THE KINEMATICS OF MACHINERY. 



87 



POP V and every point moves through the same angle, which 

 we may call r As the figure may have any form- we choose, 

 let us suppose it so extended as to contain a line which is the 

 same length as 00 V and which makes with 00 1 the angle <p v 

 that is to say, the angle through which the figure moves about 

 0. Such a line is shown in Fig. 4 by 



FIG. 4. 



We have, then, a line MM l forming a part of the figure 

 PQ, equal in length to 00 1} the points and M coinciding, 

 and the angle O l MM l being = ^> 1 . Then when the figure has 

 completed its motion about 0, MM l and 00 1 must coincide. 

 Take further similarly M^M^ X 2 and so placed that when 



M l coincides with O v /. O^M^M^ = fa, then when the figure 

 takes its third position, completing the turning about O v M l 

 J/o coincides with 0^^. Similarly we can obtain MJ\f v &c. 



