TWISTS AND WRENCHES. 



11 



If a rigid body be acted upon by several wrenches, then these wrenches 

 could be replaced by one wrench which is called the resultant wrench. 



A twist about a screw a requires six algebraic quantities for its complete 

 specification, and of these, five are required to specify the screw a. The sixth 

 quantity, which is called the AMPLITUDE OF THE TWIST, and is denoted by 

 a , expresses the angle of that rotation which, when united with a translation, 

 constitutes the entire twist. 



The distance of the translation is the product of the amplitude of the twist 

 and the pitch of the screw, or in symbols, a p a . The sign of the pitch 

 expresses the sense of the translation corresponding to a given rotation. 



If the pitch be zero, the twist reduces to a pure rotation around a. If 

 the pitch be infinite, then a finite twist is not possible except the amplitude 

 be zero, in which case the twist reduces to a pure translation parallel to a. 



A wrench on a screw a requires six algebraic quantities for its complete 

 specification, and of these, five are required to specify the screw a. The sixth 

 quantity, which is called the INTENSITY OF THE WRENCH, and is denoted by 

 a&quot;, expresses the magnitude of that force which, when united with a couple, 

 constitutes the entire wrench. 



The moment of the couple is the product of the intensity of the wrench 

 and the pitch of the screw, or in symbols, a&quot; p a . The sign of the pitch 

 expresses the direction of the moment corresponding to a given force. 



If the pitch be zero, the wrench reduces to a pure force along a. If the 

 pitch be infinite, then a finite wrench is not possible except the intensity be 

 zero, in which case the wrench reduces to a couple in a plane perpendicular 

 to a. 



In the case of a twisting motion about a screw a. the rate at which the 

 amplitude of the twist changes is called the TWIST VELOCITY arid is denoted 

 by a. 



8. Restrictions. 



It is first necessary to point out the restrictions which we shall impose 

 upon the forces. The rigid body M, whose motion we are considering, is 

 presumed to be acted upon by the same forces whenever it occupies the same 

 position. The forces which we shall assume are to be such as form what is 

 known as a conservative system. Forces such as those due to a resisting medium 

 are excluded, because such forces do not depend merely on the position of 

 the body, but on the manner in which the body is moving through that 

 position. The same consideration excludes friction which depends on the 

 direction in which the body is moving through the position under considera 

 tion. 



