The transition curves in the modern highway and railway construction are route elements equally crucial as alignment and curve (circular). In order to prevent a sudden change of the centrifugal force, the transition curve must be applied due to the impact of the motion in a sharp curve. Over the years the application of the clothoid has become widespread in many countries in the world. However, in this study, in order to eliminate the problems concerning the road dynamics, created by clothoid for vehicles at high speed, sinusoid is examined. The possibility of using sinusoid in defining transition curves during design of transportation facilities is analysed in this paper. Basic properties of sinusoid, their fundamental mathematical expression, calculation of point coordinates, driving-dynamic characteristics of sinusoid are described (especially for Transrapid using), and the function of change in curvature and lateral impact along the sinusoid is presented. Sinusoid is dealt with as ideal curvature diagram which has curve and superelevation ramp in the articles.