Dynamic analysis of a novel spatial multiple-loop mobile lunar landing mechanism: An efficient approach based on explicit dynamics

The Movable lunar landing leg is a novel multi - closed parallel mechanism with sub-closed loop. Moreover, there are multiple passive and active joint variables in the mobile lunar landing legged mechanism (MLLLM), Due to the complex dynamic relationship between the passive joint variables and the active joint variables, it is difficult to derive the dynamic modeling of parallel mechanisms by the non-redundant parallel mechanism using the traditional Lagrangian formulation method. In order to solve this problem, the utilization of the virtual work principle makes the application of the Lagrangian formulation for parallel mechanisms possible and efficient. The MLLLM is divided into several serial open-loop sub-chains. Explicit dynamic equations of each sub-chain can be derived by using the Lagrangian formalism straightforwardly with respect to their own local generalized coordinates. Secondly, when transforming between different generalized coordinates, the dynamic equation is transformed into different coordinate subsystems by using the principle of virtual work, and the Jacobian matrix and Hessen matrix are introduced as constraints to ensure the explicit form of the dynamic equation, by combining the differential dynamics equations of each subsystem with the virtual work principle, the explicit dynamics model of the MLLLM under the active generalized coordinates is obtained. Finally, the position error of the end-effector caused by the active and passive joints of the parallel mechanism was evaluated. Compared with the previous methods, the inverse dynamic analysis formula presented in this paper is more concise, the calculation efficiency is higher, and the position error evaluation method is more accurate than the traditional method.