ABSTRACT

This research presents the mathematical modelling of kinematic and complete dynamic analysis of a novel over-constrained parallel mechanism, which consists of two universal-prismatic-revolute joint limbs and one revolute-revolute-universal joint limb. The kinematic model is constructed based on the closed-loop vector method and the velocity Jacobian matrix is deduced, velocity-mapping relationships between all moving components and moving platform are also performed. Afterwards, inertia and applied forces are analysed, the complete dynamic equations with the classical Stribeck friction model of the proposed structure is established based on the principle of virtual work. A theoretical numerical example is given to solve kinematics and dynamics solutions, and theoretical forces from developed dynamic formulation are verified by the physic model simulation in Simscape and the rigid-flexible coupling model simulation in Adams. A good agreement between the theoretical results and multi-body software simulation is found.

摘要

本研究提出了一种新型过约束并联机构的运动学和完整动力学分析的数学建模，该机构由两个万向棱柱旋转关节肢和一个旋转旋转万向关节肢组成。基于闭环矢量法建立运动学模型，推导速度雅可比矩阵，并进行各运动部件与运动平台的速度映射关系。然后，对惯性和作用力进行分析，基于虚功原理建立了具有所提出结构的经典 Stribeck 摩擦模型的完整动力学方程。给出了一个理论数值例子来求解运动学和动力学解，Simscape 中的物理模型模拟和 Adams 中的刚柔耦合模型模拟验证了来自开发的动态公式的理论力。发现理论结果与多体软件模拟之间具有良好的一致性。