基于傅氏级数的球面四杆机构函数综合的代数求解  

Algebraic solution for function synthesis of spherical four-bar mechanism based on Fourier Series

作　　者：冯立艳 石安宇 李学刚 张英[2] FENG Li-yan;SHI An-yu;LI Xue-gang;ZHANG Ying(College of Mechanical Engineering,North China University of Science and Technology,Tangshan 063210;School of Automation,Beijing University of Posts and Telecommunications,Beijing 100876)

机构地区：[1]华北理工大学机械工程学院,河北唐山0063210 [2]北京邮电大学自动化学院,北京100876

出　　处：《机械设计》2023年第4期43-47,共5页Journal of Machine Design

基　　金：国家自然科学基金资助项目(51375059,51605036)。

摘　　要：文中提出了一种可实现球面四杆机构多点位函数综合的代数求解新方法。首先,建立了用傅氏级数描述球面四杆机构输出转角函数的数学公式,然后将由傅氏级数表示的输出转角函数代入球面四杆机构输入输出转角函数方程,经变量代换,分析得到了输出转角函数傅里叶系数与机构设计参数间的函数关系,并据此关系建立了球面四杆机构的函数综合设计方程。求解方程,得到球面四杆机构的设计参数。通过综合设计实例验证了该方法的有效性和可行性。In this article,a novel algebraic approach based on Fourier series is proposed to realize multi-point function synthesis of the spherical four-bar mechanism.Firstly,the output rotation-angle function is formulated according to the Fourier Series components of the input angle.Then,the output rotation-angle function represented by the Fourier Series is substituted into the function relationship between the input angle and the output angle of the spherical four-bar mechanism,and the relationship between the design parameters of the linkages and the Fourier coefficients of the output function is obtained by means of the variable substitution analysis.On the basis of this,the new design equations which are simplified with the universal formula of the trigonometric function are worked out.By solving the equations,the design parameters of the spherical four-bar mechanism are obtained.Finally,it is verified from some design examples that this method is effective and feasible.

关 键 词：球面四杆机构 函数综合 傅氏级数 代数法 

分 类 号：TH112[机械工程—机械设计及理论]