A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments

Abstract

Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

Modeling of large-deflection links for compliant mechanisms

“…The idea of PRBM was also applied to the modeling of initially curved, largedeflection links in compliant mechanisms [10]. Saxena et al [11] modified the PRBM by introducing two linear springs to restrain the change of the characteristic radius factor for different load modes. Lyon [12] decomposed a flexible link into two segments, each of which is approximated by a PRBM.…”

Application of trained NiTi SMA actuators in a spatial compliant mechanism: Experimental investigations

“…These research works were focused on the coupled effect of force developed due to SMA actuation and force required for elastica deflection of the central superelastic pillar. The available literature related to large deflection analysis of compliant mechanisms [9,10] were formulated considering the orientation of force as fixed with respect to the tip deflection and by treating the tip moment as constant. For the mechanism under development, both the force and the moment have been considered continuously varying in orientation with tip deflection.…”

Large deflection of flexible tapered functionally graded beam

“…This approach has been used for developing a pseudo-rigid body model of a flexible uniform isotropic cantilever beam subjected to end forces only [16]. Numerical schemes have also been proposed [17] where the forces, along with moments, are applied only at the free end of a uniform isotropic compliant cantilever. The large deflection problem under combined end loadings has been solved using elliptic integrals and differential geometry in a flexible uniform isotropic beam [18].…”