A novel motion equation which can realize coordinate transform described by position, momentum or time is proposed, in this paper. With this equation, coordinate transform of external force which has not been treated by canonical equation is described. In addition, a condition which is essential for canonical transform is omitted and the transform is given without solving partial differential equations. Thus, any task can be described easily and intuitively. Mobile-hapto is treated as an example of controllers based on the proposed motion equation. Its validity is confirmed by some simulations and experiments.