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Interrelationship between screw systems and corresponding reciprocal systems and applications

机译:螺杆系统与相应的往复系统和应用之间的相互关系

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摘要

This paper discusses the relationship between a screw system and its corresponding reciprocal system based upon set theory, proposes a theorem, makes a proposition with corollaries to specify the relationship between the two screw systems and characterises all cases in screw systems. The theory is then applied to the one-, two-,and three-systems and their corresponding reciprocal five-, four-and three-systems, and used to predict reciprocal screws and the subsequent relationship with the existing screw system. A further application is given by selecting screws to design a system such that a certain intersection is desirable between the system and its reciprocal system. As a result, a method of generating a one-system of reciprocal screw from a five-system and of generating a reciprocal system from a co-reciprocal system is given.
机译:本文基于集合论讨论了一个螺丝系统及其对应的相互系统之间的关系,提出了一个定理,并用推论提出了两个螺丝系统之间关系的命题,并描述了螺丝系统中的所有情况。然后,将该理论应用于一,二和三系统及其对应的倒数五,四和三系统,并用于预测倒数螺钉以及与现有螺钉系统的后续关系。通过选择螺钉来设计系统来给出进一步的应用,使得系统与其往复系统之间需要一定的交点。结果,给出了一种从五系统生成单系统往复螺杆并且从共往复系统生成往复系统的方法。

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