THEORY OF SCREWS. 



CHAPTER I. 



TWISTS AND WRENCHES. 



I. Definition of the word Screw. The direct problem 

 offered by the Dynamics of a Rigid Body may be thus 

 stated. To determine at any instant the position of a 

 rigid body subjected to certain constraints and acted 

 upon by certain forces. We may first inquire as to the 

 manner in which the solution of any such problem ought 

 to be presented. Adopting one position of the body as 

 a standard of reference, a complete solution of the pro- 

 blem must provide us with the means of deriving the 

 position at any subsequent epoch from the standard 

 position. We are thus led to inquire into the most na- 

 tural method of specifying one position of a body with 

 respect to another. 



To make our course plain let us consider the case of 

 a mathematical point. To define the position of the point 

 P with reference to a standard point A, there can be no 

 more natural method than to indicate the straight line 

 along which it would be necessary for a particle to travel 

 from A in order to arrive at P, as well as the length of 

 the journey. Now, there is an analogous method of de- 

 fining the position of a rigid body with reference to a 



B 



