THE KINEMATICS OF MACHINERY. 



81 



contact, the one enclosing the other, and are therefore called 

 closed or lower pairs of elements. They are, moreover, the 

 only closed pairs which exist. They are further the only 

 pairs in which all points of the moving element have similar 

 paths. 



Every point of an eye, for instance, moves in a circle about 

 the same axis. If there were attached to it a body of any 

 size or form whatever, all its point would move about the 

 same axis. The " point-paths " would all be concentric circles. 

 Again, whatever the external size or shape of a nut, every 

 point in it moves in a helix of the same pitch about the axis 

 of the screw ; the point-paths, that is, would be similar. 



The general condition of determinateness of motion can, 

 however, be fulfilled by an immense number of other pairs of 

 elements. The theory of these is too large a subject to be 

 entered into just now, I must merely direct your attention to 

 the existence of such combinations. 



u 



Fio. 1. 



Fig. 1 represents one of the simplest that can be used. 

 Here one of the elements is an equilateral triangle, ABC, 

 the other is the "duangle" R P S Q. The latter moves 

 within the former, touching it always in three points, or rather 

 along three lines. Its motion is just as absolutely determinate 

 as the motion of a pin in an eye. It is free to move at 

 any instant only about the point in which the three normals 

 to the triangle at the points of contact intersect (as ,Q in the 

 Fig.) The models before you show a few of the many forms 



