含关节间隙的3-CPaRR并联机构的运动学和动力学分析

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (18) : 9-17.

论文

朱景原1,4，王见1,4，丁泽华1,4，周辉1,4，曹毅1,2,3,4

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Kinematics and dynamics analysis of a 3-CP_aRR parallel mechanism with joint clearance

ZHU Jingyuan1,2,WANG Jian1,2,DING Zehua1,2, ZHOU Hui1,2,CAO Yi1,2,3,4

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摘要

为研究关节间隙对并联机构动态特性的影响，本文以3-CPaRR并联机构为研究对象。基于该并联机构的运动学约束，首先研究了该并联机构的运动学规律，表明该并联机构驱动圆柱副可等效分解为驱动移动副和被动转动副；其次，利用正态分布概率统计模型建立了含间隙转动关节径向和轴向的运动学模型，进而建立了含关节间隙的支链运动学模型；然后，根据关节元素间接触运动学模型，基于Flores接触力模型和修正的Coulomb摩擦模型分别建立了转动关节的法向接触力和切向接触力模型，并基于非完整系统的Lagrange方程法建立了含关节间隙并联机构的动力学模型；最后，通过实例计算详细分析了转动关节间隙对并联机构运动学特性和动态响应的影响；此外，通过与标准正态分布模型参数μ对比，分析了定义关节元素初始接触时的间隙量为μ值时的物理意义；上述研究可为其他含关节间隙多体系统的研究提供新的研究方法和理论基础。

Abstract

In order to study the effect of joint clearance on the dynamic characteristics of parallel mechanisms, a 3-CP_aRR parallel mechanism was taken as an example.First, the kinematics of the parallel mechanism was studied synthetically by analyzing the constraints.It shows that the cylindrical pair of the parallel mechanism can be equivalent to a driving-sliding pair and a passive-revolute pair.Next, a normal distribution statistic model was used to establish the kinematic model of the revolute joint with clearance in radial direction and axial direction, and a branch kinematics model was also established.The normal contact force between the joint elements was evaluated based on the Flores contact model, and the tangential contact force was evaluated according to the modified Coulomb friction model.Then, the dynamic model of the parallel mechanism with joint clearance was established based on the non-holonomic systems Lagrange equation method.Finally, the effect of revolute joint clearance on the parallel mechanism’s kinematics and dynamic response was analyzed in detail through a numerical example.In addition, compared with the parameter of standard normal distribution model, the physical meaning of defining the initial contact clearance value as μ was analyzed.The research provides a new research approach and builds a theoretic foundation for the analysis of multi-body systems with clearance.

导出引用

朱景原1,4，王见1,4，丁泽华1,4，周辉1,4，曹毅1,2,3,4. 含关节间隙的3-CPaRR并联机构的运动学和动力学分析[J]. 振动与冲击, 2018, 37(18): 9-17

ZHU Jingyuan1,2,WANG Jian1,2,DING Zehua1,2, ZHOU Hui1,2,CAO Yi1,2,3,4. Kinematics and dynamics analysis of a 3-CP_aRR parallel mechanism with joint clearance[J]. Journal of Vibration and Shock, 2018, 37(18): 9-17

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