paths of kinematically indeterminate systems without considering elastic deformation is studied in this paper. Based on the equilibrium matrix theory, mechanism displacement is decomposed into combinatorial displacement of independent inextensional mechanisms and displacement resulted from the length modifications of members. The reasonable combination coefficient of inextensional mechanisms is determined by the gradient of the potential energy. An analysis algorithm is developed to simulate the kinematic paths of rigid pin-bar assemblies. The validity and accuracy of the algorithm proposed in this paper is illustrated by three typical examples.