A simple linear complementarity approach for sliding cable modeling considering friction. (1st September 2019) - Kan, Ziyun; Peng, Haijun; Chen, Biaoshong
Highlight: A LCP-based approach is proposed for sliding cable modeling with friction. This approach is mathematically elegant, simple, and easy to implement. Uniqueness of sliding length under a given configuration has been proved. Examples are presented to demonstrate the robustness and versatility. Influence of friction on deployment of a clustered tensegrity is investigated. Abstract: Sliding cable system with friction is encountered in many engineering applications. This system is typically characterized by existence of complex and diverse motion states of sliding nodes (pulleys), which leads to significant difficulties for analysis. This paper aims at developing a simple method for analyzing the global response of a sliding cables system. A linear complementarity approach is proposed for both static and dynamic analysis of sliding cable with friction. Within this approach, the challenging and significant issue of determination of motion states of sliding nodes can be handled in a standard linear complementarity formulation. The proposed approach is mathematically elegant, simple, and easy to implement. It allows us to capture the complex and diverse motion states of pulleys in a rather direct way. It also offers a new way to study theory problems such as prove or disprove the existence and uniqueness of the solution by using complementarity theories. Multiple examples are presented to demonstrate the robustness and versatility of the proposed approach, as well as to reveal novel phenomena involved in sliding cable systems considering sliding friction.