考虑球面副间隙的并联机构动力学模型

Dynamic modeling for a parallel mechanism considering spherical joint clearance

基于连续接触模型研究空间球面副间隙对新型减振平台(4-SPS/CU并联机构)动力学性能影响。将4-SPS/CU并联机构中一条驱动支链与下平台相连球面副间隙视为一刚性无质量杆。建立球面副间隙数学模型及该并联机构含关节间隙的位置方程;利用达朗贝尔原理建立理想4-SPS/CU并联机构动态静力学平衡方程并导出该机构所有关节反力;将理想机构运动副反力位置角近似等于该机构球面副中无质量间隙杆方位角;通过对含关节间隙的驱动支链受力重新分析建立该机构含关节间隙的动力学模型。数值计算、对比分析该并联机构考虑关节间隙与理想关节条件下球面副关节反力随时间变化,分析关节间隙对该并联机构运动学特性及驱动力影响,为该并联机构间隙补偿与控制策略提供理论依据。

Joints with clearance are essential components of multi-body systems,and impact forces exist among joint elements,they induce vibrations and noise,reduce component life,and lead to a loss of precision.Joint clearance of a mechanical system is necessary to allow the relative motion of connected bodies.Here,a dynamic modeling for a novel vibration reduction platform （4-SPS/CU parallel mechanism）with spherical joint clearance was presented based on the continuous contact model.One of the driving chains was connected to the lower part of the platform with a spherical joint, and the clearance in this spherical joint was taken as a no-mass rigid link in the 4-SPS/CU parallel mechanism.Firstly, the mathematical model of the spherical joint clearance and the position equations for the parallel mechanism with clearance were built.Secondly,the kinetostatic equilibrium equations of an ideal parallel mechanism were successfully established via d＆#39;Alembert principle.All of the joint reactions were induced by solving the kinetostatic equilibrium equations.On the basis of the above results,the position angles of the ideal mechanism＆#39;s joint reactions corresponding to kinematic pairs were assumed to be approximately equal to the orientation angles of the no-mass rigid link in the spherical joint.Lastly,the dynamic equations of the mechanism with clearance were built by doing again force analysis of the driving chain with joint clearance.The driving forces,kinematic characteristics and joint reactions of the parallel mechanism were analyzed with numerical calculation considering spherical joint dearance and ideal joint,respectively. The study results provided a theoretical basis for design of parallel mechanisms.