2 8o APPLIED SCIENCE 



three joints, and all connected by an ideal geometrical joint 

 without friction at the point of intersection (which, in the case 

 of parallel forces, will be at an infinite distance). Thus element 

 b, Fig. 3, may be replaced by the half links 1, 2, 3, intersecting 

 at the geometrical joint B, Fig. 3a; links 1 and 3 would be 

 half links in tension, link 2 a half link in compression. The 

 direction of the arrows shows the direction of the stress in the 

 links replacing b. The directions of the links 1, 2, and 3 do 

 not coincide with those of the geometrical axes of a, c, and d ; 

 indeed, these elements may be stiff bars having many other 

 joints; but if we know that the element b is moving relatively 

 to a, c, and d, as shown by the arrow, then one condition deter- 

 mining the directions of links 1, 2, 3 is given us, for these 

 directions must make the stated angle with the surfaces of the 

 joints fea, fee, bd. In Fig. 3a the links 1, 2, and 3 are therefore 

 shown, not passing through the centres of the circles at the 

 joints, but passing on that side of the centre on which the force 

 represented in the link would resist the motion of the pins sup- 

 posed to be fast on b. The small arrows, Fig. 3a, show the 

 direction of rotation of these pins, and these arrows are lettered 

 b to indicate that they represent the motion of element b rela- 

 tively to a, c, and d. This plan of indicating the relative motion 

 of the surfaces at joints will be followed in future diagrams. It 

 will always be assumed that the pin is fixed in the element in- 

 dicated by the letter at the arrow. When there are more than 

 three joints, the forces supplied at each joint are such as would 

 be given by a series of half links, one for each joint, correspond- 

 ing with each line of bearing pressure, and themselves joined 

 by other links, so as to form a frame which would be in equili- 

 brium under the action of external forces equal to those in the 

 half links. 1 Thus any one of these forces may be looked upon 

 as the equilibrant of the others, and as acting upon them 

 through a series of links which are subject only to compression 

 or tension. In Fig. 4, p. 281, if the member fe is jointed with 

 members a, c, d, and e by four parallel pins, we might replace b 

 in any machine by the four half links, in Fig. 4a, 1, 3, 4, and 

 5 and a complete link 2, joining the intersection of 1 and 5 with 



1 In this frame it might be necessary to include at least one stiff bar or 

 frame to meet opposite and equal couples. 



