Abstract
AbstractThis paper presents two new solutions for transition curves that make it possible to create a smooth connection between two arbitrarily located points. For this reason, the curves are referred to as universal transition curves. The solutions are based on Degree 4 and 5 polynomials and describe the entire curved transition between the set points using only a single equation. The paper also describes a procedure for designing an arc with the use of these curves. The design process requires exact information concerning the location of the two points to be joined (i.e., P and K) as well as the directions of the tangents at these points together with the curvature radii at P and K. Such a data set is necessary owing to the form of the equations describing the universal transition curves. The design principles have been illustrated with relevant numerical examples.
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