How it Works by Archibald Williams is part of the HackerNoon Books Series. You can jump to any chapter in this book here. THE CYCLE.
There are a few features of this useful and in some ways wonderful contrivance which should be noticed. First,
THE GEARING OF A CYCLE.
To a good many people the expression "geared to 70 inches," or 65, or 80, as the case may be, conveys nothing except the fact that the higher the gear the faster one ought to be able to travel. Let us therefore examine the meaning of such a phrase before going farther.
The safety cycle is always "geared up"—that is, one turn of the pedals will turn the rear wheel more than once. To get the exact ratio of turning speed we count the teeth on the big chainwheel, and the teeth on the small chainwheel attached to the hub of the rear wheel, and divide the former by the latter. To take an example:—The teeth are 75 and 30 in number respectively; the ratio of speed therefore = 75⁄30 = 5⁄2 = 2½. One turn of the pedal turns the rear wheel 2½ times. The gear of the cycle is calculated by multiplying this result by the diameter of the rear wheel in inches. Thus a 28inch wheel would in this case give a gear of 2½ × 28 = 70 inches.
One turn of the pedals on a machine of this gear would propel the rider as far as if he were on a high "ordinary" with the pedals attached directly to a wheel 70 inches in diameter. The gearing is raised or lowered by altering the number ratio of the teeth on the two chainwheels. If for the 30tooth wheel we substituted one of 25 teeth the gearing would be—
75⁄25 × 28 inches = 84 inches.
A handy formula to remember is, gearing = T/t × D, where T = teeth on large chainwheel; t = teeth on small chainwheel; and D = diameter of drivingwheel in inches.
Two of the most important improvements recently added to the cycle are—(1) The free wheel; (2) the changespeed gear.
THE FREE WHEEL
is a device for enabling the drivingwheel to overrun the pedals when the rider ceases pedalling; it renders the drivingwheel "free" of the driving gear. It is a ratchet specially suited for this kind of work. From among the many patterns now marketed we select the Micrometer freewheel hub (Fig. 222), which is extremely simple. The ratchetwheel r is attached to the hub of the drivingwheel. The small chainwheel (or "chainring," as it is often called) turns outside this, on a number of balls running in a groove chased in the neck of the ratchet. Between these two parts are the pawls, of halfmoon shape. The drivingwheel is assumed to be on the further side of the ratchet. To propel the cycle the chainring is turned in a clockwise direction. Three out of the six pawls at once engage with notches in the ratchet, and are held tightly in place by the pressure of the chainring on their rear ends. The other three are in a midway position.
When the rider ceases to pedal, the chainring becomes stationary, but the ratchet continues to revolve. The pawls offer no resistance to the ratchet teeth, which push them up into the semicircular recesses in the chainring. Each one rises as it passes over a tooth. It is obvious that driving power cannot be transmitted again to the road wheel until the chainwheel is turned fast enough to overtake the ratchet.
THE CHANGESPEED GEAR.
A gain in speed means a loss in power, and vice versâ. By gearingup a cycle we are able to make the drivingwheel revolve faster than the pedals, but at the expense of control over the drivingwheel. A highgeared cycle is fast on the level, but a bad hillclimber. The lowgeared machine shows to disadvantage on the flat, but is a good hillclimber. Similarly, the express engine must have large drivingwheels, the goods engine small drivingwheels, to perform their special functions properly.
In order to travel fast over level country, and yet be able to mount hills without undue exertion, we must be able to do what the motorist does—change gear. Twospeed and threespeed gears are now very commonly fitted to cycles. They all work on the same principle, that of the epicyclic train of cogwheels, the mechanisms being so devised that the hub turns more slowly than, at the same speed as, or faster than the small chainwheel, according to the wish of the rider.
We do not propose to do more here than explain the principle of the epicyclic train, which means "a wheel on (or running round) a wheel." Lay a footrule on the table and roll a cylinder along it by the aid of a second rule, parallel to the first, but resting on the cylinder. It will be found that, while the cylinder advances six inches, the upper rule advances twice that distance. In the absence of friction the work done by the agent moving the upper rule is equal to that done in overcoming the force which opposes the forward motion of the cylinder; and as the distance through which the cylinder advances is only half that through which the upper rule advances, it follows that the force which must act on the upper rule is only half as great as that overcome in moving the cylinder. The carter makes use of this principle when he puts his hand to the top of a wheel to help his cart over an obstacle.




Now see how this principle is applied to the changespeed gear. The lower rule is replaced by a cogwheel, c (Fig. 223); the cylinder by a cog, b, running round it; and the upper rule by a ring, a, with internal teeth. We may suppose that a is the chainring, b a cog mounted on a pin projecting from the hub, and c a cog attached to the fixed axle. It is evident that b will not move so fast round c as a does. The amount by which a will get ahead of b can be calculated easily. We begin with the wheels in the position shown in Fig. 223. A point, i, on a is exactly over the topmost point of c. For the sake of convenience we will first assume that instead of b running round c, b is revolved on its axis for one complete revolution in a clockwise direction, and that a and c move as in Fig. 224. If b has 10 teeth, c 30, and a 40, a will have been moved 10⁄40 = ¼ of a revolution in a clockwise direction, and c 10⁄30 = ⅓ of a revolution in an anticlockwise direction.
Now, coming back to what actually does happen, we shall be able to understand how far a rotates round c relatively to the motion of b, when c is fixed and B rolls (Fig. 225). b advances ⅓ of distance round c; a advances ⅓ + ¼ = 7⁄12 of distance round b. The fractions, if reduced to a common denominator, are as 4:7, and this is equivalent to 40 (number of teeth on a): 40 + 30 (teeth on a + teeth on c.)
To leave the reader with a very clear idea we will summarize the matter thus:—If T = number of teeth on a, t = number of teeth on c, then movement of a: movement of b:: T + t: T.
Here is a twospeed hub. Let us count the teeth. The chainring (= a) has 64 internal teeth, and the central cog (= c) on the axle has 16 teeth. There are four cogs (= b) equally spaced, running on pins projecting from the hubshell between a and c. How much faster than b does a run round c? Apply the formula:—Motion of a: motion of b:: 64 + 16: 64. That is, while a revolves once, b and the hub and the drivingwheel will revolve only 64⁄80 = ⅘ of a turn. To use scientific language, b revolves 20 per cent. slower than a.
This is the gearing we use for hillclimbing. On the level we want the drivingwheel to turn as fast as, or faster than, the chainring. To make it turn at the same rate, both a and c must revolve together. In one wellknown gear this is effected by sliding c along the spindle of the wheel till it disengages itself from the spindle, and one end locks with the plate which carries a. Since b is now being pulled round at the bottom as well as the top, it cannot rotate on its own axis any longer, and the whole train revolves solidly—that is, while a turns through a circle b does the same.
To get an increase of gearing, matters must be so arranged that the drive is transmitted from the chainwheel to b, and from a to the hub. While b describes a circle, a and the drivingwheel turn through a circle and a part of a circle—that is, the drivingwheel revolves faster than the hub. Given the same number of teeth as before, the proportional rates will be a = 80, b = 64, so that the gear rises 25 per cent.
By means of proper mechanism the power is transmitted in a threespeed gear either (1) from chainwheel to a, a to b, b to wheel = low gear; or (2) from chainwheel to a and c simultaneously = solid, normal, or middle gear; or (3) from chainwheel to b, b to a, a to wheel = high gear. In twospeed gears either 1 or 3 is omitted.
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