THE KINEMATICS OF MACHINERY. 79 



these motions must certainly be studied if we are to obtain 

 a complete knowledge of the mechanism to which they 

 belong. Any method of study, therefore, which covers all 

 the kinematic conditions of the mechanism, instead of the 

 mechanical conditions of two or three points only, possesses 

 in that respect very great advantages. 



The treatment of mechanisms which I shall sketch to you 

 is intended to remedy some of the defects which I have 

 enumerated. Those of you who have studied modern 

 geometry side by side with the old methods will recognise 

 that these defects are somewhat analogous to those of 

 Euclidean geometry. The attempt to remedy them proceeds 

 in lines similar to those of modern geometry, and will 

 eventually, I believe, when more fully worked out, take 

 the same position in i's own subject. 



Let us then look first at the analysis of mechanisms. This 

 is none the less important a matter that its results are so 

 very simple in many cases. A clear understanding of these 

 elementary matters is of great assistance in clearing up 

 difficulties which occur in the more advanced parts of the 

 subject. 



In a machine or a mechanism of any kind the motion of 

 every piece must be absolutely determinate at every instant. 

 Jt will be remembered that we are at present considering 

 motion as change of position only, not in reference to velocity. 

 The motion or change of position may be determined by the 

 direction arid magnitude of all the external forces which act 

 on the body : the motion is then said to be free, but it is 

 obviously impossible to arrange such a condition of things in 

 a machine. The motions may, however, be made absolutely 

 determinate independently of the direction and magnitude 

 of external forces, and in order that this may be the case 

 the moving bodies, or the moving and fixed bodies as the 

 case may be, must be connected by suitable geometric forms. 

 Motion under these circumstances is called constrained motion. 1 



If I allow a prismatic block to slide down the surface of 

 an inclined plane its motion will be free ; it is determined 

 by the combination of external forces which act upon the 



1 Essentially it dees not differ from free motion ; the difference 

 really lies in the substitution of stresses or molecular forces, which are 

 under our complete control, for external forces. 



