Extended Static Modeling and Analysis of Compliant Compound Parallelogram Mechanisms Considering the Initial Internal Axial Force^*

Extended nonlinear analytical modeling and analysis of compound parallelogram mechanisms are conducted in this paper to consider the effect of the initial internal axial force. The nonlinear analytical model of a compound basic parallelogram mechanism (CBPM) is first derived incorporating the initial internal axial force. The stiffness equations of compound multibeam parallelogram mechanisms (CMPMs) are then followed. The analytical maximal stress under the primary actuation force only is also derived to determine the maximal primary motion (motion range). The influence of initial internal axial forces on the primary motion/stiffness is further quantitatively analyzed by considering different slenderness ratios, which can be employed to consider active displacement preloading control and/or thermal effects. The criterion that the primary stiffness may be considered “constant” is defined and the initial internal axial force driven by a temperature change is also formulated. A physical preloading system to control the initial internal axial force is presented and testing results of the object CBPM are compared with theoretical ones.