way. The two auxiliary centroids coincide with the two circular primary centroids A and B; ab and be are point-paths (here epicycloids) described by the points a and c of the circle B; d e and ef are epicycloids described by the points d and g of the circle A; glid is a portion of a curtate epitrochoid described by the point e of the wheel B; aid a similar curve described by the point b of A. Simultaneous contact takes place in a, b and c, the normals to these points of restraint all passing through the point 0; after a very small rotation in the one or the other direction the point e comes into contact with g h, or k with a I.
Fig. 110.
It may sometimes be required to combine this method of con- structing profiles with one of the others, such mixed methods are occasionally used in drawing the teeth of wheels.
§35.
Fifth Method.—Parallels or Equidistants to the
Roulettes as Profiles.
If we have obtained by any of the methods now described the profiles a P and b P corresponding to the centroids A and B, and from the centre of curvature of the element P of a P describe a circle with a radius larger by any amount, P P v than the radius of
