KINEMATICS. 



angle as to shut off the steam when the crank makes a certain 

 angle with the direction of motion of the piston. It fol- 

 lows that the fraction of stroke completed before cut-off takes 

 place is affected by the obliquity of the connecting rod. The 

 rates of cut-off are therefore different in the forward and back- 

 ward strokes. In the forward stroke, the effect of the obliquity 

 is to put the piston in advance of the position it would have 

 if the connecting rod were of infinite length ; in the return, 

 stroke, i.e. when 6 is greater than TT, the piston lags behind. 



153. An analytical expression for the deviation due to obliquil 

 is readily obtained from Fig. 35. We have 



MN= PN- PM= I ( i - cos 



. 2 msf . < 



= ms sm^ - = (2 sm > 

 2 4\ 



or approximately, since <f> is small, 



ms . 

 ' 4 S11 



Also, as in Art. 149, -= ; 

 sin u m 



hence 



s 

 4m 



The greatest value of J/7Vis thus seen to be s/^m ; for instanct 

 if the connecting rod be four times the length of the crank, th< 

 deviation due to obliquity cannot exceed 1/16 of the stroke. 



154. Exercises.* 



1 i ) Construct a polar diagram exhibiting the position of the piste 

 for all angles by laying off on the crank arm O Q a length ON ] = 

 and joining the points N 1 by a continuous curve. 



(2) Construct the curves of piston velocity indicated in Art. 148. 



* These problems are taken with slight modification from COTTERILL'S Applii 

 mechanics, 1884, p. 112. 



