The Geometry of Linkages

Publication date

DOI

Document Type

Bachelor Thesis

Collections

Open Access logo

License

CC-BY-NC-ND

Abstract

Kempe's Universality Theorem states that using linkages made only of rigid bars and freely rotating joints, any algebraic curve can be constructed. This thesis concerns Abbott and Barton's reparation of Kempe's flawed proof, and produces a computer program that visualizes these universal linkages. In contrast, visualizing an arbitrary linkage is proven NP-complete. Finally, we will study the geometry of linkages' configuration spaces.

Keywords

linkage; geometry; algebraic curve; algebraic set; kempe's universality theorem; constructibilty; p versus np; configuration space

Citation