Road and railway transition curves have again become the subject of im
portant scientific research and serious traffic engineering analyses b
ecause of high driving speeds and demands for automatic drive (i.e., c
ar pilots). This article shows, in an original way, how to define or r
econstruct the track of a vehicle when passing the elements of a conti
nuous curve (straight lines, circles) so the track (curve) suits all r
equirements to which transition curves must be adapted. The praxis whe
reby a known mathematical curve (e.g., a cubic parabola, lemniscate, o
r chlotoid) was assumed as a transition curve and its suitability was
analyzed has been passed over. On the basis of assumed kinematics mode
ls of the motion of a vehicle along joint alignment elements with a ch
anging radius of curvature, the writers have analyzed different transi
tion curves resulting in safe, comfortable, and economic driving. The
curve resulting from a parabolic velocity chart of front wheel rotatio
n during such movement which found the most suitable has been named PO
LUSA; a geometrical analysis of POLUSA has been performed and a manual
for practical use completed.