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Physical deformation configuration of a spatial clamped cable based on Kirchhoff rods

Hongwang Du (Dalian Maritime University, Dalian, China)
Wei Xiong (Dalian Maritime University, Dalian, China)
Haitao Wang (Dalian Maritime University, Dalian, China)
Zuwen Wang (Dalian Maritime University, Dalian, China)

Assembly Automation

ISSN: 0144-5154

Article publication date: 14 December 2017

Issue publication date: 23 January 2018




In this study, a modeling method for a clamped deformable cable simulation based on Kirchhoff theory is proposed. This methodology can be used to describe the physical deformation configuration of any constrained flexible cable in a computer-aided design/manufacturing system. The modeling method, solution algorithm, simulation and experimental results are presented to prove the feasibility of the proposed methodology. The paper aims to discuss these issues.


First, Kirchhoff equations for deformable cables are proposed based on the nonlinear mechanics of thin elastic rods, and the general solution of the equations described by the Euler angles is given in the arc coordinate system. The parametric form solution of the Kirchhoff equations, which is easy to use, is then obtained in a cylindrical coordinate form based on Saint Venant’s theory. Finally, mathematical expressions that reflect the clamped cable configuration are given, and the deformable process is simulated based on an open source geometry kernel and is then tested by a 3D laser scanning technology.


The method presented in this paper can be adapted to any boundary condition for constrained cables as long as the external force and torque are known. The experimental results indicate that both the model and algorithm are efficient and accurate.

Research limitations/implications

A more comprehensive study must be executed for the physical simulation of more complicated constrained cables, such as the helical spring and asymmetric constraint. The influence of the material properties of the cable on the calculation efficiency must be considered in future analysis.


The semi-analytical algorithm of the cable simulation in cylindrical coordinates is a novel topic and is more accurate and efficient than the common numerical solution.



The work presented in this paper is supported by the National Natural Science Foundation of China (51175053) and the Fundamental Research Funds for the Central Universities of China (3132016073, 3132016353). The authors thank LetPub ( for its linguistic assistance during the preparation of this manuscript.


Du, H., Xiong, W., Wang, H. and Wang, Z. (2018), "Physical deformation configuration of a spatial clamped cable based on Kirchhoff rods", Assembly Automation, Vol. 38 No. 1, pp. 26-33.



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