High-Accuracy and High-Computational-Efficiency Dynamic Modeling of a Flexible Hydraulic Manipulator Based on Multibasis Function Combination

The increased flexibility and introduced coupling between links and cylinders pose challenges for modeling flexible hydraulic manipulators (FHMs). The traditional assumed mode method (AMM) encounters the problems of low computational accuracy resulting from a single basis function, as well as the low computational efficiency of multidegree-of-freedom calculations. In this article, a novel dynamic modeling method utilizing Lagrange’s dynamic equation with a multibasis function combination is proposed. To increase the modeling accuracy, flexible deflections are determined through a linear combination of several basis functions. All these basis functions are derived using the Rayleigh–Ritz method by considering geometric deformation boundary conditions and curvature changes in the links. To improve computational efficiency, the flexible link system is divided into two virtual rigid and flexible parts, which are analyzed separately to minimize the impact of coupling terms. Deflections in the dynamic equation affect only the flexible eigenmatrix and its derivative term such that the dynamic equations are simplified. The experiments on a 13-m FHM verify that, compared with the traditional AMM, the proposed modeling method can effectively increase accuracy while improving computational efficiency.