Clock Pendulum Parts
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![]() GOOD ANTIQUE PENDULUM FOR CLOCK US $9.99
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![]() ANTIQUE SETH THOMAS SHELF MANTEL CLOCK 1897 BEAUTIFUL BUTTERSCOTCH COLOR US $283.00
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Do you know the theory of watches' PENDULUMS?
I believe in the old China, most family have the clock, which is long and big, like a box, in it there are a big pendulums, which can show the second fly, and make a nice voice to show what time it is.
Most people know its name is pendulums, which can also judge from its shape, but few people know its working theory, include me. Recently I found an article about the pendulums, here share it with you, and hope it can improve your knowledge about the pendulums.
Pendulums, like many other things, may have been invented several times over in different ages, or even in the same. In an old edition of the Encyclopædia Britannica it is said that ‘the ancient astronomers of the east employed pendulums in measuring the times of their observations, patiently counting their vibrations during the phases of an eclipse or the transit of the stars, and renewing them by a little push of the finger when they languished. Gassendi, Riccioli, and others, in more recent times followed their example.'
The application of it to the regulating of clocks however is a different thing, as that required invention as well as observation. To be sure, all that was needed was to omit one of the weights in De Vick's balance, and set it in a vertical instead of a horizontal plane, and it is strange enough that this slight but valuable alteration should have waited three centuries to be made.
It would then assume this form (fig. 7), which is the same as the other in all but the position of the parts and the omission of one arm and weight of the balance. The bent end of the arm (called the fork) is substituted for a weight in this drawing, because it was afterwards found better to hang the pendulum independently, and connect it with that arm, called the crutch, by means of the fork. But I have seen small clocks of the last century, and even some modern French ones, with the crutch itself made into a pendulum by merely putting a ball at the end of it.
There seems no doubt however that the first person who investigated PENDULUMS. 22 and established the mathematical theory and properties of the pendulum was Huyghens, the Dutch philosopher, in the seventeenth century; but it seems equally certain that the first pendulum clock was made for St. Paul's Church in Covent Garden, by Harris, a London clock-maker in 1621, though the credit of the invention was claimed also by Huyghens himself, and by Galileo's son, and Avicenna, and the celebrated Dr. Hooke, the undoubted inventor of the balance spring of watches, and the discoverer of its theory. The main point of Huyghens's discovery seems at first sight a long way off any connection with what we now understand by a pendulum, viz., a weight or bob at the bottom of a long rod, which is hung by a string or a thin spring at the top, and the bob therefore swinging in a circular arc, or something CYCLOIDAL CHEEKS. 23 very near it. For he proved that the curve in which a bob hung by a string of insensible weight must move in order to be isochronous in its vibrations, is not a circle, but a cycloid, or the curve traced out by a point in the rim of a circle rolling upon a straight line, e.g., a nail in the tire of a carriage wheel rolling on a smooth road, or P in circle DEP rolling on BGC in fig. 8; and he showed how a certain other property of the cycloid might be made use of to enable a pendulum bob to describe a cycloidal instead of a circular arc.
It is not worth while to fill these pages with demonstrations which may be found in any mathematical treatise on mechanics, especially as I must assume the reader to have some of the knowledge which is only to be got from such books, in order to understand the demonstrations if I gave them. Therefore we may as well begin at this point, that a body moving by gravity in a cycloid (with the curve downwards, as BPFC in fig.
does describe both large and small arcs in the same time; the reason of which is that the force may be proved to be always in proportion to the distance along the curve from its lowest point point, F. But how is a pendulum bob, hung by a string or wire from a fixed point, to be persuaded to describe a cycloid? It so happens that if a cycloid BFC is cut in two, and one half BF removed as a solid with a convex edge to AC (making AG = FG = DE), and the other half to AB, the end P of a string = AF, fixed at A, and moving between those ‘cycloidal cheeks' will redescribe the old cycloid BFC.
This is mathematically expressed by saying that the involute of a cycloid is another equal cycloid, and therefore also the evolute is; the evolute being the cheeks, and the involute the curve described from them: the proof of this belongs of course to geometry, not mechanics, and is of no consequence to us at present. Huyghens therefore proposed to hang clock pendulums by a string or a thin spring between cycloidal cheeks, CIRCULAR ERROR. 24 and that was for some time thought a very superior method of making clocks. I have no doubt there are some still in existence, as I have seen them.
But after a time it was found that clocks went rather worse with these cheeks than without them; and then it occurred to somebody that the cycloidal theory is only true for what is called in mathematics a simple pendulum, or one in which not only the bob, but the centre of the bob, is alone supposed to have any weight; and of course there is no such thing possible, for the rod must have some thickness, or it is not stiff enough to work, or to be driven by the clock, and if you make the bob very heavy, with the view of rendering the weight of the rod insignificant, then the bob itself must be large, and differs considerably in its mechanical effect from a single imaginary heavy point at its centre.
And besides that, the spring or string cannot be made to act against the cheeks without friction and other disturbing causes; all which things are said to have been proved to produce greater deviations from isochronism than a variation of several degrees in the arc. Indeed we shall see hereafter that the common clock escapements tend to produce an error of their own, which the deviation from cycloidal vibration (commonly called the circular error) is actually useful in counteracting. Nevertheless the cycloidal theory is valuable to this extent: it shows why a common pendulum is very nearly isochronous for different small arcs; for the string AP will evidently describe very nearly the same curve near the bottom F, whether the cheeks are there or not: in other words, a bob vibrating in a small circular arc is almost identical with one in a cycloidal arc described by a string of the same length.
The actual time of a circular vibration cannot be calculated without the aid of the higher branches of the integral calculus, and even then it can only be exhibited in the form of a rather awkward series, which would be little better than useless, except for small arcs; and for them it is quite sufficient to take only the two first terms of it. The whole calculation may be found in Pratt's Mechanics, or in the 8th edition of the Encyclopædia Britannica, under article Pendulum. The first term is simply the expression for a cycloidal vibration, t = pl g the letters of which I have already explained at p. 17, for the conical pendulum, whose time of vibration you now see is less than that of a plane pendulum of the same length in the proportion of cosine of the angle which the conical one makes with the vertical axis.
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