The Geometry of Linkages
Summary
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.