New Solutions for General Transition Curves

This paper presents new solutions in the area of general transition curves. General transition curves describe a curvilinear transition between two rectilinear directions using only one equation. The curves ensure continuous change of curvature all over the curvilinear transition. Along such curves, the curvature rises from zero at the start point to a certain maximum value, and then drops to zero again at the end point. The present paper introduces two new families of general transition curves: with smooth and nonsmooth curvature diagrams. This means that the general transition curves could be considered as an alternative to the geometric systems formed by classical geometric elements (first transition curve - circular arc - second transition curve; first transition curve - second transition curve). The use of general transition curves is advantageous from the viewpoint of vehicle motion dynamics. It also extends the possibilities of modifying the arc geometry to obtain the assumed radius of curvature.