ALE-ANCF circular cross-section beam element and its application on the dynamic analysis of cable-driven mechanism

A new fully parameterized beam element with circular cross-section based on arbitrary Lagrange-Euler absolute node coordinate formulation (ANCF) is proposed to model the variable length cable in the cable-driven mechanism. The formulation of the elastic force, the additional generalized inertial force, and their corresponding Jacobian matrices of the proposed element are deduced. The enhanced continuous mechanics approach is used to alleviate the Poisson locking effect. The rigid end-effector is modeled by the absolute nodal coordinate formulation reference node, so that the rigid-flexible system can be integrated within the ANCF framework. In order to consider the pre-tension of the cable, the static equilibrium equation of the cable-driven mechanism is established. The initially deformed configuration of the cable is solved and used as the initial value for the dynamic simulation of the cable-driven mechanism. Based on the dynamic model of the cable-driven mechanism considering the cable pre-tension, the influence of different end-effector suspension positions on cable tension in the cable-driven mechanism is studied. Numerical examples show the correctness of both the new element and the proposed cable-driven mechanism model.

Automated summary

A new fully parameterized beam element has been proposed in this paper for modeling the variable length cable in the cable-driven mechanism. The formulation of elastic force, additional generalized inertial force, and their corresponding Jacobian matrices for the proposed element have been derived. The enhanced continuous mechanics approach has been applied to alleviate the Poisson locking effect. The rigid end-effector is modeled using the absolute nodal coordinate formulation reference node, and the pre-tension of the cable is considered.