A simple and versatile topology optimization formulation for flexure synthesis

S. Koppen*, M. Langelaar, F. van Keulen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)
180 Downloads (Pure)


High-tech equipment critically relies on flexures for precise manipulation and measurement. Through elastic deformation, flexures offer extreme position repeatability within a limited range of motion in their degrees of freedom, while constraining motion in the degrees of constraint. Topology optimization proves a prospective tool for the design of short-stroke flexures, providing maximum design freedom and allowing for application-specific requirements. State-of-the-art topology optimization formulations for flexure synthesis are subject to challenges like ease of use, versatility, implementation complexity, and computational cost, leaving a generally accepted formulation absent. This study proposes a novel topology optimization formulation for the synthesis of short-stroke flexures uniquely based on strain energy measures under prescribed displacement scenarios. The resulting self-adjoint optimization problem resembles great similarity to ‘classic’ compliance minimization and inherits similar implementation simplicity, computational efficiency, and convergence properties. Numerical examples demonstrate the versatility in flexure types and the extendability of additional design requirements. The provided source code encourages the formulation to be explored and applied in academia and industry.

Original languageEnglish
Article number104743
Number of pages15
JournalMechanism and Machine Theory
Publication statusPublished - 2022


  • Compliant mechanisms
  • Flexures
  • Kinematics
  • Manufacturability
  • Strain energy
  • Stress
  • Topology optimization


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