Development of a novel synthesis method of a rigid-body four-bar linkage into a compliant mechanism

The four-bar linkage mechanism is widely used in various machinery applications. This study presents a synthesis method to transform a rigid-body four-bar mechanism into a compliant mechanism using four leaf-type hinges based on linear theory and Castigliano's Theorem. The objective is to determine the dimensions and configuration of a flexible four-bar mechanism that replicates the behavior of the initial rigid-body mechanism. The meeting point between the two mechanisms is the flexure hinge of the compliant mechanism, which is determined using the Pseudo-Rigid-Body model (PRBM). To validate the proposed method, a program based on non-linear theory is employed. The results confirm that the dimensional differences between the two are minimal, ranging from 0% to 0.13%. This study demonstrates the feasibility of synthesizing a Rigid-Body Four-Bar Mechanism into a compliant mechanism using the PRBM, as long as the deformations are within the linear domain.