多直线导向机构轨迹综合的代数求解  

The Algebraic Solution for Path Synthesis of Multi-Straight-Lines Mechanism

作　　者：张丽娟 李学刚 冯立艳[1] 张英 ZHANG Lijuan;LI Xuegang;FENG Liyan;ZHANG Ying(College of Mechanical Engineering,North China University of Science and Technology,Tangshan Hebei 063210,China;School of Automation,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]华北理工大学机械工程学院,河北唐山063210 [2]北京邮电大学自动化学院,北京100876

出　　处：《机械设计与研究》2021年第4期57-61,74,共6页Machine Design And Research

基　　金：国家自然科学基金资助项目(51375059、51605036)。

摘　　要：以带有可调节杆的四杆机构为研究对象,提出了一种基于傅氏级数的多直线导向机构轨迹综合的代数求解新方法。首先,依据左侧杆组设计参数与曲线谐波参数间的函数关系,建立机构左侧杆组的综合设计方程。通过求解方程组,得到机构设计参数的部分结果。在此基础上,建立含有机构剩余设计参数与连杆曲线谐波参数的综合设计方程。利用Groebner基代数法进行消元,将综合设计方程化简为含有右侧设计参数与连杆曲线谐波参数的一元三次方程,得到剩余机构设计参数计算的通用公式。通过上述两步求解得到了机构轨迹综合的全部设计参数。最后,通过仿真程序对所得机构进行运动分析,得到满足设计要求的机构。给出了数值实例,验证了该方法的有效性和可行性。The research object is a four-bar mechanism with an adjustable bar.A novel algebraic approach is presented to solve the path synthesis problems based on Fourier series for multi-straight-lines mechanism.First,according to the functional relationship between the design parameters of the left bar and the curve harmonic parameters,the comprehensive equations of design parameters of the left bar were established.By solving those equations,the partial results of mechanism path synthesis design parameters were obtained.On this basis,the synthetic design equation containing the remaining unknown design parameters on the right side of the mechanism and the harmonic parameters of the linkage curve was obtained.By using Groebner basis algebra method,the comprehensive design equation was simplified to a cubic equation containing the design parameters of the mechanism and the harmonic parameters of the linkage curve,and the general formula for calculating the integrated design parameters of the residual mechanism path was gained.All design parameters of the mechanism path synthesis were obtained by solving the above two steps.Finally,through the simulation program,the comprehensive results were verified.And the design parameter value which met the requirements can be finally obtained.An example was provided to verify the validity and feasibility of the proposed method.

关 键 词：多直线导向机构 轨迹综合 傅氏级数 代数法 

分 类 号：TH112[机械工程—机械设计及理论]