Assembly variation analysis of compliant mechanisms by combining direct linearization method and Lagrange’s equations

Abstract

Purpose

This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis procedure extends the application area of direct linearization method (DLM) to compliant mechanisms and also illustrates the dimensional interaction within multi-loop compliant structures.

Design/methodology/approach

By applying DLM to both geometrical equations and Lagrange’s equations of the second kind, an analytical deviation modeling method for mechanisms with compliant joints are proposed and further used for statistical assembly variation analysis. The precision of this method is verified by comparing it with finite element simulation and traditional DLM.

Findings

A new modeling method is proposed to represent kinematic relationships between joint deformations and parts/components deviations. Based on a case evaluation, the computational efficiency is improved greatly while the modeling accuracy is maintained at more than 94% rate comparing with the benchmark finite element simulation.

Originality/value

The Equilibrium Equations of Incremental Forces derived from Lagrange’s equations are proposed to quantitatively represent the relationships between manufactured deviations and assembly deformations. The present method extends the application area of DLM to compliant structures, such as automobile suspension systems and some Micro-Electro-Mechanical-Systems.

Citation

Niu, Z., Li, Z., Jin, S. and Liu, T. (2019), "Assembly variation analysis of compliant mechanisms by combining direct linearization method and Lagrange’s equations", Assembly Automation, Vol. 39 No. 4, pp. 740-751. https://doi.org/10.1108/AA-10-2018-0151