Stiffness Compensation Through Matching Buckling Loads in a Compliant Four-Bar Mechanism

Abstract

In this paper a novel alternative method of stiffness compensation in buckled mechanisms is investigated. This method involves the use of critical load matching, i.e. matching the first two buckling loads of a mechanism. An analytical simply supported four-bar linkage model consisting of three rigid links and four torsion springs in the joints is proposed for the analysis of this method. It is found that the first two buckling loads are exactly equal when the two outer springs are three times stiffer than the two inner springs. The force-deflection characteristic of this linkage architecture showed statically balanced behavior in both symmetric and asymmetric actuation. Using modal analysis, it was shown that the sum of the decomposed strain energy per buckling mode is constant throughout the motion range for this architecture. An equivalent lumped-compliant four-bar mechanism is designed; finite element and experimental analysis showed near zero actuation forces, verifying that critical load matching may be used to achieve significant stiffness compensation in buckled mechanisms.

Structural function from sequential, interacting elastic instabilities

“…Nonetheless, there are a handful of examples in published literature which contradict the traditional narrative and deliberately exploit the properties of interacting instabilities for functionality. For example, interacting instabilities have been used to design compliant mechanisms with a near-zero stiffness snap-through response, which is achieved by compressing a beam with two coincident buckling modes [33][34][35]. Another example is found in meta-materials, where structures consisting of an array of snap-through arches have been used to create programmable solids [36], and for the purposes of energy dissipation [37].…”