A nonlinear analysis of spatial compliant parallel modules: Multi-beam modules

Guangbo Hao, Xianwen Kong, Robert L. Reuben

Research output: Contribution to journalArticlepeer-review

60 Citations (Scopus)


This paper presents normalized, nonlinear and analytical models of spatial compliant parallel modules-multi-beam modules with a large range of motion. The models address the non-linearity of load-equilibrium equations, applied in the deformed configuration, under small deflection hypothesis. First, spatial nonlinear load-displacement equations of the tip of a beam, conditions of geometry compatibility and load-equilibrium conditions for a spatial three-beam module are derived. The nonlinear and analytical load-displacement equations for the three-beam module are then solved using three methods: approximate analytical method, improved analytical method and numerical method. The nonlinear-analytical solutions, linear solutions and large-deflection FEA solutions are further analyzed and compared. FEA verifies that the accuracy of the proposed nonlinear-analytical model is acceptable. Moreover, a class of multi-beam modules with four or more beams is proposed, and their general nonlinear load-displacement equations are obtained based on the approximate load-displacement equations of the three-beam module. The proposed multi-beam modules and their nonlinear models have potential applications in the compliant mechanism design. Especially, the multi-beam modules can be regarded as building blocks of novel compliant parallel mechanisms. © 2010 Elsevier Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)680-706
Number of pages27
JournalMechanism and Machine Theory
Issue number5
Publication statusPublished - May 2011


  • Compliant mechanisms
  • Nonlinear analysis
  • Spatial modules


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