I will conclude this part with a few examples of combinations for which I neglected to find a place in the previous pages.

DIFFERENTIAL DETENTS.

474. Ratchet wheels are sometimes employed in machinery which requires them to be moved through very small angles, or

Fig. 322.

B

But

angles with very small differences. Thus the teeth become weak. this defect can be remedied by the arrangement shown in fig. 322. A is an ordinary ratchet wheel with strong teeth, Bb, Cc, Dd are three detents, of which Bb is holding the wheel by butting against the radial side of the tooth at b. The weight. W suspended by a cord coiled round a pully E is merely introduced to represent the direction of the force acting to resist the rotation of the wheel. The graduations by which the upper teeth are each divided into three equal angles are also given to facilitate the explanation of the principle of this peculiar mechanism.

W

It will be seen that Bb abuts as already said against the radial side of the tooth at 1; the second detent Cc is resting on the upper part of the tooth 2c at a distance of one-third of its pitch, from the radial side of the tooth 2c; the third detent Dd rests at a distance of two-thirds of the pitch from the radial side of the tooth 3d. Neither Cc nor Dd are employed for holding the wheel.

If the wheel be now turned by grasping the lever EF or pulling the small weight w in the direction for raising the weight W through a space of one-third of the pitch of the teeth, the butting end c of the detent Cc will drop into the space 1, 2, behind it and abut against its radial side 2c. If the wheel be again moved, the butting side d of Dd, which was brought by the last motion within one-third of the pitch towards the radial side 3d, will now drop into the space 2, 3, and hold the wheel. A third motion will bring the end b of the detent Bb to drop over the radial side of the tooth marked o. The result is that this wheel, with 20 teeth,

* Vide p. 239.

can be held fast in positions that are measured by three times that number of small angles. The size of the teeth gives strength to resist heavy strains.

By employing more detents, e.g. five, which is readily effected by arranging their butting sides at distances equal to one-fifth of the pitch, instead of one-third as in the figure, smaller angular motions are obtained. These arrangements are employed in power looms.

SAXTON'S DIFFERENTIAL PULLY.*

475. This contrivance was intended to enable a team of horses travelling on an ordinary highway to drive a coach at a rate of 30 miles an hour. It was proposed in

1833 by an

American engineer named Saxton, in the infancy of railroads; but the only journeys it performed were in the Adelaide Gallery, where a working model was exhibited for a considerable time. Like many really valuable kinematic combinations, this contrivance, wholly inapplicable to the purpose that its inventor intended it to fulfil, may be applied with good effect to other machinery. The diagrams, figs. 323 and 324, represent elevations of the face and end of a model of the parts on which the action depends.

A long narrow horizontal board VQ fig. 323, PQ fig. 324, to which a vertical board ST is jointed, sustains the moving parts. These are 1st, the cylindrical wheel W, whose circumference rolls in a groove sunk in the base-board at a, fig. 324, and indicated by the dotted line above VQ in fig. 323. A double-grooved

* Vide Art. 386.

pully is attached to the face of the wheel W. In this model the acting radii AB, AC, of the grooves are as 2 to 3.

At the ends of the vertical board pullies E and F are fixed, of such a diameter as will enable their upper tangent line EF to touch the acting diameter of the small carriage-pully YB, and the lower tangent line GH to touch the diameter XC of the large carriage-pully.

The four pullies, EG, BYB, FH, CXC, are connected by the endless band which is supposed to be extended along the road, upon which the carriage is to be drawn. Suppose now that a force is applied at K to pull the rope band in the direction Kk, the pully at FH causes the lower portion HG to travel in the opposite direction.

At every instant, therefore, the vertical radius AC of the great double pully being solicited by two equal and opposite forces applied to B and C, the radius AC turns about an instantaneous center D bisecting the line BC. Thus the point A is carried in the direction of the radial motion with a velocity

=

AD

BD

× velocity of B. Evidently the point A moves with the velocity (V) of the carriage, and the point B with the velocity (v) of the horse. Let the larger radius AC of the double pully=R, and the lesser vel. of carriage_ V_AD_R+r. vel. of horse v BD R -r

Then

= =

=

radius AB=r.

