基于Kane方程的Delta并联机器人刚柔耦合动力学研究  

Research on Rigid-flexible Coupling Dynamics of Delta Parallel Robot Based on Kane Equation

作　　者：商德勇[1,2,3] 黄欣怡 黄云山 张天佑 SHANG Deyong;HUANG Xinyi;HUANG Yunshan;ZHANG Tianyou(School of Mechanical and Electronic Engineering,China University of Mining and Technology(Beijing),Beijing 100083;Institute of Intelligent Mining and Robotics,China University of Mining and Technology(Beijing),Beijing 100083;Key Laboratory of Intelligent Mining and Robotics,Ministry of Emergency Management,Beijing 100083)

机构地区：[1]中国矿业大学(北京)机械与电气工程学院,北京100083 [2]中国矿业大学(北京)智慧矿山与机器人研究院,北京100083 [3]煤矿智能化与机器人创新应用应急管理部重点实验室,北京100083

出　　处：《机械工程学报》2024年第7期124-133,共10页Journal of Mechanical Engineering

基　　金：国家自然科学基金(52174154);国家自然基金创新研究群体项目(52121003)资助项目。

摘　　要：针对Delta并联机器人在高负载和高速运行时,由刚度较小的从动臂发生弹性变形而造成的机器人定位精度降低和系统运行失稳等问题,采用假设模态法对从动臂杆件进行离散化处理,并基于Kane方程和增广拉格朗日乘子法建立了Delta并联机器人系统的刚柔耦合动力学方程,从而量化了从动臂连杆变形对机器人定位精度造成的影响。通过对比在相同跟踪轨迹下ADAMS模型仿真与MATLAB数值分析结果,两者的动平台质心运动轨迹基本重合且主动关节旋转角度偏差小于0.01rad,验证了刚柔耦合动力学方程的正确性。最后,通过数值分析和Adams-Matlab联合仿真分析,得到机器人在不同负载条件下,末端动平台在X和Z方向的最大位移偏移量及主动关节驱动力矩最大偏差值,仿真结果反映了从动臂柔性对机器人动力学性能的影响规律,为机器人的精确控制提供了理论支撑。In order to solve the problems of the robot positioning accuracy reduction and system instability caused by the elastic deformation of the follower arm with low stiffness when the Delta parallel robot is running at high load and high speed,the hypothesized mode method is adopted to discretize the follower arm member.Based on Kane equation and augmented Lagrange multiplier method,the rigid-flexible coupling dynamic equation of Delta parallel robot system is established,and the influence of follower arm deformation on robot positioning accuracy is quantified.By comparing the results of ADAMS model simulation and MATLAB numerical analysis under the same tracking trajectory,the trajectory of the moving platform's center of mass basically coincides and the rotation Angle deviation of the active joint is less than 0.01 rad,which verifies the correctness of the rigid-flexible coupling dynamic equation and provides theoretical support for the precise control of the robot.Finally,through numerical analysis and Adams-Matlab co-simulation analysis,the maximum displacement offset of the end moving platform in the X and Z directions and the maximum deviation of the driving torque of the active joint are obtained under different load conditions.The simulation results reflect the law of the influence of the flexibility of the follower arm on the dynamic performance of the robot.

关 键 词：Delta机器人 高速重载 刚柔耦合 KANE方程 动力学建模 

分 类 号：TH113[机械工程—机械设计及理论]