The dimensional synthesis of spherical four-bar linkages mechanism, which contains function generation, path synthesis and rigid-body guidance synthesis, is an important part of linkage design. For integral period dimensional synthesis of spherical four-bar linkages mechanism by using Fourier series theory, firstly the mathematical model of spherical four-bar linkages mechanism is established and the Fourier transform’s function expression is given. The relationship between output function and the basic dimensional type is found out. Then the spherical four-bar linkages mechanism’s harmonic characteristic parameters database is created.Secondly, by using the fuzzy identification theory, the best suitable basic dimensional type of spherical four-bar linkages mechanism for prescribed output function is obtained. Thus, it achieves the purpose of spherical four-bar linkages mechanism function generation. For non-integral period dimensional synthesis of linkage mechanism, the Fourier series theory can not be analyzed and integrated. In many applications, the design requirement is non-integer periodic function. Therefore, the purpose of this study was to propose a new numerical atlas method to apply to the non-integer periodic function generation problem of spherical four-bar mechanism. The wavelet function has a good analysis ability in both time and frequency, which is its unique advantage for non-integral period dimensional synthesis of linkage mechanism. By taking advantage of the multi-resolution characteristic of the wavelet function, this paper presents the Haar wavelet feature parameter method for the non-periodic function generation of spherical four-bar linkages mechanism. Based on the analysis by wavelet theory of non-integral period output function of the spherical four-bar mechanism, the connection between the wavelet feature parameters of output function by translation or scaling and the wavelet feature parameters of primitive function could be discovered. Then a self-adaptive database of basic dimensional type of spherical four-bar linkages mechanism could be created, which contained 148 995 groups of basic dimensional types. Based on the created database and fuzzy recognition theory, a method of matching recognition was proposed by using the relationship between the wavelet feature parameters of basic dimensional type and the wavelet feature parameters of the given non-periodic function. And the given design interval of the spherical four-bar mechanism non-periodic function generation was realized. Based on the recognized result and the immanent connection between output function and wavelet feature parameters, the optimization object function could be created by using genetic algorithm. Then the result was optimized. This paper took the pendulum disc type cutting mechanism of combine as an example to illustrate the effectiveness and practicality of this method. To optimize the spherical four-bar mechanism function output result, the genetic algorithm was adopted, the population size was set as 200, the crossover probability was 0.08, the mutation parameter was 0.06 and the crossover operator was used. The percent error of the firstset mechanism was 1.92%, and that of the second set mechanism was 2.31%, which indicated that the pendulum disc type cutting mechanism of combine met the requirement of actual testing, which was 3%. The study for the function generation and the pendulum disc type cutting mechanism of combine provides a very important theoretical basic and reference for the design, analysis and further study on path synthesis and rigid-body guidance synthesis.%针对傅立叶级数理论不能进行非整周期函数综合问题，该文提出了应用Haar小波进行球面四杆机构非整周期函数综合的方法。首先，对球面四杆机构非整周期函数输出的小波成分进行了分析，发现了给定机构机架旋转后所得到的函数输出小波特征参数与原函数输出小波特征参数之间的内在联系，从而建立了包含148995组球面四杆机构基本尺寸型的自适应函数输出特征数据库。其次，给出了在建立的特征数据库中检索出满足设计要求的球面四杆机构基本尺寸型的匹配识别算法。再次，建立了优化目标函数，通过遗传算法对匹配识别结果进行了优化，进一步提高了该方法的设计精度。最后，对联合收割机中摆盘式切割机构进行了设计。设计结果表明第1组机构输出的最大正误差为0.04369°，最大负误差为−0.04027°，其最大误差百分比为0.0335%，第2组机构输出最大误差为0.0406°，最大负误差为−0.0589°，其最大误差百分比为0.0402%，从而证明了该方法对球面四杆机构的非整周期设计要求函数综合问题的有效性。该研究可为连杆机构非整周期后续的轨迹综合、刚体导引综合提供参考。
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