Kinematic analysis of cable-driven parallel mechanisms based on minimum potential energy principle

Abstract

The forward kinematic analysis of the cable-driven parallel mechanism has been a challenging and interesting problem since 10 years ago. This work converts the forward kinematic analysis problem of the cable-driven parallel mechanism to an optimization problem, whose objective is to minimize the potential energy of mobile platform. In order to simplify the optimization problem further so that it can be solved with any simple optimization algorithm in short time, some constraints are introduced to design variables. We utilize the sequential quadratic programming algorithm to solve the simplified optimization problem in this article. The efficiency and effectiveness of the proposed approach are validated with some numerical examples. Furthermore, due to the fact that a required pose may be not stable, the availability of its inverse kinematic solution should be supervised. The aforementioned approach provides a valid tool for solving this type of problems by contrasting the distinction between the required pose and the actual pose calculated by it. The feasibility of applying our proposed method to execute the inverse kinematic analysis of cable-driven parallel mechanism is proved with several examples in this article.