Analyses of Three Dimensional Deformations of Planar Offset Four-Link Mechanisms

In the design of planar link mechanisms, moving links are arranged in parallel offset planes in order to avoid their mutual interferences. Therefore, not only the input moment, the transmitted force and the output moment but also bending and torsional moments in planes containing moving links (motion planes) act on each link. In this paper, the spatial closed loop equations with very small torsional and bending deflections of moving links of the planar offset four-link mechanism are deduced. Equilibrium conditions of torsional and bending moments acting on moving links are expressed in linear equations of their very small deflections and the torsional rigidity about the revolute axis of the driving link. By solving simultaneously the spatial closed loop equations and the equilibrium equations, the equivalent torsional rigidity and very small deflections of moving links are obtained.