288 . APPLIED SCIENCE 



fulfilled. BANKINE'S conditions are, however, generally fulfilled 

 in all important designs of machinery, and when this is the case 

 we may, without serious error, assume all the actions to take 

 place in one plane parallel to the plane of action in the machine, 

 and this hypothesis will be adopted in all that follows when the 

 contrary is not stated. 



11. Simple and Compound Dynamic Frames. The dynamic 

 frame of a complete machine must contain a driving link or 

 couple and a resisting link or couple, together with the links 

 necessary to connect the driving and resisting links or couples 

 in such a way as to form a self-strained frame. A complete 

 machine may be either simple or compound. Simple machines 

 are those having dynamic frames which cannot be decomposed 

 into two or more self- strained frames, such that the resisting 

 link or couple of the one becomes the driving link or couple of 

 the other. Compound machines have dynamic frames so formed 

 that they can be decomposed into the frames of simple machines 

 so connected that the resisting link of one becomes the driving 

 link of the next. If we exclude rigid bars as members, there is 

 only one frame which can be self-strained, and which is yet in- 

 capable of analysis into two distinct self-strained frames. This 

 frame has been already described, and consists of a quadrilateral, 

 with two diagonals, as shown in Figs. 8 and 9, p. 28 1 . There is no 

 essential difference between those two figures, which each consist 

 of a quadrilateral figure 2, 3, 4, 5, having opposed angles joined 

 by the two links 1 and 6. This simplest self-strained frame will be 

 shown to be the dynamic frame of many elementary combinations 

 in machinery. The driving and resisting links may in this 

 frame be arranged in two ways. 1 . They may, as in the examples 

 hitherto given, be represented by two links, such as 1 and 6, 

 2 and 4, or 3 and 5, which are not joined together ; any one of 

 these pairs may be considered as diagonals of a quadrilateral 

 joined by the four remaining links, and each pair may be called 

 conjugate links. For the convenience of description, when these 

 link are placed as 2 and 4, or 1 and 6, Fig. 8, they may be called 

 opposite links. 2. The driving and resisting links may be ad- 

 jacent ; that is to say, they may, as in the case of 1 and 4, or 2 

 and 6, have a common intersection or joint. When the driving 

 and resisting links are adjacent, as 1 and 4, those links which 



