136 THE THEORY OF SCREWS. [146- 



The chord joining any impulsive screw A to the corresponding instantaneous 

 screw A envelops a conic, and the point of contact, I, divides the chord into 

 segments, so that the ratio of A I to A I is proportional to the square of the 

 twist velocity acquired about A by the unit impulsive wrench on A. 



147. Constrained Motion. 



We can now give another demonstration of the theorem in 90, which is 

 thus stated : 



If a body, constrained to twist about the screw a, be acted upon by an 

 impulsive wrench on the screw 77, then the twist velocity acquired varies as 



W 2 



The numerator in this expression is the virtual coefficient of the two 

 screws, and the denominator is the function of 134, which is proportional 

 to the kinetic energy of the body when twisting about a with the unit of 

 twist velocity. 



Let a and t] be represented by A and I respectively (Fig. 29), and let A 



Fig. 29. 



be the impulsive screw which would correspond to A if the body had been 

 free to twist about any screw whatever on the cylindroid defined by A and 

 A . Let K be reciprocal to A . 



The impulsive wrench on / is decomposed into components on K and A. 

 The former is neutralized by the constraints ; the latter has the intensity 



KI 

 KA 



whence the twist velocity &&amp;gt;, acquired by A , is ( 141) proportional to 



KI HO 

 KA HO 



