! 4 GEOMETRY OF MOTION, 



which represents an ellipse, since the determinant 



a x f ) z +y fz , 2ay f 

 -2ay' y 



[27. 



is necessarily positive. 



In general, therefore, the points of the figure describe 

 ellipses ; O' describes a circle ; A and B describe straight lines, 

 and so does every point on the circle of diameter AB. It is 

 this fact that by rolling a circle within a circle of double diam- 

 eter the points of the smaller circle are made to describe seg- 

 ments of straight lines, which makes this form of motion of 

 practical importance : it may serve to transform circular into 

 rectilinear motion. 



27. Elliptic Motion (continued) : Two points A, B of a plane 

 figure move along two fixed lines inclined to each other at an 

 angle a> (Fig. 8). 



Fig. 8. 



This case is readily reduced to the preceding one. The 

 instantaneous centre is found as before ; its distance OC from 

 the intersection of the fixed lines OA, OB is again constant 



