This section is from the book "Spons' Mechanics' Own Book: A Manual For Handicraftsmen And Amateurs", by Edward Spon. Also available from Amazon: Spons' Mechanics' Own Book.
Fig. 1109. A very simple form of the epicyclic train, in which F, G is the arm, secured to the central shaft A, upon which are loosely fitted the bevel-wheels C, D. The arm is formed into an axle for the bevel-wheel B, which is fitted to turn freely upon it. Motion may be given to the two wheels C, D, in order to produce aggregate motion of the arm, or else to the arm and one of said wheels in order to produce aggregate motion of the other wheel.
Fig. 1110. Ferguson's mechanical paradox, designed to show a curious property of the epicyclic train. The wheel A is fixed upon a stationary stud, about which the arm C, D, revolves. In this arm are 2 pins M, N, upon one of which is fitted loosely a thick wheel B gearing with A, and upon the other are 3 loose wheels E, F, G, all gearing with B. When the arm C, D, is turned round on the stud, motion is given to the 3 wheels E, F, G, on their common axis, namely, the pin N; the 3 forming with the intermediate wheel B and the wheel A 3 distinct epicyclic trains. Suppose A to have 20 teeth, F 20, E 21, and G 19; as the arm E, C, D, is turned round F will appear not to turn on its axis, as any point in its circumference will always point in one direction, while E will appear to turn slowly in one, and G in the other direction, which - an apparent paradox - gave rise to the name of the apparatus.
Fig. 1111. Aneroid gauge, known as the Bourdon gauge, from the name of its inventor, a Frenchman. B is a bent tube closed at its ends, secured at C, the middle of its length, and having its ends free. Pressure of steam or other fluid admitted to tube tends to straighten it more or less, according to its intensity. The ends of tube are connected with a toothed sector-piece, gearing with a pinion on the spindle of a pointer, which indicates the pressure on a dial.
Fig. 1112. Pressure gauge now seldom used. Sometimes known as the Magdeburg gauge, from the name of the place where first manufactured. Face view and section. The fluid whose pressure is to be measured acts upon a circular metal disc A, generally corrugated, and the deflection of the disc under the pressure gives motion to a toothed sector e, which gears with a pinion on the spindle of the pointer.
Fig. 1113. An epicyclic train. Any train of gearing the axes of the wheels of which revolve around a common centre is properly known by this name. The wheel at one end of such a train, if not those at both ends, is always concentric with the revolving frame. C is the frame or train-bearing arm. The centre wheel A, concentric with this frame, gears with a pinion F to the same axle, with which is secured a wheel E that gears with a wheel B. If the first wheel A be fixed, and a motion be given to the frame C, the train will revolve round the fixed wheel, and the relative motion of the frame to the fixed wheel will communicate through the train a rotary motion to B on its axis. Or the first wheel as well as the frame may be made to revolve with different velocities, with the same result except as to the velocity of rotation of B upon its axis.
In the epicyclic train as thus described, only the wheel at one extremity is concentric with the revolving frame; but if the wheel E, instead of gearing with B, be made to gear with the wheel D, which, like the wheel A, is concentric with the frame, wo have an epicyclic train, of which the wheels at both extremities are concentric with the frame. In this train we may either communicate the driving motion to the arm and one extreme wheel, in order to produce an aggregate rotation of the other extreme wheel, or motion may be given to the 2 extreme wheels A and D of the train, and the aggregate motion will thus be communicated to the arm.
Fig. 1114. Another simple form of the epicyclic train, in which the arm D carries a pinion B, which gears both with a spur-wheel A and an annular wheel C,both concentric with the axis of the arm. Either of the wheels A, C, may be stationary, and the revolution of the arm and pinion will give motion to the other wheel.
Fig. 1115. Another epicyclic train in which neither the first nor last wheel is fixed. m, n is a shaft to which is firmly secured the train-bearing arm k, I, which carries the 2 wheels d, e, secured together but rotating upon the arm itself. The wheels b and c are united, and turn together freely upon the shaft m,n; the wheels f and g are also secured together, but turn together freely on the shaft m, n. The wheels c, d, e, and f, constitute an epicyclic train, of which c is the first and f the last wheel. A shaft A is employed as a driver, and has firmly secured to it 2 wheels a and h, the first of which gears with the wheel b, and thus communicates motion to the first wheel c of the epicyclic train, and the wheel h drives the wheel g, which thus gives motion to the last wheel f. Motion communicated this way to the two ends of the train produces an aggregate motion of the arm k, I, and shaft m, n.
This train may be modified; for instance, suppose the wheels g and f to be disunited, g to bo fixed to the shaft m, n, and f only running loose upon it. The driving shaft A will, as before, communicate motion to the first wheel c of the epicyclic train by means of the wheels a and b, and will also by h cause the wheel g, the shaft m, n, and the train-bearing arm k, I, to revolve, and the aggregate rotation will be given to the loose wheel /.
Fig. 1116. Another form of epicyclic train, designed for producing a very slow motion. m is a fixed shaft, upon which is loosely fitted a long sleeve, to the lower end of which is fixed a wheel D, and to the upper end a wheel E. Upon this long sleeve there is fitted a shorter one which carries at its extremities the wheels A and H. A wheel C gears with both D and A, and a train-bearing arm m, n, which revolves freely upon the shaft m, p, carries upon a stud at n the united wheels F and G. If A have 10 teeth, C 100, D 10, E 61, F 49, G 41, and H 51, there will be 25,000 revolutions of the train-bearing arm m, n, for one of the wheel C.