Dynamic Modeling, Uncertainty Analysis, and Experimental Study of a New Cable-Driven Parallel Robot With Interval Variables

Abstract

Based on the Chebyshev polynomial method (CPM) and interval theory, this article establishes the relationship between uncertain parameters and the dynamic response of a new cable-driven parallel robot (CDPR). Meanwhile, the time-varying characteristic of uncertain parameters in the dynamic uncertainty analysis of the model is considered in this article, effectively enhancing the accuracy of the dynamic response. The mechanical design and kinematic modeling are conducted, and the dynamic model is established based on the Lagrangian method. Thus, uncertain parameters including the length of the lifting arm L, the angle of the lifting arm rotation on the support plate α, and the length of the payload l are defined as interval variables, and the dynamic equilibrium equation with interval variables is derived. Numerical examples show that the CPM has a higher accuracy than the first-order interval perturbation method (FOIPM), and a higher efficiency than the Monte Carlo method (MCM) when it comes to solve the dynamic response of the CDPR with uncertain parameters. Experimental results demonstrate the effectiveness of dynamic modeling and the CPM in achieving efficient dynamic response and show that the largest relative error between the theoretical and experimental values for the dynamic response of the CDPR with uncertain parameter L is 1.466%; the largest relative error with uncertain parameter α is 0.783%; the largest relative error with uncertain parameter l is 0.857%; and the largest relative error with multiple uncertain parameters is 1.513%.