130 



THE THEORY OF SCREWS. 



[142- 



Let X, Y (Fig. 23) be the two principal screws of inertia. Let A be 

 an impulsive screw, and A the corresponding instantaneous screw. Draw 



Fig. 23. 



through -A the line AH parallel to XY. Join HA , and produce it to 

 meet the homographic axis at fl. Let a be the twist velocity generated by 

 an impulsive wrench of unit intensity at X, and let /3 be the corresponding 

 quantity for F. 



It may be easily shown that the triangle AA X is similar to YA Cl, and 

 that the triangle AA Y is similar to XA l ; whence we obtain 



A YflA 



__ 

 AX~~ OF AY 



The unit wrench on A can be decomposed into components on X and F of 



respective intensities 



AY AX 



XY XY 



AX 



These will generate twist velocities 



AT 



a ~XY 



Let &amp;lt;w be the resulting twist velocity on A , then the components on X and F 

 must be equal to the quantities just written ; whence 



A Y AY 



XY 



A X 

 XY 



= a. 



and we obtain 



or, 



XY 



ZF 



CIA 

 &quot;OF 5 



a : /3 :: OF: 



we thus see that O is a fixed point wherever A and A may be. 



