Extended nonlinear analysis of exactly-constrained compliant compound parallelogram mechanisms

Extended nonlinear analysis of compliant compound parallelogram mechanisms is conducted in this paper. The analytical nonlinear model of a compound basic parallelogram mechanism (CBPM) is first derived incorporating the initial internal axial force. The stiffness equations of compound multi-beam parallelogram mechanisms (CMPMs) are then followed. The effect of initial internal axial forces on the primary motion is further analyzed, which can be employed to consider active displacement preloading control and thermal effects etc. It is shown that negative initial internal axial force will reduce the primary stiffness, and vice versa. The criteria for which the primary stiffness may be considered "constant" is defined and the initial internal axial force driven by temperature change is also formulated. The dynamic analysis of a CMPM using nonlinear finite element analysis (FEA) is finally carried out to show the modal frequency and the forced excitation response in the primary motion direction.