Abstarct: Abstract With the advancement of technology and industry, the use of robotic mechanisms and tools is increasingly expanding. Accordingly, the design of advanced robotic equipment has brought significant attention to the field of motion mechanism design. The theories used for designing planar and even spatial mechanisms have seen substantial progress. There are even studies in which four-bar mechanisms have been synthesized to pass through a high number of precision points—up to 90 precision points in some cases. However, in the case of spherical mechanisms, not only is there a lack of extensive research, but the synthesis problem has typically been addressed for only a small number of precision points. Considering the practical applications and importance of spherical mechanisms in various fields, this study aims to optimize spherical mechanisms in the context of function generation. Initially, the synthesis problem is investigated for five and six precision points using a numerical solution approach baxsed on the HCM. Furthermore, efforts are made to increase the number of precision points to ensure the absence of an exact solution and bring the problem closer to real-world applications. Therefore, the problem is also solved for 10 and 20 precision points, utilizing the PSO (Particle Swarm Optimization) algorithm for the synthesis process. The numerical and optimization methods are implemented and executed in MATLAB. Subsequently, the resulting mechanisms obtained from each method are modeled in CATIA software, and their accuracy in reaching the designated precision points is evaluated.