Purpose

In this paper, a novel and unified method for geometry configuration simulation of flexible cable under certain boundary conditions is presented. This methodology can be used to realize cable assembly verification in any computer-aided design/manufacturing system. The modeling method, solution algorithm, geometry configuration simulation and experimental results are presented to prove the feasibility of this proposed methodology. The paper aims to discuss these issues.

Design/methodology/approach

Considering the gravity, bending and torsion, modeling of cable follows the Kirchhoff theory. For this purpose, Euler quaternions are used to describe its spatial geometry configuration by a carefully chosen set of coordinates. Then the cable is discretized by the FEM, and the equilibrium condition per element is computed. In this way, the global static behavior is independent of the discretization. The static evolution of the cable is obtained by numerical integration of the resulting Kirchhoff equations. Then the manner is demonstrated, in which this system of equations can be decoupled and efficiently solved. Geometry configuration simulation examples with different boundary conditions are presented. Finally, experiment validation are given to describe the effectiveness of the models and algorithms.

Findings

The method presented in this paper can be adapted to computer-aided assembly verification of flexible cable. The experimental results indicate that both of the model and algorithm are efficient and accurate.

Research limitations/implications

The method should be extended to flexible cables with multiple branches and more complex constraints (holes, curved surfaces and clamps) and non-circular sections. Dynamic assembly process simulation based on the Kirchhoff theory must be considered in the future.

Originality/value

Unlike in previous approaches, the cable behavior was independent of the underlying discretization, and the finite element approach enables physically plausible cable assembly verification.

中文翻译：

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虚拟装配系统中柔性电缆的物理建模和几何形状配置仿真

目的

本文提出了一种新颖的统一方法，用于在一定边界条件下对柔性电缆的几何构型进行仿真。该方法可用于在任何计算机辅助设计/制造系统中实现电缆组件验证。提出了建模方法，求解算法，几何构型仿真和实验结果，证明了该方法的可行性。本文旨在讨论这些问题。

设计/方法/方法

考虑重力，弯曲和扭转，电缆的建模遵循基尔霍夫理论。为此，欧拉四元数用于通过精心选择的一组坐标来描述其空间几何构型。然后，通过有限元法将电缆离散化，并计算每个单元的平衡条件。这样，全局静态行为与离散化无关。通过对所得的基尔霍夫方程进行数值积分可以获得电缆的静态演变。然后说明了该方程组可以解耦并有效求解的方式。给出了具有不同边界条件的几何构型仿真实例。最后，通过实验验证来描述模型和算法的有效性。

发现

本文提出的方法可适用于柔性电缆的计算机辅助组装验证。实验结果表明，该模型和算法均有效且准确。

研究局限/意义

该方法应扩展到具有多个分支和更复杂的约束条件（孔，曲面和夹具）和非圆形截面的柔性电缆。将来必须考虑基于基尔霍夫理论的动态装配过程仿真。

创意/价值

与以前的方法不同，电缆的行为独立于底层的离散化，而有限元方法可实现物理上合理的电缆组装验证。