Structural and Multidisciplinary Optimization

, Volume 60, Issue 4, pp 1475–1489 | Cite as

Design of compliant revolute joints based on mechanism stiffness matrix through topology optimization using a parameterization level set method

  • Li LiEmail author
  • Xiaojin Zhu
Research Paper


The main difficulties for designing compliant revolute joints include controlling the rotational angle with high precision and realizing a larger rotational angle range. Aiming at these two critical issues, this article presents an approach for designing compliant revolute joints based on a mechanism stiffness matrix using structural topology optimization. The compliant revolute joint is modeled as a kinetoelastic model considering the kinematic properties and structural elastic properties simultaneously. Thus, a mechanism stiffness matrix is established to synthetically describe the kinematic and elastic characteristics of a compliant revolute joint. Meanwhile, the topology optimization formulation is defined as an eigensystem optimization problem of the mechanism stiffness matrix. The parameterization level set method-based structural optimization is implemented with the finite element method, and shape sensitivity analysis is stated for this optimization problem. Numerical examples of compliant revolute joint design by topology optimization in two-dimension (2D) are investigated as a benchmark test for the proposed method and the influence of parameters is researched and discussed. Additionally, the guidance for parameter selection in this topology optimization problem is provided. The results indicate that the proposed kinetoelastic approach can be an effective method for designing compliant revolute joints through structural topology optimization.


Compliant revolute joint Kinetoelastic model Mechanism stiffness matrix Topology optimization Eigensystem optimization A parameterization level set method 


Funding information

This work was supported by the National Natural Science Foundation of China (51405280, 51575328).

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechatronic Engineering and AutomationShanghai UniversityShanghaiChina

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