This principle may be conveniently applied to the communication of motion to various parts of machinery which are mounted on travelling frames, as for example in the manner of the mule carriages of spinning and weaving mechanism. In the footnote*

An Investigation of the Principle of Mr. Saxton's Locomotive Differential Pulley and Description of a Mode of Producing Rapid and Uninterrupted Travelling by Means of a Succession of such Pulleys set in Motion by Horses or by Stationary Steam Engines,' by John Isaac Hawkins (Third Report of British Association, p. 424, 1833). He concludes by stating that 'in this way 388 horses, each acting, at their most effective or walking pace of two miles and a half per hour, on a mile of rope, might easily drive a coach containing eight persons from London to Edinburgh in 13 hours at the rate of 30 miles an hour, the coach passing from truck to truck without stopping, and the truck returning to take another coach every five minutes: 500 passengers a day for the whole distance would be very moderate labour for that number of horses.'

I quote from the third Report of the British Association (1833) a paper written by Mr. J. H. Hawkins, then a leading engineer, which will show the wild ideas concerning travelling by steam which were entertained by the inventors of that day.

screws

TROUGHTON'S DIFFERENTIAL FOOT-SCREW.

476. The portable astronomical instruments which rest upon a flat tripod require, for the purpose of levelling them, that each arm (or rather foot) should be provided with a foot-screw. These are vertical and are tapped with fine-threaded screws, each received in a hole near the extremity of one of the feet. small cup a sunk The lower end of the screw is flat and rests in on the top of the table or support, which is placed on the ground or floor on which the apparatus rests.

The foot-screws are employed to level the instrument, for which purpose the thread must be fine and accurately true in every part.

Troughton's differential screw enables the fineness of the thread to be dispensed with, in the manner shown by fig. 325, which represents a vertical section through the axis of one of the screws made transversely to one of the feet CD.

Fig. 325.

B

Each screw is double, consisting of an outer and inner one, each having a milled head. The outer screw, whose head is A, is tapped into the hole of the tripod foot. The inner screw is finer than the outer one, and is tapped into a hole bored in the axis of the latter. In the instrument described in the 'Memoirs of the Astronomical Society,' vol. i., p. 37, the exterior screw A has 30 turns, and the inner screw B 40 turns in the inch. The action of the contrivance is as follows.

F

(1.) If we turn A and B together, the effect in raising or depressing the end of the tripod is that which is due to the natural of the screw A.

range

(2.) If we turn B alone, it is that which is due to the the screw B.

range

of

(3.) If we turn A alone, the friction of the foot of B in the cup of the support will prevent B from moving, and the effect upon the foot of the tripoa is equal to the difference of the ranges of the two screws.

One complete revolution of A clockwise will cause it to descend into its nut, which is the end of the tripod, through of an inch, which, if A rested on the support, would raise the tripod by that quantity. But A, in descending one revolution, is carried downwards by the thread of B through of an inch, and this motion is also communicated to the tripod, consequently the combined result raises the tripod-end through (1—4)=11⁄2 of an inch.

40

AMERICAN WINDING STOP.

477. The principle of the hunting cog* is employed in American clocks to prevent the over-winding of the spring.

B

Fig. 326.

19

18

For this purpose the winding arbor C has a pinion A of 19 teeth fixed to it close to the front plate. A pinion B of 18 teeth is mounted on a stud so as to be in geer with the former. A radial plate CD is fixed to the face of the upper wheel A, and a similar plate FE to the lower wheel B. These plates terminate outward in semicircular noses D, E, so proportioned as to cause their extremities to abut against each other as shown in the figure when the motion given to the upper arbor by the winding has brought them into the position of contact. The clock being now wound up, the winding arbor and wheel A will begin to turn in the opposite direction. When its first complete rotation is effected the wheel B will have gained one tooth distance from the line of centers, so as to place the stop D in advance of E and thus avoid a contact with E, which would stop the motion. As each turn of the upper wheel increases the distance of the stops, it follows from the principle of the hunting cog, that after 18 revolutions of A and 19 of B the stops will come together again and the clock be prevented from running down too far. The winding key being applied, the upper wheel A will be rotated in the opposite direction, and the winding repeated as above. 478. The following property of numbers is susceptible of appli

* Vide p. 261, above.