Degree Of Constraint Research Articles

Load-displacement behavior of fundamental flexure modules interconnected with compliant elements

To avoid stiffness loss in the bearing direction of flexure mechanisms, researchers usually amplify the stiffness of the constitutive beams of the mechanism using intermediate stiffeners which are usually assumed to be perfectly rigid. The ultimate objective of this paper is to put this assumption under question and provide more accurate load-displacement relationships as well as strain energy expression for the planar motion of the compliant mechanisms. Employing the principle of virtual work, the load-displacement of the mechanisms’ final stage is derived and verified using FE simulations. The degree of constraint (DoC) and degree of freedom (DoF) stiffnesses of the system are then obtained which are also in well agreement with FE results. Parametric studies are carried out to better realize the effect of the interconnected compliant element on the stiffnesses of the system. As a case study, a comb-drive assembly suspended over a simple flexure is modeled using the proposed formulation. It is observed that with the assumption of semi-rigid reinforcement elements, the actuation effort can be considerably decreased in almost the same travelling strokes. The formulation presented in this paper can be employed to improve the performance of flexure-based high precision units by means of providing more accurate predictions for the error motions and stiffness components.

STIFFNESS ANALYSIS OF TWO COMPLIANT PIVOTS USED IN SERIES ELASTIC ACTUATORS

A compliant pivot used in series elastic actuators (SEAs) can be of great practical use for saving structure space. The analysis of load-deflection behavior for such pivots can provide an analytical mechanical design method. In this paper, two pivots are proposed for the corresponding implementation. Based on the Awtar accurate approximations, the two annulus compliant pivots are further simplified to linear stiffness behavior for the SEAs applications. Specifically, an annulus compliant pivot based on parallel leaf-springs is firstly analyzed. After that, we focus on a special kind of annulus compliant pivot whose degree of constraint (DOC) was released. Finally, the accuracy characteristics of the models are identified by comparing with the results obtained by nonlinear finite element analysis.