Joint (mechanics)

“ In order to allow for the finite stiffness and strength of materials, the least distance of the centre of resistance inward from the nearest edge of the joint is made to bear a definite proportion to the depth of the joint measured in the same direction, which proportion is fixed, sometimes empirically, sometimes by theoretical deduction from the laws of the strength of materials. That least distance is called by Moseley the modulus of stability. ”

“ Coupling of Intersecting Axes—Hooke’s Universal Joint.—Intersecting axes are coupled by a contrivance of Hooke’s, known as the “universal joint,” which belongs to the class of linkwork (see fig. 111) . Let O be the point of intersection of the axes OC1, OC2, and θ their angle of inclination to each other. The pair of shafts C1, C2 terminate in a pair of forks F1, F2 in bearings at the extremities of which turn the gudgeons at the ends of the arms of a rectangular cross, having its centre at O. This cross is the link; the connected points are the centres of the bearings F1, F2. ”

“ If the first structure have stability of friction, the second structure will have stability of friction also, so long as the effect of the projection is not to increase the obliquity of the resistance at any joint beyond the angle of repose. ”

“ It is very rarely the case that fixed joints have their pins subject to simple compression in the direction of their length, though they are frequently subject to simple tension in that direction. A good example is the joint between a steam cylinder and its cover, where the bolts have to resist the whole thrust of the steam, and at the same time to keep the joint steam-tight. ”

“ Where great resistances have to be overcome, but where the distance through which the resistance must be urged is short, the lever or the screw is generally found to be the most appropriate means of [Pg 150] increasing power. When, however, the resistance has to be moved a considerable distance, the aid of the pulley, or the wheel and axle, or sometimes of both combined, is called in. The wheel and axle is the form of mechanical power which is generally used when the distance is considerable through which a weight must be raised, or through which some resistance must be overcome. ”

“ When extraneous forces act on the bars themselves the stress in each bar no longer consists of a simple longitudinal tension or thrust. To find the reactions at the joints we may proceed as follows. Each extraneous force W acting on a bar may be replaced (in an infinite number of ways) by two components P, Q in lines through the centres of the pins at the extremities. In practice the forces W are usually vertical, and the components P, Q are then conveniently taken to be vertical also. We first alter the problem by transferring the forces P, Q to the pins. ”

“ When cordage is engaged in the formation of any part of a machine, it has hitherto been considered as possessing perfect flexibility. This is not the case in practice; and the want of perfect flexibility, which is called rigidity, renders a certain quantity of force necessary to bend a cord or rope over the surface of an axle or the groove of a wheel. During the motion of the rope a different part of it must thus be continually bent, and the force which is expended in producing the necessary flexure must be derived from the moving power, and is thus intercepted on its way to the working point. ”

“ The joint then possesses the high strength of a wrought-iron one and at the same time the good frictional qualities of a brass surface. Leakage past moving metal joints can be prevented by cutting the surfaces very accurately to fit each other. ”

“ We first make the plane a b horizontal, and bring down the pulley c so that the cord shall be parallel to the plane; we find that a force must be applied by the cord in order to draw the truck along the plane: this force is of course the friction, and by a suitable weight at p the friction may be said to be counterbalanced. But we cannot expect that the friction will be the same when the plane is horizontal as when the plane is inclined. ”

“ Nor is there any essential difference between the apparatus of Fig. 38 and that of Fig. 20. In Fig. 38 the bar is pulled down by a force at each end, one a weight, the other a spring balance, while it is supported by the upward pressure of the steel edge. In Fig. 20 the bar is being pulled upwards by a force at each end, and downwards by the weight. The two cases are substantially the same. In each of them we find a bar acted upon by a pair of parallel forces applied at its extremities, and retained in equilibrium by a third force. ”

“ A gigantic hammer might force in a nail by the mere weight of the head resting on the nail, but with the help of inertia we drive the nail by blows from a small hammer. We have here inertia aiding in the production of a mechanical power to overcome the considerable resistance which the wood opposes to the entrance of the nail. To drive in the nail usually requires a direct force of some hundreds of pounds, and this we are able conveniently to produce by suddenly checking the velocity of a small moving body.
Fig. ”

“ At the same time, the ligaments of the joints are violently stretched, which must tend to diminish the completeness of the apposition of the joint-surfaces, and thus diminish precision and rapidity of motion. ”

“ The man-made universal joint has a wider range of movement, possesses greater strength, and is more perfect mechanically. A universal joint is a piece of mechanism between two elements, which enables them to be turned, or moved, at any angle relative to each other. ”

“ To facilitate the making of ground and scraped joints it is preferable that the surface of the joint, both on the cylinder and the cover, project from the rest of the flange, from the bolt holes to the bore in the one case, and from the bolt holes to the body in the cover in the other, so that the bearing surface of the joint shall extend from the inside edge of the bolt holes to the cylinder bore only. ”

“ An iron rod a b, capable of revolving round an axis passing through its centre p, is shown in Fig. 28.
The centre of gravity lies at the centre b, and consequently, as is easily seen, the rod will remain at rest in whatever position it be placed. But let a weight r be attached to the rod by means of a binding screw. The centre of gravity of the whole is no longer at the centre of the rod; it has moved to a point s nearer the weight; we may easily ascertain its position by removing the rod from its axle and then ascertaining the point about which it will balance. ”

“ The next class of simple machines, which present themselves to our attention, is that which we have called the cord. If a rope were perfectly flexible, and were capable of being bent over a sharp edge, and of moving upon it without friction, we should be enabled by its means to make a force in any one direction overcome resistance, or communicate motion in any other direction. ”

