含有冗余支链的3-RPS/3n-SPS并联机构逆动力学建模

提出一类含有冗余支链的3-RPS/3n-SPS并联机构, 为解决该类机构的逆动力学问题, 首先对机构进行运动学分析, 建立支链与动平台末端的速度、加速度映射关系, 并对运动学模型进行仿真验证; 之后对3-RPS/3n-SPS机构进行受力分析, 列出的平衡方程数目少于未知量个数, 基于机构分支作用力与动平台末端位姿误差间的协调关系构建动力学补充方程, 求解出该类机构中所有运动副的约束反力和机构分支作用力; 基于达朗贝尔原理对机构进行逆动力学建模, 建立了机构末端力和各杆件惯性力与机构分支作用力间的关系表达式, 求解了3-RPS/3-SPS机构分支作用力、运动副约束反力及动平台位姿误差, 通过分析机构分支作用力、运动副约束反力、动平台位姿误差随时间的变化规律, 验证本文建立的3-RPS/3n-SPS并联机构动力学模型的正确性。所得到的动力学结果为该类机构的进一步研究和工程应用奠定了理论基础, 此外该逆动力学建模方法也可用于其他含有冗余支链的并联机构中。

Abstract

In this study, a wave 3-RPS/3n-SPS parallel mechanism with redundant limbs was proposed. To solve the inverse dynamics of the mechanism, the kinematics of the mechanism were first analyzed. The velocity and acceleration mapping relationships between the branch chains and center of the moving platform were established. Then, the kinematics model was verified by simulation, and a force analysis of the 3-RPS/3n-SPS mechanism was performed. Dynamics supplementary equations were constructed based on the coordinated relationships between acting forces of the branch chains and the position and attitude errors of the moving platform. These forces were derived from the fact that the number of force balance equations are less than the number of unknown variables. The constrained forces of all the joints and the acting forces of the branch chains were solved. Based on the DAlembert principle, an inverse dynamics model of the mechanism was established. In addition, the relationship between the forces of end effectors, the inertial force of each link, and the acting forces of the branch chains were expressed mathematically. The constrained force of the kinematic pairs and the position and attitude errors of the moving platform were solved. The dynamic model of the 3-RPS/3n-SPS parallel mechanism was thus verified by analyzing the change rules of the forces of the branch chains, the constrained force, and the position and attitude errors of the moving platform at different times. This research establishes a theoretical foundation for further research and engineering application of this type of mechanism. In addition, the inverse dynamic modeling method established in this study can be applied to other types of parallel mechanisms with redundant limbs.

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