Optimal Synthesis of Zero-Stiffness Compliant Mechanisms Based on Potential Energy Principle

Zero-stiffness compliant mechanisms (ZSCM) can provide constant or zero force over a range of motion without the issues caused by the inherent stiffness of compliant mechanisms (CM). The large-deflection curved beams in ZSCM enhance the mechanism’s performance but pose significant modeling challenges. As an effective method for modeling curved beams, chained pseudo-rigid-body model (CPRBM) can be an intuitive method to implement in ZSCM synthesis. However, its difficulty in solving reaction forces limits its usability in the frequently-used force-based ZSCM synthesis. To address the problem, this article proposes an energy-based method for CPRBM-based ZSCM synthesis, without calculating the reaction force. This method synthesizes the mechanisms with zero-stiffness characteristics by optimizing the energy recorded from the analysis based on the principle of minimum potential energy. Two optimization models based on energy characteristic are developed for constant force CM (CFCM) and statically balanced CM (SBCM), respectively. Synthesis cases and experimental studies are used to verify the proposed method. The results demonstrate that the synthesized ZSCM have good performances and the proposed method can be a user-friendly tool for ZSCM synthesis.