Topology optimization of compliant circular path mechanisms based on an aggregated linear system and singular value decomposition

A. Takezawa*, M. Kitamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This paper proposes a topology optimization method for the design of compliant circular path mechanisms, or compliant mechanisms having a set of output displacement vectors with a constant norm, which is induced by a given set of input forces. To perform the optimization, a simple linear system composed of an input force vector, an output displacement vector and a matrix connecting them is constructed in the context of a discretized linear elasticity problem using FEM. By adding two constraints: 1, the dimensions of the input and the output vectors are equal; 2, the Euclidean norms of all local input force vectors are constant; from the singular value decomposition of the matrix connecting the input force vector and the output displacement vector, the optimization problem, which specifies and equalizes the norms of all output vectors, is formulated. It is a minimization problem of the weighted summation of the condition number of the matrix and the least square error of the second singular value and the specified value. This methodology is implemented as a topology optimization problem using the solid isotropic material with penalization method, sensitivity analysis and method of moving asymptotes. The numerical examples illustrate mechanically reasonable compliant circular path mechanisms and other mechanisms having multiple outputs with a constant norm.

Original languageEnglish
Pages (from-to)706-725
Number of pages20
JournalInternational Journal for Numerical Methods in Engineering
Issue number6
Publication statusPublished - 2012 Feb 10
Externally publishedYes


  • Compliant mechanisms
  • Finite element method
  • Path generation
  • Sensitivity analysis
  • Singular value decomposition
  • Topology optimization

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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