After a brief theoretical introduction to the transition curve, and a
description of a graphical construction according to Muller, an analyt
ical procedure for computing the position of the points on such a curv
e is described. It is then proved that, for each coupler position, the
re is a maximum of two pairs of real points, each with the same abscis
sa, that describe coupler curves with coincident double points. (C) 19
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