A timepiece mechanism including a first component and a second component configured to cooperate with each other in a relative motion on a trajectory in an interface area, wherein a first path of the first component includes magnetic and/or electrostatic actuation components, configured to exert a contactless stress on complementary magnetic and/or electrostatic actuation components included in a second path belonging to the second component. Throughout a monotonous relative movement of the second path with respect to the first path, interaction energy between the first component and second component has a variable gradient with at least one position of discontinuity of the gradient, which corresponds to a variation in the contactless stress, the position of discontinuity of the gradient corresponding, in a variant, to an abrupt variation in the contactless stress.