

264.] PLANE MOTION. 



A corresponding proposition holds of course for four bar 

 linkages with crossed bars I 2 4 3, or I 3 2 4. 



264. Lever-crank. The linkage considered in the preceding 

 article becomes a mechanism, or linkwork, as soon as one of its 

 four links is fixed. It occurs in machines under a variety of 

 forms some of which are referred to below. 



Let the link 3 4 be fixed ; then the centre 7 34 (Fig. 59) dis- 

 appears ; C^ falls into 4, C 23 into 3, and C 12 becomes the inter- 

 section 5 of 4 i and 32. If i 2 were fixed instead of 34, 34 

 would have its centre at 5. 



Similarly, if either 41 or 2 3 be fixed, the centre of the other 

 is 6. 



Fig. 60. 



Hence whichever of the four links be fixed, the centres of 

 all the links lie at some of the six vertices of the complete 

 quadrilateral 1234. 



If 34 be the fixed link (Fig. 60), the ratio of the angular 

 velocities co 1 of 4 i and o> 2 of 3 2 can be found. For if o> denote 

 the angular velocity of i 2 about 5, we have 



4 i o) 1 =5 i -o), 3 2-6> 2 =5 2-00; 

 hence 



*>i S 2 51 32/41 

 or, by the proposition of Menelaus : 



^ = 3? 



