As a novel internal planetary gearing with small tooth number difference, the spider reducer has been found its wide applications in many industrial fields such as energy, mining, electricity and irrigation. Despite its successful applications for decades, the mechanical mechanism of the spider reducer has been rarely investigated. The reason for less investigations of the spider reducer may lie in two aspects. One is the complexity of the reducer's structure and the other is the property of over-constraints in the transmission. The lack of in-depth understanding of system's mechanics results in the premature fatigue of planetary bearings and severe vibrations in some application occasions. In order to obtain a fully understanding of the mechanics principle of this kind of transmission, this paper presents an elasto-static model for the spider reducer by using the method of sub-structure synthesis. With consideration for the structural features of the spider reducer, the overall transmission system is divided into three sub-systems, i.e., the spider gear sub-system, the spider shaft sub-system and the output shaft system. The static equilibrium equations of each sub-system are derived based on Newtonian theory. Since the transmission system is over constrained, some compatibilities are required. Thus, the deformation compatibility conditions for the spider reducer are then derived by analyzing the relationships between the deflections of different component. The considered deflections include those of internal gearings, planetary bearings as well as torsional deformations of spider and output shafts. With the proposed compatibility conditions, the equations of each sub-system are assembled and the global elasto-static governing equations are obtained. By solving the elasto-static governing equations, the static responses on each component in a working cycle can be simulated numerically. The static loads of internal gearings, the planetary bearings and the torques on crank shafts during one cycle are depicted. The simulation results indicate that the meshing forces of internal gearings in two parallel phases change periodically. The two phases of meshing forces share the same variation rules but there exists a 180 degree of phase angle difference. This is coincident with the structural symmetry of the spider reducer whose two parallel phases of mechanism are 180 degree configured. The fluctuations of meshing force curves are very small, which implies that the meshing procedure of the internal gearings in the spider reducer is quite stable. This is agreeable with the long service span of internal gearing in this kind of transmission. On the contrary, the simulations reveal that the load conditions on planetary bearings are quite severe. To be specific, the planetary bearings on input shaft demonstrate high load amplitudes while the planetary bearings on spider shafts come through a remarkable fluctuation during a working cycle. Both the high load amplitudes and the fierce variation shorten the service life of planetary bearings. This gives an explicit explanation for the premature fatigue of planetary bearings in application occasions. The elasto-static analysis of the spider reducer indicates that the dimensions of internal gearings and planetary bearings are open to optimization during the design stage in order to extend serve span of planetary bearings and achieve better transmission performances.%针对目前少齿差星轮型减速器在机械应用中行星轴承易烧毁的现象，对其进行力学分析以寻求解决的途径。综合考虑内啮合齿轮副、行星轴承的变形以及各轴的扭转变形，构造少齿差星轮型减速器的变形协调条件，并采用子结构法建立该类传动系统的弹性静力学模型。通过求解系统的弹性静力学方程，获得系统各环节的受力，并给出了一个运动周期内两相机构的齿轮啮合力、行星轴承力和各曲轴扭矩的变化规律。弹性静力学仿真表明，少齿差星轮型减速器两相机构各环节的受力均呈周期性变化，且二者的变化规律基本相同，仅存在180°相位差。两相机构中齿轮副的啮合较为平稳，其啮合力在一个运动周期内仅存在微小波动；但行星轴承的载荷状况较为恶劣，其中星轮轴行星轴承的载荷波动较大，而输入轴行星轴承的载荷幅值较大，这恰与星轮型减速器应用中行星轴承易烧蚀的现象相吻合。该研究可为少齿差星轮型减速器的强度设计和结构优化提供准确的力学依据。
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