Abstract: It is proved that arc coordinates of a directed curve cannot be used as ordinary coordinates or generalized coordinates for the motion of an Appell-Hamel particle without a fixed orbit, but they can be used as quasi coordinates. It is pointed out that the method leading into arc coordinates of a directed curve and the conclusion that the orbit of the Appell-Hamel particle is generally helical are correct. It is proved that the viewpoint that the Appell-Hamel constraint is holonomic and the s coordinates are generalized coordinates in the motion of an Appell-Hamel particle is incorrect. Ultimately the mechanical nature of constraints of mechanical systems does not depend on the selection of coordinates and space.