Roulette (curve) in this case, the point lies on the circle then the roulette is a cycloid. A related concept is a glissette, the curve described by a point attached to a given curve as it slides along two (or more) given curves. Formally speaking, the curves must be differentiable curves in the Euclidean plane. The "fixed curve" is kept invariant; the "rolling curve" is subjected to a continuous congruence transformation such that at all times the curves are tangent at a point of contact that moves with the same speed when taken along either curve (another way to express this constraint
Riemannian connection on a surface space rolling without slipping or twisting on a horizontal plane. The point of contact will describe a curve in the plane and on the surface. As for the sphere, the usual curvature of the planar curve equals the geodesic curvature of the curve traced on the surface. This geometric way of viewing parallel transport can also be directly expressed in the language of geometry. The envelope of the tangent planes to "M" along a curve "c" is a surface with vanishing Gaussian curvature, which by Minding's theorem, must be locally isometric to the Euclidean plane. This identification allows parallel transport