“ These substances all vary in their elasticity, qualities of density, hardness, and powers of resisting heat, cold and moisture. The duty of a joint must, therefore, be well considered before the material is chosen, after which the recess in which it is to lie must be carefully designed so as to firmly hold the material and with the least possible waste. ”

“ Sliding Contact: Forms of the Teeth of Spur-wheels and Racks.—A line of connexion of two pieces in sliding contact is a line perpendicular to their surfaces at a point where they touch. Bearing this in mind, the principle of the comparative motion of a pair of teeth belonging to a pair of spur-wheels, or to a spur-wheel and a rack, is found by applying the principles stated generally in §§ 36 and 37 to the case of parallel axes for a pair of spur-wheels, and to the case of an axis perpendicular to the direction of shifting for a wheel and a rack. ”

“ In all these systems of pulleys, every wheel has a separate axle, and there is a distinct wheel for every turn of the rope at each block. Each wheel is attended with friction on its axle, and also with friction between the sheave and block. The machine is by this means robbed of a great part of its efficacy, since, to overcome the friction alone, a considerable power is in most cases necessary. ”

“ Any staring or opening of an oblique joint is destructive of the effect of such workmanship, as it is of the strength of the joint which is glued together, and requires absolute contact of the parts to be joined. ”

“ One of the chief advantages of the method of transmitting motion between wheels and axles by straps or cords, is that the wheel and axle may be placed at any distance from each other which may be found convenient, and may be made to turn either in the same or contrary directions. ”

“ When, therefore, a pulling bar, a crank and fly, or any other prime mover, applied at the joint a, carries that joint (say) toward the pillar D, that motion takes place without any rubbing of surface either above or below; for, when the upper section has rolled under the ceiling A H, into the position n p q, the lower section has rolled upon the plate s t, into the position q r s: in such sort that the analogous angles o t, p r of both sectors are always found in the same perpendicular line—or plane—o t, p r ”

“ If the power to be transmitted is so much as to render it desirable to have the strength of the laced joint more nearly approach that of the solid belt than is obtainable with a single row of holes, a double row is provided, as shown in Fig. ”

“ In Figure 5, the driver A is twice the diameter of the driven wheel B, and the latter makes two revolutions for one of A, but the speed at the periphery of the two wheels is the same. A pull of one pound at the point a produces a pressure of one pound at b, and this in turn produces a lift of one pound at c because the levers in each wheel are perfectly balanced, that is, each lever has equal effort and weight arms. ”

“ Like the weighing machine for carriages, the fulcrum of each lever is at one end, and the force is diminished in passing to the spring, in the ratio of the length of its arms. The spring moves a pinion by means of a rack, upon which pinion a hand is placed, indicating by divisions upon a circular dial-plate, the amount of the force employed. ”

“ In order to investigate the amount of power lost by winding the rope upon an axle of this size, I shall place a certain weight—suppose 56 lbs.—upon one hook f, and then I shall ascertain what amount of power hung upon the other hook e will be sufficient to raise f. There is here no mechanical advantage, so that the excess of load which e must receive in order to raise f is the true measure of the friction. ”

“ In this case, there is something transmitted from my hand along the string to the weight in consequence of which the weight moves: that something is a force. I can also move the weight by pushing it with a stick, because force is transmitted along the stick, and makes itself known by producing motion. The archer who has bent his bow and holds the arrow between his finger and thumb feels the string pulling until the impatient arrow darts off. Here motion has been produced by the force of elasticity in the bent bow. ”

“ If the body revolve on a cylindrical rod, the forces A G and B F would produce a strain upon the axis, while the third force in the direction B A would have a tendency to make the body slide along it.
(183.) If the force applied to the body be directed upon the axis, and at right angles to it, no motion can be produced. In this case, if the body be supported by pivots at A and B, the force K L, perpendicular to the line A B, will be distributed between the pivots, producing a pressure on each proportional to its distance from the other. ”

“ The power of the wheel and axle being expressed by the number of times the diameter of the axle is contained in that of the wheel, there are obviously only two ways by which this power may be increased ”

“ Balanced Lateral Pressure of Guides and Bearings.—The most important part of the lateral pressure on a piece of mechanism is the reaction of its guides, if it is a sliding piece, or of the bearings of its axis, if it is a turning piece; and the balanced portion of this reaction is equal and opposite to the resultant of all the other forces applied to the piece, its own weight included. There may be or may not be an unbalanced component in this pressure, due to the deviated motion. ”

“ However, drawing an object on wheels is a decided improvement over sliding it along the road, for two reasons: the sliding friction at the axle is reduced to a minimum by choosing materials that will slide upon each other with comparatively little resistance, by polishing them smooth and by lubricating them. But even if these precautions were not taken there would be a distinct advantage in the use of wheels because of the relatively shorter travel at the axle than at the rim of the wheel. ”

“ We have defined the moment of a force (Art. 64) , and proved that the moments of two parallel forces about the point of application of their resultant are equal.
255. In the lever of the first order there are two parallel forces, one at each end; these are compounded into a resultant, and it is necessary that this resultant be applied exactly over the steel edge or fulcrum in order that the bar may be maintained at rest. In the levers of the second and third orders, the power and the load are two parallel forces acting in opposite directions ”

“ Let it be required to find the vertical force which must act at the pitch radius of the last wheel t to balance exactly a force ƒs acting vertically downwards on the arm at the point indicated in the figure. The two links concerned are the last wheel t and the arm s, the wheel r being the fixed link of the mechanism. The virtual centres Ors, Ost are at the respective axes of the wheels r and t, and the centre Ort divides the line through these two points externally in the ratio of the train of wheels. ”