Stiffness Formulations of Planar Kinematics

TLDR: In this paper, a simple theory using the stiffness concept is presented for linkage-motion analysis, and the nonlinear incremental mechanism equations are established and their solution procedure is proposed, which can be incorporated into existing finite element computer program systems and can be applied to general three-dimensional mechanisms.

Abstract: A simple theory using the stiffness concept is presented for linkage-motion analysis. The nonlinear incremental mechanism equations are established and their solution procedure is proposed. The kinematic system is first regarded as an instable elastic structure. The tangent stiffness equations are updated for current mechanism configurations. The obtained singular stiffness matrix is then used to predict incremental nodal displacements. The stress-associated deformation is designated as numerical error. The proposed stiffness method follows successively the mechanism motion in an incremental-iterative manner. Computed numerical examples show that the elastic deformation can easily be removed with a few iterations. The proposed stiffness approach to kinematics may be incorporated into existing finite-element computer program systems and can be applied to general three-dimensional mechanisms.