70 



THE CI\IL ENGINEER AND ARCHITECT'S JOURNAL. 



[March, 



First, let the crank and connecting rod be in tlie position A, B, C, 

 fig. 3; the crank revolvirg in the direction of the arrow, and Amoving 



Fig. 3. 



towards A„; wh(?n it reaches A™ the position will be that of the 

 dotted line A^ B„ C, the crank and rod being in a straigl}t line ; the 

 momentum will carry the crank on, and as A^ now begins to retro- 

 grade, Tiken it reaches some point A, the crank will have arrived at 

 the position Bj C. The next position is A^ B,, C, tig. 4; and the 

 next Aj B, C, the crank now being coincident with the rod. The 

 next position is A,; B^ C ; and before A reaches A, the crank will 

 have completed one whole revohition. We need not trace the motion 

 after the position A, Bj C; it will be readilv seen that when A re- 

 tnrns, the motion continues as before, and when A has got back to 

 A^ the crank and rod will again be in the jiosition Aj B^ C, and 

 another revolution will have been accomplished. 



Hence one complfte vibration of A will correspond to two revolu- 

 tions of the crank. The only dilTerence betvfepn this crank and the 

 ordinary crank now actually used is its position ; here the pivot about 

 which the crank revolves is opposite the middle point of A's course; 

 at present it is put in a continuation of the line of A's course, and 

 therefore there is only one revolution for every stroke. 



Fig. 5 representi a combination of the idea of figs. 3 and 4 with 



Fig. 5. 



that of fig. 1. In this case the multiplication is four times; the figure 

 requires but little explanation — for every course of A in its groove 

 B will move twice in its groove, for every course of B the crank 

 C D revolves twice, and therefore four times for every stroke of A. 



We have said that it is quite immaterial whether the alternating 

 points move in straight grooves or be attached to beams describing 

 arcs; citlier plan niav be used exclusively, or the two combined in any 

 way found convenient. Fig. G represents a case in which there are no 

 grooves ; the multiplication is here eight times. It must not be sup- 

 posed that thf mechanism is complicated because a great many lines 

 appear in the figure — the dark lines represent the whole machinery, 

 the dotted lines lines merely show the different parts in their extreme 

 positions, Aj Bi is the prime moving beam, oscillating about the pivot 



B ; for every oscillation of A, the point Aj of the second beam Aj Cj 

 will oscillate in its dotted arc twice, owing to the connection by the 



Fig. 6. 



rod Aj Ao ; similarly, for every oscillation of the second beam, the 

 beam A„ C, will oscillate twice ; and lastly, from what we have said 

 before, it will be seen that for everv oscillation of the third beam the 

 crank D, E, will revolve twice ; the motion will therefore, on the 

 whole, have been multiplied eight times. 



Having considered various methods by which reciprocating may 

 produce multiplied circular motion, we may proceed to a method by 

 which circular motion may produce multiplied circular. The method 

 is extremely simple. A B fig. 7, is a crank revolving about A, and 



Fig. 7. 



Fig. 8. 



connected by a rod B D of the same length as A B itself, with a. 

 smaller crank C D about two-thirds or one-half the size of A B ; 

 C D revolves about C, and the distance A C = C D. For every 

 revolution of A B, C D will revolve twice. 



It is rather difficult to shew this by diagrams, but if the reader will 

 exercise his ingenuity in tracing the motion by the successive posi- 

 tions of the two cranks represented in the above figures, he will see 

 the truth of the statement. The same letters mean the same things 

 in all five figures, and the cranks are supposed to move in the same 

 direction as the hands of a clock do. 



In fig. 7 A B is just past its highest position and begins to descend ; 

 CD begins to descend also. (When A B is in the dotted line A i, 

 C D lies along C A.) 



In fig. 8, A B is still descending; C D is also descending, till it 

 reachfs its lowest position C, (/, alter which it rises — A, B, however 

 continues its descent. 



In fig. 9, A B is now almost at its lowest position, and C D has 

 risen almost to its highest again. When A B is actually at the lowest 

 point, C D will have completed one revolution for the half revolution 

 uf AB. 



