Analytic theories around the simplest screw

TL;DR

This paper reviews various analytic theories related to screw functions, using the simplest screw line as a case study, without introducing new findings.

Contribution

It synthesizes existing analytic theories about screw functions and explores their interrelations through the example of the simplest screw line.

Findings

Analysis of screw functions and their relations

Clarification of theoretical connections without new results

Illustration using the simplest screw line

Abstract

We present several analytic theories and their relations to each other related to screw functions, taking the screw function of the simplest screw line as an example. Note that this article does not contain any new results.