﻿Motion transmitted by Hookes Joint. 159 



obtaining (G) we take the case in which the speed of 

 the driving shaft is uniform. 



From (5) the maximum speed of the driven shaft 

 is readily seen to be co{l + 2rc/(l — ?*)} or w sec a ; the 

 minimum speed is seen to be <w{l — 2n/(l-\-ii)} or « cos a, 

 a) being the angular velocity of the driving shaft. 



When the angle between the shafts is not large, (G) may 

 be written 



"(a)' w 



Thus the maximum angular acceleration of the driven 

 shaft is very approximately 4?z&> 2 . If a = 15° and co = 

 GO radians per sec, the maximum angular acceleration 

 is almost 250 radians per sec. per second. 



Fig. 2. 



d *<t> • A 



t^- = — 4n sm 



dt 1 ' 



3. In the mechanism of the oscillating cylinder engine, 

 and the quick return crank and slotted-lever mechanism 

 (fig. 2), we have 



sin <f> _ sin ty _ sin (# + <£) 



or 



sin (p = -sin (6 + (f>) = n sin (# + </>), where ?i= -. 

 c v 



g2ty(l_ ne *e) = l_ w < 



/6> 



,2/0 _ 



(l-ne- i9 )/(l-ne ie ), 



