Each realization of a link or knot has a thickness assigned to it.
The thickness τ of a link allows us to introduce a scale with respect to which we can then define the ropelength of a link.
There exist several possible definitions of thickness that coincide for smooth enough curves.
From this definition we can deduce that the local thickness is at most equal to the local radius of curvature.
The thickness of a link is defined as This definition ensures that a normal tube to the link with radius equal to τ(L) will not self intersect, and so we arrive at a "real world" knot made out of a thick string.