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 "g". The condition "QAQ=0" implies "Q" "g" "g" "Q" = 0 and hence that "Q" "g" "g" "Q" =0. There is another kinematic way of understanding parallel transport and geodesic curvature in terms of "rolling without slipping or twisting". Although well known to differential geometers since the early part of the twentieth century, it has also been applied to problems in engineering and robotics. Consider the 2-sphere as a rigid body in three-dimensional 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. At each