Mathematical Description of a Flexible Connection of Links and its Applications in Modeling the Joints of Spatial Linkage Mechanisms

Abstract

The general mathematical model of a flexible connection of links by means of spring-damping elements is presented in the paper. The formalism of homogeneous transformation matrices is used to derive formulas for the energy of spring deformation and the Rayleigh dissipation function of the spring-damping elements. The formulas have convenient forms to connect them to Lagrange equations of the second order. The replacement models of the spherical and revolute joint are presented as a particular case of the general model and are used for dynamics analysis of a one-DOF RSRRP linkage mechanism. The numerical results obtained here using the replacement models were compared with the results from the cut-joint technique.

Keywords:
modeling; replacement model; spherical joint; revolute joint; statics analysis; dynamics analysis; spatial mechanism; cut-joint technique