Reduced Dynamic Modeling for Heavy-Duty Hydraulic Manipulators With Multi-Closed-Loop Mechanisms

Abstract

A reduced dynamic modeling approach is introduced to systematically establish explicit closed-form dynamic equations for the main motion system of a heavy-duty hydraulic manipulator with multi-closed-loop mechanisms. The harmonious combination of the reduced system dynamic method with Lagrangian formulation, the principle of virtual work and screw theory greatly reduces the tedious calculation and largely simplifies the derivation of explicit control-orientated closed-form dynamic equations for complex multi-closed-loop mechanisms. Only three coupled subsystems, two Jacobian matrices, and two Hessian matrices are involved, thereby greatly reducing the order and the complexity of the closed-form dynamic equations. In addition to calculating the two Jacobian matrices by screw theory, the two Hessian matrices are also calculated straightforwardly by screw theory, thereby avoiding the difficulty in obtaining Hessian matrices by differentiating the Jacobian matrices and simplifying the calculation of the two Hessian matrices. No parts of dynamic equations are neglected in the derivation of the dynamic model. Thus, the accurate dynamic motion equations for the main motion system are obtained concisely. The derived closed-form dynamic equations are explicit with respect to the system inputs, which facilitate dynamics analysis and controller design. The experiments on the main motion system of the heavy-duty hydraulic forging manipulator demonstrate the efficiency of the proposed approach.

Keywords

• Dynamic modeling
• heavy-duty hydraulic manipulator
• multi-closed-loop mechanism
• reduced system dynamic method
• screw theory