EQUILIBRIUM OF A RIGID BODY. 39 



about which the body could be twisted would only con- 

 sist of the members of that lower screw complex. 



Since the amplitudes of the n twists about A . . . A n 

 are [arbitrary, it might be thought that there are n dis- 

 posable quantities in the selection of a screw S from a 

 screw complex of the n th order. It is, however, obvious 

 from 1 7 that the determination of the position and pitch 

 of S depends only upon the ratios of the amplitudes of the 

 twists about A lf . . . A n and hence in the selection of a 

 screw from the screw complex of the n th order, we have n - i 

 disposable quantities. 



44. Constraints. An essential feature of a system 

 of constraints consists in the number of independent 

 quantities which are necessary to specify the position of 

 the body when displaced in conformity with the require- 

 ments of the constraints. That number which cannot be 

 less than one, nor greater than six, is the order of the 

 freedom. To each of the six orders of freedom a certain 

 type of screw complex is appropriate. 



The study of the six types of screw complex as here 

 defined is a problem of kinematics, but the statical and 

 kinematical properties of screws are so interwoven that 

 we derive great advantages by not attempting to rele- 

 gate the statics and kinematics to different chapters. 

 We shall not require any further mention of the con- 

 straints. Every conceivable condition of constraints must 

 have been included when the six screw complexes are 

 discussed in their most general form. Nor does it come 

 within our scope, except on rare occasions, to specialize 

 the enunciation of any problem, further than by men- 

 tioning the order of the freedom permitted to the body. 



45. Screw Reciprocal to a Complex. If a screw X 

 be reciprocal to n screws, A l9 &c., A, belonging to a 

 screw complex of order n, then X is reciprocal to every 

 other screw A which belongs to the same screw com- 



