含柔性动平台并联机器人动力学建模方法研究  

Dynamic Modeling Method of Parallel Robot with Flexible Moving Platform

作　　者：刘凉[1,2] 汪博深 冯建峰 赵新华[1,2] LIU Liang;WANG Boshen;FENG Jianfeng;ZHAO Xinhua(Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,School of Mechanical Engineering,Tianjin University of Technology,Tianjin 300384,China;National Demonstration Center for Experimental Mechanical and Electrical Engineering Education(Tianjin University of Technology),Tianjin 300384,China)

机构地区：[1]天津理工大学天津市先进机电系统设计与智能控制重点实验室,天津300384 [2]机电工程国家级实验教学示范中心(天津理工大学),天津300384

出　　处：《农业机械学报》2023年第12期417-430,共14页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家重点研发计划项目(2017YFB1303502);天津市重点研发计划科技支撑重点项目(20YFZCGX01050);天津市企业科技特派员项目(22YDTPJC00460)。

摘　　要：针对含柔性动平台的空间并联机器人刚柔耦合问题,基于Bézier三角形与绝对节点坐标法提出一种高阶柔性三角形厚板单元模型和连续性约束条件,基于该模型分析动平台变形状态及其对系统动力学特性的影响。利用自然坐标法与绝对节点坐标法建立刚柔耦合系统动力学模型,通过引入板单元第4个面积坐标的二阶梯度来描述厚度方向上的变形并解决泊松闭锁问题,结合广义-α法与牛顿迭代法求解动力学方程,并对系统静力学模型和动力学模型进行仿真分析。结果表明,动平台在运动过程中产生的周期性凹陷变形对机器人空间位姿的影响与机构布局方式、质量分布和负载作用方式完全一致,系统刚性构件与柔性动平台的运动耦合方式符合多体动力学模型的非线性规律;运动轨迹误差低于1.2×10^(-12)mm,动力学方程和约束方程迭代误差均小于设定阈值10^(-6)和10^(-14),求解精度能满足工程应用要求;基于不同参数开展仿真对比分析,验证了所述方法的有效性和通用性。In order to solve the coupling problem of a spatial rigid-flexible parallel robot with flexible moving platform,a high-order flexible triangular thick plate element and its continuity constraints were proposed based on the Bézier triangle and absolute nodal coordinate formulation(ANCF).The deformation of the platform was divided by the element and its effects on dynamics were analyzed.The robotic dynamics was established by natural coordinate formulation(NCF)and ANCF.The second-order gradients of the fourth area coordinate were introduced to describe the element deformation in thickness.Besides,the Poisson locking problem was solved accordingly.The Lagrange dynamics equations were solved via the generalized-αmethod and the Newton's method.The statics and dynamics models of the system were simulated.The results showed that the periodic concave deformation of the moving platform had an impact on the spatial posture of the robot which was exactly consistent with the mechanism layout,mass and load distribution.The coupling mode between the rigid components and flexible moving plaform conformed to the nonlinear characteristics of multibody dynamics.The trajectory error was less than 1.2×10-12 mm.The errors of dynamics and constraint equations were less than the preset thresholds of 10-and 10-14,which met the requirements of engineering applications.Meanwhile,the validity and versatility of the method were verified by comparative analysis based on different system parameters.

关 键 词：机器人 三角形厚板单元 刚柔耦合 多体动力学 

分 类 号：TH113[机械工程—机械设计及理论]