132] FREEDOM OF THE SECOND ORDER. 119 



132. Reaction of Constraints. 



We shall now consider the following problem : A body which is free to 

 twist about all the screws of a cylindroid C receives an impulsive wrench on 

 a certain screw 77. It is required to find the screw X, a wrench on which 

 constitutes the impulsive reaction of the constraints. Let C represent the 

 cylindroid which, if the body were perfectly free, would form the locus of 

 those screws, impulsive wrenches on which correspond to all the screws of C 

 as instantaneous screws. Since a wrench on 77, and one on \, make the body 

 twist about some screw on C, it follows that the cylindroid (77, X) must have 

 a screw p in common with C . The wrench on X might be resolved into two, 

 one on 77, and the other on p, and the latter might be again resolved into 

 two wrenches on any two screws of C . It therefore follows that X must 

 belong to the screw system of the third order, which may be defined by 77, 

 and by any two screws from C . Take any three screws reciprocal to this 

 system, and any two screws on C. We have then five screws to which X is 

 reciprocal, arid it is therefore geometrically determined ( 26). 



When X is found, the cylindroid (77, X) can be drawn, and thus p is deter 

 mined. The position of p on C will point out the screw on C, about which 

 the body will commence to twist, while the position of p on (77, X), and the 

 known intensity of the wrench on 77, will determine the intensity of the 

 wrench on X. 



