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在金属切削领域里，运动几何问题还缺少完整的研究。目前关于这方面问题的讨论还仅限于用直观说理、图解、及图解解析方法。由于这些方法的特点所限，往往妨碍了我们去揭发运动几何中更深刻的规律。 这里，我们采用了纯解析法来讨论磨削中的运动几何，因此有助于我们从问题的要求值到有关定理，获得一个统一的概念。其中对于用旋转单叶双曲面形砂轮磨削非可展直纹面，如阿基米德蜗杆。 蜗杆，以及旋转单叶双曲面等，作了较多的分析。 由于作者水平所限，文章中免不了要出一些错误，希望同志们多多指正和讨论。 本文承郑平、刘培德、杨长癸，谭家岱等同志给予很多指导与帮助，深表感谢。
In the field of metal cutting, there is still a lack of complete research on the geometric problems of movement. The current discussion on this issue is limited to the use of intuitive reasoning, graphic, and graphical analysis methods. Due to the nature of these methods, they often prevent us from revealing the deeper laws of the geometry of the movement. Here, we use a pure analytic method to discuss the geometric motion of grinding, which helps us to obtain a unified concept from the value of the problem to the relevant theorem. Among them, it is necessary to grind non-developable ruled surfaces such as Archimedean worm with rotary single-leaf hyperboloid grinding wheel. Worm, as well as rotating single-leaf hyperboloid, made more analysis. Due to the author’s limited level, the article will inevitably come up with some mistakes, I hope a lot of comrades correct and discuss. In this paper, Zheng Ping, Liu Peide, Yang Changkui, Tan Jidai and other comrades give a lot of guidance and help, I am deeply grateful.