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Sound and Music: Conical

Conical wheels.

Rack work.

Belts, bands, and chains.

Cranks, single and double.

The universal joint.

The ball and socket.

Spiral gearing, is when the cogs or teeth are cut obliquely, to act with slight friction. Conical drums, inverted to each other, increase and decrease velocity, as desirable. Wheels of different diameters, on parallel axis, put in and out of gear, effect the same purpose; also, by an eccentric crown-wheel, which varies the velocity. Tilting-hammers, fulling-hammers, etc., are raised by crans or wipers, which are connected with the axis of motion. A reciprocating crank converts a rectilinear into a circular motion, by two opposed joints which turn two wheels into one another. The encycloidal wheel is a very simple means of converting rectilinear into circular motion. The toggle-joint is a lever of oblique action. A machine merely directs and modifies the force which has been transferred to it. Universally to determine the power of a machine, divide the velocity of the action by the velocity of the power. For the actual effect, multiply this by the force of the power, and deduct a fourth for friction.

In wheel-machinery, to determine the number of revolutions of the last-moved part for one of the first-moved part, divide the product of the cogs in the drivingwheels by the product of the cogs in the driven. Reversing a motion is merely crossing a belt, or making one wheel work into another.

A force of 50 lbs. per second, imparted to a loaded wheel, so accumulates, as to enable it to overcome a resistance of nearly 500 lbs. in ten seconds; and this is a FLY-WHEEL. This not only equalizes power, but it is accumulated by making this large and heavy wheel acquire a great velocity. A vane, or fly, in machinery, has such a surface, that a too rapid motion is corrected by a resistance of the fluid it revolves in. The composition and resolution of forces may be effected by the construction of a parallelogram, whose sides are the forces; and many forces may combined in one resultant, or diagonal, by taking each pair separately, and using the resultant as datum for a new construction. Or, the resultant, or diagonal, in force and direction, may be determined by adding the square of one force to the square of the other, then adding or subtracting (as the forces are, or are not in the same direction) twice the product of the two forces by the natural cosine of the angle of their directions; and of this sum, extracting thes quare-root, which is the resultant force.- Then the angle of the resultant with the major force, is a division of the product of the minor or other force, by the natural sine of their angle, by the major force, added to the product of the natural cosine of their angle by the other force. The quotient is the natural tangent of the angular direction of the resultant, in relation to the first force. Three forces, not in the same plane, are strictly the diagonal of a parallelopipedon, and may be so resolved by construction, etc.; or they may be brought into one plane by multiplying the eccentric force by the cosine of the angle, which its direction makes with the plane of the others.

It is the principle of virtual velocities, that if a system of bodies be in a state of equilibrium, in consequence of the action of any forces whatever, on certain points in the system; then if the equilibrium is for a moment destroyed, the small space moved over by each of these points, will express the virtual velocity of the power applied to it. And, if each force be multiplied into its virtual velocity, the sum of all the products when the velocities are in the same direction, will be equal to the sum of all those in the opposite.

Our moving powers, or first movers, are steam derived from air, currents of water, and wind, descending weights, the elasticity of air, and fibres of steel. We use, besides the muscular re-action of animals against the ground, which we deflect for special purposes, through the superior limbs of bipeds, and the alternate limbs of quadrupeds. In all, action and re-action are equal, and we gain power on the patient by increasing the velocity of the agent: matter and velocity in agent and patient being always equal. The primum mobile is the two-fold motion of the Earth, and the rest are its deflections.

The Mechanical Powers for varying velocity may be reduced to three; but they are usually expressed as six, the Lever, the Wheel and Axle, the Pulley, the Inclined Plane, the Screw, and the Wedge.

In a single movable pulley, the power gained is double. In a continued combination it is twice the pulleys, less 1. motion. axle.

In levers, the power is reciprocally as the lengths on each side to the fulcrum of The power gained in the wheel and axle, is as the radius of the wheel to the On an inclined plane, the power gained is as the length of the plane to the length of the base. The velocity, in descending to that, falling perpendicularly, is as the height to the length, and the force is the same. For a body acquires the same velocity as in falling perpendicularly through the height of the plane; and a body acquires the same velocity in falling down any number of planes, or down a curve, as perpendicularly from the whole height. in I.

A body, moving down an inclined plane, moves 4 times as far in 2 seconds as The power of the screw is as the circumference to the distance of the threads, or 6.2832 that distance.