( 21 ) 



CHAPTER III. 



RECIPROCAL SCREWS. 



22. Reciprocal Screws. If a body only free to twist 

 about a screw a be in equilibrium, though acted upon 

 by a wrench on the screw /3, then conversely a body 

 only free to twist about the screw j3 will be in equili- 

 brium, though acted upon by a wrench on the screw a. 

 The principle of virtual velocities states, that if the 

 body be in equilibrium the work done in a small dis- 

 placement against the external forces must be zero ; but 

 the condition for this is, that the virtual coefficient should 

 vanish (13), or 



(f a + f ft ) cos O - d sin O = o. 



The symmetry shows that precisely the same condi- 

 tion is required whether the body be free to twist about 

 , while the wrench act on j3, or vice versa. A pair 

 of screws are said to be reciprocal when their virtual coeffi- 

 cient is zero. 



23. Particular Instances. Parallel or intersecting 

 screws are reciprocal when the sum of their pitches is 

 ^ero. Screws at right angles are reciprocal either when 

 they intersect, or when one of the pitches is infinite. 

 Two screws of infinite pitch are reciprocal, because a 

 couple could not move a body which was only susceptible 

 of translation. A screw whose pitch is zero or infinite 

 is reciprocal to itself.* 



* For other particular instances see Professor Everett " On a New Method 

 in Statics and Kinematics," 27 ; " Messenger of Mathematics," New Series, 

 JS T o. 39, 1874. 



