Cycloidal Cyclical Surfaces

Sa？etak The paper presents a family of cycloidal cyclical surfaces, which are created by a movement of a circle alongside the special spatial cycloidal curve, where the circle is located in the curve normal plane and its centre is on this curve. The spatial cycloidal curve can be created by simultaneous revolution of a point about three different axes 3^o, 2^ o and 1^o in the space. The form of the cycloidal curve and also of the cycloidal cyclical surface depends on the relative position of the three axes of revolutions, on multiples of angular velocities and orientations of separate revolutions. The analytic representation, the classification of surfaces and some of their geometric properties are derived