基于Lagrange方程和二阶影响系数矩阵的Delta并联机构约束力分析及仿真研究  

Constraint force analysis and simulation of the Delta parallel mechanism basedon Lagrange equation and second-order influence coefficient matrix

作　　者：张勇[1] 郭志飞 甄希金[2] 张敬芳[1] ZHANG Yong;GUO Zhi-fei;ZHEN Xi-jin;ZHANG Jing-fang(Department of Mechanical Engineering,Hebei Institute of Mechatronic Technology,Xingtai 054001,China;Shipbuilding Technology Research Institute,Shanghai 200032,China)

机构地区：[1]河北机电职业技术学院机械工程系,河北邢台054001 [2]上海船舶工艺研究所,上海200032

出　　处：《机电工程》2021年第7期857-864,共8页Journal of Mechanical & Electrical Engineering

基　　金：河北省高等学校科学技术研究重点资助项目(ZD2020322);河北机电职业技术学院轧辊清洗包装智能装备创新中心资助项目(202001)。

摘　　要：针对并联机构约束力分析过程复杂、计算量较大的问题,以三平移Delta并联机构为例,对其约束力进行了仿真分析和实验研究。首先,建立了Delta并联机构的Lagrange动力学模型,采用二阶影响系数矩阵建立了驱动滑块的加速度数学模型,并进行了求解验证;然后,对并联机构中的驱动滑块进行了受力分析,得到了球铰处的约束力方程,并使用MATLAB求解了该方程,在ADAMS中验证了该方程的正确性;最后,使用Delta并联机构和陀螺仪进行了试验,得到了驱动滑块的加速度和竖直方向约束力数据。研究结果表明:使用Lagrange方程和二阶影响系数矩阵对Delta机构进行约束力分析,不仅能得到正确的约束力分析结果,还可以简化分析过程,得到较为规范、简洁的球铰约束力方程,并大幅度降低理论推导过程的复杂度;该结果可以推广至其他并联机构的约束力分析,为并联机构约束力分析提供新的方法。Aiming at the problem of complex process and large amount of calculation for the constraint force of parallel mechanism,the Delta parallel mechanism was taken as an example to make theoretical derivation,simulation analysis and experimental verification of its constraining force formula.First,Lagrange dynamics model of Delta parallel mechanism was established.The second-order influence coefficient matrix was used to establish the acceleration mathematical model of the driving slider.Then the force analysis of the driving slider was carried out to obtain the constraint force equation.The constraint force equation was solved with MATLAB and its correctness was verified with ADAMS.The binding time curve of the ball hinge of the driving slider was obtained.Finally,the acceleration and vertical constraint data of the driving slider were obtained with Delta parallel mechanism and gyroscope.The experiment results show that the analysis of constraint force and simulation of the Delta parallel mechanism based on Lagrange equation and second-order influence coefficient matrix can not only get the correct constraint analysis result,simplify the analysis process,obtain a relatively standard and concise constraint equation of ball hinge,but also greatly reduce the complexity of derivation.Moreover,it can be extended to other parallel mechanism and provide a new method for binding analysis of parallel mechanism.

关 键 词：并联机构 动力学分析 约束力 LAGRANGE方程 影响系数矩阵 

分 类 号：TH112[机械工程—机械设计及理论]