Physical modeling and geometry configuration simulation for flexible cable in a virtual assembly system

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.

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.

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.

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.

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