DYNAMICS OF A RIGID BODY. 1 05 



a, reciprocal screw. The second plane is that drawn 

 through the point, and through the other screw of equal 

 pitch on the cylindroid, to that which passes through 

 the point. 



We have, therefore, solved in the most general manner 

 the problem of the equilibrium of a rigid body with two 

 degrees of freedom.- We have shown that the necessary 

 and sufficient condition is, that the resultant wrench be 

 about a screw reciprocal to the cylindroid expressing 

 the freedom, and we have seen the manner in which the 

 reciprocal screws are distributed through space. We 

 now add a few particular cases. 



98. Particular Cases. A body which has two degrees 

 of freedom is in equilibrium under the action of a force, 

 whenever the line of action of the force intersects both 

 the screws of zero pitch upon the cylindroid. 



If a body acted upon by gravity have freedom of the 

 second order, the necessary and sufficient condition of 

 equilibrium is, that the vertical through the centre of 

 inertia shall intersect both of the screws of zero pitch. 



A body w r hich has freedom of the second order will 

 be in equilibrium, notwithstanding the action of a couple, 

 provided the axis of the couple be parallel to the nodal 

 line of the cylindroid. 



A body which has freedom of the second order will 

 remain in equilibrium, notwithstanding the action of a 

 wrench about a screw of any pitch on the nodal line of 

 the cylindroid. 



99. The Impulsive Cylindroid and the Instantaneous 

 Cylindroid. A rigid body M is at rest in a position P, 

 from which it is either partially or entirely free to move. 

 If M receive an impulsive wrench about a screw Ji, it 

 will commence to twist about an instantaneous screw A iy 

 if, however, the impulsive wrench had been about X z or 

 JT 3 (M being in either case at rest in the position P) 



