Common cycloid-gear boring equipment has the problems of low efficiency and low precision. In this paper, a special boring machine for the cycloid-gear coordinate hole is proposed and its overall structure is designed. To improve the machining precision of the special boring machine, it is necessary to understand the effects of geometric error elements on the precision of the special boring machine and control the major elements that have the largest effect. The geometric error elements of the special boring machine are analyzed. Based on the multi-body system theory and homogeneous coordinate transformation, the geometric error model of the special boring machine is established. The correctness of the error model is verified by comparing the calculation results of the model with those of the triangulation method. The sensitivity equation of each geometric error element is established by the sensitivity analysis method, and the sensitivity coefficient of each geometric error element is determined through normalization processing. The geometric error element that has the greatest impact on the machining accuracy of the special machine is obtained. Based on the sensitivity analysis results, the key components of the special boring machine are selected.