*evolute*

n. [ L. evolutus unrolled, p. p. of evolvere. See Evolve. ] (Geom.) A curve from which another curve, called the involute or evolvent, is described by the end of a thread gradually wound upon the former, or unwound from it. See Involute. It is the locus of the centers of all the circles which are osculatory to the given curve or evolvent. [ 1913 Webster ]

☞ Any curve may be an evolute, the term being applied to it only in its relation to the involute. [ 1913 Webster ]