Stability Analysis for Compliant Constant-Force Compression Mechanisms

Abstract

Stability analysis in compliant mechanism (CM) design is of utmost importance. From a practical point of view, a CM that is unstable is of no significance (has no practical value). Three useful plots were considered in the evaluation of each of the dynamic models of nine configurations of compliant constant-force compression mechanisms (CCFCMs) for their stability characteristics, which includes the polar plot based on the Routh-Hurwitz stability criterion, the Bode plot, and the Nyquist diagram which considers stability in the real frequency domain. Frequency-domain stability criterion is very useful for determining suitable approaches to adjusting the CCFCM parameters in order to increase its relative stability. The results obtained show that the CCFCMs investigated do exhibit higher relative stability for higher values of damping ratio, and for zero damping ratio, all the CCFCMs investigated were unstable. The result also show that for the CCFCMs investigated to be stable, damping ratio must be greater than 0.03 (ξ > 0.03) and depending on what attributes are most desirable, the CCFCM parameters can be optimized to achieve the desired results. Nyquist criterion provides us with suitable information concerning the absolute stability and furthermore, can be utilized to define and ascertain the relative stability of a system.