Page:The Kinematics of Machinery.djvu/181

 upon the normal bisector 3 of the arc 2' 3', at the intersection of the curves 2' and 3'. Relatively to the three-cornered ceii- troid E describes a point only; relatively to the other centroid however it describes a straight line right and left of R, being a point in the circumference of a smaller Cardanic circle rolling within a larger. R C and R D are these lines and their pro- longations. If we complete the rolling of the inner centroid upon the other we obtain the four sides of the square as the pro- file for the outer element. Only the necessary restraint for the inner element is now required. For this purpose we must find

a point homologous to R for each of the two remaining sides of the inner centroid; such points we obviously have in P and Q (as shown

. lu.

by the dotted arcs), and these like R have their paths along the central portions of the sides of the square. To obtain the restraint we have then only to draw from R, P and Q the equi-distant curves P Q, Q R, and R P, and we obtain the curve triangle as a profile.