It is well known that there are trefoil knots without tritangent planes, and with 3d printers one can print these beautiful objects and make them roll on planes. (An example:https://www.youtube.com/watch?v=IpSsOfe5dMk (8:50) )
At any instant of time there are exactly 2 points of contact between the knot and the plane. I'm curious about (assuming rolling without slipping) how one can compute the trajectory of contact points, the trajectory of the center of mass, etc.
Does anyone know how to compute such things or give a reference about this sort of problem?
(I have printed a model based on the torus knots described by Morton (1991) and the trajectories of the contact points look like "deformed cycloids")