用快速傅里叶变换进行球面四杆机构连杆轨迹综合

Synthesis of Coupler Curves of Spherical Four-bar Mechanism Through Fast Fourier Transform

根据给出的球面四杆机构连杆轨迹的数学模型,借助傅里叶级数这一数学工具,对连杆轨迹的谐波成分进行理论分析,发现连杆轨迹的谐波成分与其相应转角函数谐波特征参数和机构尺寸参数的内在联系。确定球面四杆机构的基本尺寸型,在此基础上建立包含600余万组机构基本尺寸型的球面四杆机构连杆轨迹的谐波特征参数数值图谱库。利用傅里叶级数理论建立球面四杆机构处于空间任意位置时连杆曲线的数学方程,推导出计算机构的实际安装尺寸、连杆上点的位置和机构安装尺寸参数的理论计算公式。利用建立的谐波特征参数数值图谱和推导的理论公式解决了球面四杆机构的轨迹综合问题,最后给出算例证明本方法的可行性。

The geometrical model of spherical four-bar mechanism is proposed, the harmonic component of the coupler curves is analysed by using the Fourier series theory. The relationship between the harmonic component of the coupler curves and the harmonic component of the rotation-angle function and the dimensional type of spherical four-bar mechanism is discovered. Based on the basic dimensional type of spherical four-bar mechanism, a numerical atlas database of harmonic characteristic parameters of the spatial four-bar mechanism comprising more than 6 millions of basic dimensional types is build up. Mathematic equations for spherical four-bar generator on an arbitrarily arranged position are set up by using Fourier theory. The formulas which can compute the position for coupler point, real size and installing dimensions of the spherical four-bar mechanism are deduced. Based on those theoretical formulas and the numerical atlas database of the harmonic characteristic parameters, making the spherical four-bar mechanism path generation is possible. Finally, an example is given to prove the feasibility of the method.