CHAPTER VI.

SUBSTITUTION OF WINDING COILS FOR RUBBING FRICTION.

505. IN 1699 M. Perrault introduced a crane for raising heavy

weights, in which the rubbing friction of the axles of pullies was dispensed with.

Figs. 353, 354 represent the model which I have constructed for lectures, and are sufficient to show the principle of the machine.

Fig. 354 is a perspective sketch, and fig. 353 an elevation.

A pully P, grooved in its circumference, is fixed to a plain cylinder Qq. Fig. 353.

Fig. 354.

E

LO

to be raised, which in the model is represented by a single weight W. The peculiar form of the hook GH is required for the purpose of obtaining two separate suspending eyes at G and H; for if the cords were brought down to a single hook above the weight, the latter would, by increasing the tension of the cords, compel them to twist round each other.

Fig. 353 shows that if the pully be made to rotate clockwise the cords Ee, hH will be simultaneously wound about the cylinder, and also as they are suspended from points D, E, h, g which are wider apart above than below, the winding will be in spirals upon the cylinder, and no superposition will occur.

The weight w is placed in equilibrium by a cord kK coiled about the large pully P as shown in the figures.

ek

he

Neglecting the weight of the pully and cylinder, it is evident that the parallel cords, of which the middle one eE is fixed at its upper extremity and the outer ones pendent, will hold the cylinder in equilibrium at all altitudes if Wx he=w. ek. In the figure 3, and a weight of three pounds balances one, and a small power acting upon w will cause the pully and cylinder with the attached load to mount upwards or descend at the pleasure of the operator. Let the weight of the pully and cylinder=S, their center of gravity is in the axis of the cylinder, and if L=the weight that will counterbalance them we have

This elegant contrivance is manifestly unsuited to the purpose of a crane for lifting heavy weights. But its quiet and steady action in a model shows that it may be applicable to instruments for the frictionless communication of motion in mechanism which is not exposed to great strains.

DIFFERENTIAL PULLY FOR RAISING WEIGHTS.

506. This pully is formed in one piece, with two pully grooves turned in its circumference whose radii are Aa= R and Ab=r. The pivot or axis of this pully is fixed to it, and the whole sustained by a staple Ak which embraces the pully and receives the axis in its eyes as at A. Let the radius of the pivot=p. The load W is suspended from a single pully B.

An endless cord or chain connects the upper pully with the lower pully, and is applied to the pullies in the following order. Beginning at a it passes over the large pully to b, then downward to c under the small pully B, then up to d and over the small upper pully to e and thence hangs down in a loop PQ.

The load W is therefore sustained by the two parts cb, cd of the endless cord, and is only prevented from running down by the friction of the pivot A.

The grasp of a workman's hands at P is sufficient to turn the pully. But when the pully is thus turned it will draw the weight upwards on the side bc, and let it down on the side dc. But as it is drawn up from the side of the larger pully at b and let down by the smaller pully at d, it is really raised by the difference of these motions.

Let R, r, p be the respective radii of the large pully the small pully and the pivot, and ƒ= friction of the pivots in the eyes, we have the moment of friction= Wfp,

W

and the action of the weight W= (R−r).

R-r

2

If be equal to or less than f, the weight

P

W will be supported whatever be its magnitude, but if greater the weight will descend.

Fig. 355.

A

६

k

But the peculiar convenience of this machine is that any heavy load within the strength of its construction may be hauled up and sustained at any height when the raising force is withdrawn, by applying hands to the rope at P, and similarly be let down by pulling at the other side at Q. This pully appears to have been invented in 1830 by Mr. Moore of Bristol, an amateur mechanic; the principle is identical with that of the Chinese windlass * (vide fig. 281, p. 314 above), but is freed from the inconvenience of requiring a great quantity of rope, which is inseparable from that machine.

The differential pully was afterwards described in Dr. Carpenter's

* The Chinese windlass has remained in an incomplete form for ages, like most other Chinese inventions. It is not perhaps generally known, that a windlass of this kind was seen by the Allies to be in use for raising one of the drawbridges of the city of Pekin.' Extract from The Engineer, December 2, 1865.

'Mechanical Philosophy &c.,' 1844, and patents taken by Mr. Weston in 1859, and by others, as appears from a law-suit tried in December 1865, and fully reported in The Engineer,' p. 409, of that year.

The cord must not be allowed to slide in the pully grooves, and therefore in Weston's construction, chains acting on pins or hollows in the grooves are employed.

PART THE FIFTH.

ON UNIVERSAL JOINTS.

CHAPTER I.

HISTORY AND APPLICATIONS.

507. DR. JOHNSON gives seven different definitions of the word 'joint,' of which the second is that which is applicable to mechanism; namely, Hinge; junctures which admit motion of the parts; or rather, of parts that are connected.

But in scientific language I prefer to employ the term 'lines of flexure' for hinge-joints. Such joints were termed in Old English, gimmals or gimbals. The derivation of these words is doubtless from the French gémeaux (gemella, Lat.), twins; which is applied properly not only to a hinge composed of two portions of exactly similar form and size jointed together, but to anything else which is formed of twin pieces of like dimensions united in any manner.'

*

The contrivances which bear the name of universal joints'. have been employed for two different purposes.

First, to connect any object, such as a lamp, mariner's compass, chronometer, or wheel-carriage, with its base or support, in such a manner that when the support is moved into different angular positions the object shall remain parallel to its normal position. The connection must have the property of compelling the two parts, object and base, to preserve one constant point in common, about which their relative motions are performed.

Secondly. As a point of flexure to connect in such a manner, two rods or shafts whose directions meet in a constant point, as to enable one to bend or incline in all aspects with respect to the

* Vide Promptorium, p. 194, by A. Way; published by the Camden Society. London, 1843.