TWISTS AND WRENCHES. 5 



tient just referred to. Remembering the definition of a 

 screw, ( i), we may use the phrase, wrench on a screw, 

 meaning thereby, a force directed along the screw and 

 a couple in a plane perpendicular to the screw, the mo- 

 ment of the couple being equal to the product of the force 

 and the pitch of the screw. Hence, we may state, that 



The canonical form to which all the forces acting on a 

 rigid body can be reduced is a wrench on a screw. 



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. 



5. Notation for Twists, Wrenches, and Twisting Mo- 

 tions. 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, or metric 

 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 o'/ a . 



If the pitch be positive (tiegative}, the direction of the 

 translation portion of the twist bears the same relation 

 to the direction of the rotation portion of the twist as the 

 direction of the translation of a nut on an ordinary right- 

 handed (left-handed] screw bears to the direction of the 

 rotation of the nut. 



If the pitch be zero, the twist reduces to a pure rota- 

 tion 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 quanti- 

 ties for its complete specification, and of these, five are 



