28.] 



PLANE MOTION. 



and =AB/sm a ; for O, A, C, B all lie on a circle whose centre 

 O' bisects OC; hence 



The motion is therefore produced by the rolling of this circle 

 of diameter AB/sm o> within a circle of twice this diameter 

 described about O ; it is not essentially different from the pre- 

 ceding case (Art. 26). This will also be seen if we take OA as 

 axis of x, the perpendicular to it through O as axis of y. This 

 perpendicular Oy intersects the circle OAB in a point B', which 

 is the end of the diameter AO'B' and moves along Oy during 

 the motion. The points A, B 1 of the figure move, therefore, 

 along the rectangular lines Ox, Oy, just as in the problem of 

 Art. 26. 



28. Connecting Rod Motion : One point A of the figure describes 

 a circle, while another point B moves on a straight line, passing 

 through the centre O of the circle (Fig. 9). 



Fig. 9. 



With OB as polar axis, the equation of the fixed centrode is 

 r* cos 2 d - 2 ar cos 2 6 + a 2 = / 2 . 



This, as well as the equation of the body centrode, is of the 

 sixth degree in rectangular Cartesian co-ordinates. But the 

 graphical construction presents no difficulties. 



