On the Geometry of Spatial Polygons and Screw Polygons

Abstract

In this paper we study spatial polygons which are closed figures composed of ordered sets of lines and their common normals. It is shown how to solve for up to six of the parameters which define a polygon’s geometry, after all the other parameters are specified. It is also shown that when screws are used instead of lines, the resulting figures, called screw polygons, can be analyzed in order to determine up to twelve parameters, provided all the other parameters which define the screws and the screw polygon are known. Finally, it is pointed out that these results have many potential uses in kinematics.