(243) The wheel =L= forms a part of the ingenious winding, or, as it is sometimes called, “the differential motion,” invented by Mr. Henry Holdsworth. This is one of the class of epicyclic wheel trains, of which many instances are known and which are very interesting. Fig. 137 is a drawing on an enlarged scale of this motion, the reference letters, with the exception of =L= and =N=, being used for this figure specially. Upon the shaft =A= a fixed cast-iron tube is placed, upon which the wheel =L= and the compound wheel =D N= revolve. The jack shaft =A= revolves in the tube, and on the shaft is fastened a bevel wheel =B= which gears with similar pinions =C= and =E=. These are carried in bearings formed in the wheel =L= at equal distances from its centre, and have perfect freedom of revolution. They also engage with the bevel wheel =D=, cast in one piece with the spur wheel =N=, which is known as the “bobbin wheel.” The latter gears with a spur pinion carried in a double swing frame =O O^{ 1}= (Fig. 134), centred on the jack shaft and attached at its other end to the bobbin rail. In this way, as the latter rises and falls, the swing frame or “swing”—as it is shortly called—oscillates on its centre, and the spur pinion rolls round the bobbin wheel =N=, being always in full gear. By means of a carrier wheel—also borne by the swing—the motion of the bobbin wheel is communicated to a spur wheel on one of the bobbin shafts, and by equal sized pinions on each shaft to the other. Thus, the bobbins are driven by a train of wheels, which are always in gear, no matter what the vertical position of the bobbin may be. The bobbin wheel and its compound bevel run loose upon the cast-iron tube, as previously stated.
(244) The foregoing description of the winding motion will serve to show the principle of its construction, and its mode of action can now be explained. Suppose first, that the bearings of the pinions =C= and =E= are fixed instead of revolving with the wheel =L=, and that the shaft =A= is revolved, it is obvious that the revolution of the wheel =B= would be communicated to =C= and =E=. These would rotate on their axes, and would consequently drive the wheel =D N= at the same speed as =B=, but in the opposite direction. This may be called one pole of the operation of this motion. The other is reached when the plate wheel =L= is rotated in the same direction as =B= at an equal velocity, the wheel =D N= being then carried round in the same direction, and at the same speed as =B=. But if the relative velocity of =L= is reduced, there will be a lessened speed communicated to the wheel =D N= in the proportion of two revolutions less than that of =B= for every revolution of =L=. That is to say, if =B= was running at 20 revolutions per minute and =L= in the same time made one revolution, =D N= would make 18 revolutions. This gives rise to a curious result in working. When the number of revolutions made by =L= is half of those made by =B=, the motion of =D N= entirely ceases, but as the proportion is varied so as to be slower than =B=, the velocity of =D N= is reduced as described, but its direction of rotation will be different. That is, if =L= makes more than half as many revolutions as =B=, the wheel =D N= will move in the same direction as =B=; but if it makes less than half, =D N= will rotate in the opposite direction to =B=. This motion is admirably treated in Professor Goodeve’s “Elements of Mechanism,” where its rationale is fully described, and where the student will find ample explanations of the operation of this class of mechanism. It is sufficient for the present purpose, however, to reiterate that the loss of motion in the bobbin wheel =D N=, is equal to two revolutions of =B= for each one of =L=; and that the direction of motion of =D N= depends on the speed of =L=. It may be said, in amplification, that when =L= revolves at less than half the speed of =B=, the velocity of =D N= increases as that of =L= decreases; while if the plate wheel =L= makes more than one-half the number of turns of =B= the speed of =D N= increases with that of =L=. The middle point thus becomes a sort of zero, a fact which it is desirable to remember. Treated algebraically, the formula may be stated as follows, where _b_ = the velocity of the driving pinion =B=, _l_ = that of the plate wheel =L=, and _n_ that of the bobbin =D N=, if =L= revolves in the same direction as the shaft, _n_ = _b_ - 2_l_; but if in the contrary direction, then _n_ = -_b_ - 2_l_.