The necessity for the curves, which have much better vehicle-road dynamical properties, has arisen since the last quarter of the 20th century, because the speed used especially on the railways was increased. Although the dominance of the spiral curve as a transition curve has been still in progress by means of the common and wide knowledge base and infrastructure such as lots of ready to use software and the traditional rules of the responsible facilities, many investigations have been carried out on developing new curves, which can be used for the design of horizontal geometry and have many advantages with respect to road dynamics, because the spiral curve has been realized that it is not adequate for the road dynamics. So the transition curves superior for road dynamics have been invented by using the properties of vehicle-road dynamics, represented by the function of lateral change of acceleration that is the most important criteria to evaluate the curves in this manner. The recently invented superior curves can be considered as Sinusoidal curve, Baykal curve, Tari-1 curve, and Tari-2 curve. Sinusoidal curve is a known and applied curve joining a straight line with a circular arc by providing the condition of second-degree contact related with properties of vehicle-road dynamics. Baykal curve is a fundamental curve joining two straight lines without the necessity of a circular arc and it is the first realization of the new generation curves mentioned in the paper. Tan-1 curve is a new curve joining a straight line with a circular arc by providing the condition of second-degree contact. Tari-2 curve is a superior implementation of Baykal curve by providing the condition of second-degree contact. In this paper, each of these curves has been examined by using the function of lateral change of acceleration in motion model with constant velocity.