282 APPLIED SCIENCE 



alphabet as is used to denote the element. The geometrical 

 intersections will be marked by capital letters, whereas the ele- 

 ments are marked by italics. When there are several geome- 

 trical joints for one element, these joints will be denoted by the 

 same letter, but distinguished from each other by suffixes. The 

 substitution of links or half links for an actual element may 

 be effected even when forces are parallel, if we admit joints at an 

 infinite distance. If, now, all the elements of a machine, in their 

 relative positions at any one instant, be removed in succession, 

 and replaced by their equivalent links or half links, we shall 

 substitute for the original machine a self-strained frame of links 

 such that the stress in each link passing through a joint will be 

 in all respects equal to that on the joint, while the stresses in 

 the driving and resisting links will represent the effort and use- 

 ful resistance in the machine. Each half link at a joint of one 

 element is necessarily met and completed by the other half link 

 in the same line, due to the reaction of the second element. 



The self-strained frame, composed of links, as described 

 above, will be called the dynamic frame of the machine with its 

 elements in the given relative position. 



8. Example. An example will probably assist in showing 

 what is meant by the dynamic frame. Let a machine be com- 

 posed as the six elements, a, ft, c, d, e,f, joined as in Fig. 5, p. 279. 

 Let e be the driving element, and /the resisting element. We 

 will suppose in this and in the following examples that the 

 resulting forces all lie in one plane, although the figures may 

 not show the split joints necessary to ensure this result. For 

 the present, the effect of weight and inertia will be neglected. 

 The machine shown is a complete machine ; the element d has 

 two joints, the elements a and c have three joints, and the ele- 

 ment b has four joints. The dynamic frame may be drawn as- 

 suming the friction at the joints to be insensible, or it may be 

 drawn taking friction into account. In the former case it will 

 be represented as in Fig. 5a, which is obtained as follows : 

 Link 1 may first be drawn through the axis of e, for we know 

 that the half links at the joints ae, eb must lie normally to the 

 surface of these joints (being frictionless), and must therefore lie 

 in one straight line, passing through the centre of the pins at 

 ae and eb. For similar reasons we draw 5 and 6 through the 



