Research Goal:

1) Find a Mechanism for Every Orientable Surface with that Surface as the Configuration Space (C-Space)

Partial List of Orientable Surfaces (2D Closed, Orientable Manifolds) (Click on Image for Mechanism Webpage)

2-Sphere




Genus 1 2-Torus


Genus-2 2-Torus


Genus 3 2-Torus
\(S^2\) 2-Sphere ("Genus-0 Torus")
\(\chi\ = 2\)
Orientable

 \(T^2\) Genus-1 Torus
\(\chi=0\)
Orientable
 		\(\Sigma^2_2\) Genus-2 Torus
\(\chi = -2\)
Orientable
 \(\Sigma^2_3\) Genus-3 Torus
\(\chi = -4\)
Orientable
(The General Case is Similar)