带预定时标平面四杆机构刚体导引综合的代数求解  

Algebraic Solution for Rigid-body Guidance Synthesis of Planar Four-bar Linkages with Prescribes Timing

作　　者：李学刚[1,2] 魏世民 廖启征[1] 张英[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876 [2]华北理工大学研究生院,河北唐山063210

出　　处：《工程科学与技术》2018年第1期164-170,共7页Advanced Engineering Sciences

基　　金：国家自然科学基金资助项目(51375059);中央高校基本科研业务费专项资金资助项目(2016RC28)

摘　　要：为弥补精确点法、优化法和数值图谱法等已有方法的不足,进一步提高带预定时标平面连杆机构刚体导引综合的精度与效率,提出一种基于傅氏级数的平面四杆机构刚体导引综合的代数求解方法。依据平面四杆机构连杆转角函数是周期性函数的性质,根据傅氏级数理论,建立了用傅氏级数描述的平面四杆机构连杆转角函数的数学公式,并通过离散傅立叶变换得到连杆转角函数傅氏级数展开的谐波参数,将机构连杆转角函数表示成了以输入曲柄转角为自变量的函数,进而通过分析平面运动中刚体导引标线转角函数与机构连杆转角函数之间的内在联系,得到了二者谐波参数间的函数关系。在此基础上,根据复矢量理论,建立了平面四杆机构的封闭矢量方程,将由傅氏级数表示的连杆转角函数带入机构封闭矢量方程,通过消元、化简将方程进一步转化为仅由机构基本尺寸参数、连杆转角函数谐波参数和输入曲柄转角表示的复数方程。依据复指数的性质,得到了含有机构基本尺寸参数和连杆转角函数谐波参数的表达式,根据前面分析得到连杆转角函数与刚体导引标线转角函数谐波参数间的函数关系进行变量代换,确定了刚体导引标线转角函数谐波参数与机构基本尺寸参数间的函数关系。依据这一函数关系建立了新的平面四杆机构刚体导引综合设计方程,利用配析消元法进一步将综合设计方程化简为含有机构基本尺寸参数和刚体导引标线转角函数谐波参数的一元三次方程,求解得到了方程的解析解,建立了由刚体导引标线转角函数的谐波参数直接计算机构基本尺寸的通用公式。平面四杆机构的基本尺寸确定后,应用离散傅里叶变换计算得到刚体导引位置的谐波参数,根据刚体导引位置和连杆转角函数谐波参数间的关系,推导得到了机构实际尺寸和安装位置参数的计�In order to overcome the disadvantage of conventional precise point methods,optimization approaches and numerical atlas,and further improve the accuracy and efficiency of rigid-body guidance synthesis of planar four-bar linkages with prescribes timing,a novel analytical approach with Fourier series was presented to solve the rigid-body guidance synthesis problem of planar four-bar linkages.Firstly,according to the periodicity of the linkage rotation angle function,the series mathematical formula of the linkage rotation angle function was established by using Fourier series theory.The harmonic parameters of the linkage rotation angle function were obtained by DFT.As a result,the linkage rotation angle function was expressed as the summation of a Fourier series with the input angle as the variable.The harmonic parameters relationship between the linkage rotation angle function and the rigid-body guidance rotation angle function was obtained by analysing the internal connection between them in the planar motion.Then,according to the theory of complex vector,the vector loop equation of planar four-bar linkages was established.The linkage rotation angle function was formulated according to the Fourier series,and was substituted into a vector loop equation.By using eliminated element method,the vector loop equation was changed into a complex number equation that contained only the fundamental dimensions of mechanism,the harmonic parameters of the linkage rotation angle function and the input angle.With regard to the properties of the complex exponent,the mathematic expression containing the fundamental dimensions of mechanism and the harmonic parameters of the linkage rotation angle function was obtained.Accordingly,the relationship between the fundamental dimensions of mechanism and the harmonic parameters of the rigid-body guidance rotation angle function was obtained by variable substitution in terms of the previous harmonic parameters relationship.Based on this relationship,the new design equations for rigid-body g

关 键 词：连杆机构 刚体导引综合 傅氏级数 代数法 

分 类 号：TH112[机械工程—机械设计及理论]