摘要
提出了一种基于傅氏级数的二自由度六杆机构轨迹综合的代数求解新方法。通过将二自由度六杆机构拆分为左侧三杆组和右侧二杆组两部分,对轨迹综合设计变量进行解耦。分析得到机构设计参数与连杆曲线谐波参数间的关系,并依据这一关系建立左侧三杆组的轨迹综合设计方程,通过方程求解得到机构左侧三杆组的设计参数。同理,建立右侧二杆组的轨迹综合设计方程,利用Groebner基代数法消元,将综合设计方程化简为含有机构设计参数和曲线谐波参数的一元四次方程,求解得到了右侧二杆组设计参数的计算通用公式。通过仿真程序对综合所得机构进行运动分析,检验其是否存在曲柄,有无分支、顺序问题,并依据综合误差,最终得到了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。
A novel algebraic method was presented to solve the path synthesis problems for 2-DOF hinge six-bar mechanism.By spliting the 2-DOF hinge six-bar mechanism into the left 3-bar group and the right 2-bar group,the path synthesis design parameters were decoupled.Based on analyzing of the relationship between the design parameters of the mechanism and the harmonic parameters of the linkage curve,the equations containing the design parameters of the left 3-bar group were established.By solving the equations,the design parameters of the 3-bar group on the left side of the mechanism were obtained.In the same way,the synthetic design equation containing the design parameters of the 2-bar group on the right side were obtained.Through using Groebner basis method,the comprehensive design equations were simplified to a quartic 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 right 2-bar group was acquired.Through the simulation program,the comprehensive results were verified to check whether there were cranks,branching problems and order problems.And the design parameter value which met the requirements can be finally obtained according to comprehensive error.An example was provided to verify the validity and feasibility of the proposed method.
作者
李学刚
张丽娟
冯立艳
张英
LI Xue-gang;ZHANG Li-juan;FENG Li-yan;ZHANG Ying(College of Mechanical Engineering,North China University of Science and Technology,Hebei Tangshan 063210,China;School of Automation,Beijing University of Posts and Telecommunications,Beijing 100876,China)
出处
《机械设计与制造》
北大核心
2023年第8期27-33,共7页
Machinery Design & Manufacture
基金
国家自然科学基金资助项目(51375059、51605036)。
关键词
二自由度六杆机构
轨迹综合
傅氏级数
代数法
2-DOF Hinge Six-Bar Mechanism
Path Synthesis
Fourier Series
Algebraic Approach
