CHAPTER XXV. 



THE THEORY OF PERMANENT SCREWS*. 



360. Introduction. 



In commencing this chapter it will be convenient to recite a well-known 

 dynamical proposition, and then to enlarge its enunciation by successive 

 abandonment of restrictions. 



Suppose a rigid body free to rotate around a fixed point. There are, as 

 is well known, three rectangular axes about any one of which the body 

 when once set in rotation will continue to rotate uniformly so long as the 

 application of force is withheld. These axes are known as permanent axes. 

 The freedom of the body in this case is of a particular nature, included in 

 the more general type known as Freedom of the Third Order. The Freedom 

 of the Third Order is itself merely one subdivision of the class which, 

 including the six orders of freedom, embraces every conceivable form of 

 constraint that can be applied to a rigid body. We propose to investigate 

 what may be called the theory of permanent screws for a body constrained 

 in the most general manner. 



The movement of the body at each moment must be a twist velocity 

 about some one screw belonging to the system of screws prescribed by 

 the character of the constraints. In the absence of forces external to those 

 arising from the reactions of the constraints, the movement will not, in 

 general, persist as a twist about the same screw 6. The instantaneous screw 

 will usually shift its position so as to occupy a series of consecutive positions 

 in the system. It must, however, be always possible to compel the body to 

 remain twisting about 6. For this purpose a wrench of suitable intensity 

 on an appropriate screw 77 may have to be applied. Without sacrifice of 

 generality we can in general arrange that 77 is one of the system of screws 



* Trans. Roy. Irish Acad., Vol. xxix. p. 613 (1890). 



