Gear

[12] When a small gear drives a larger one, the mechanical advantage of this ideal lever causes the torque T to increase but the rotational speed ω to decrease.

[citation needed] However, the oldest functioning gears by far were created by Nature, and are seen in the hind legs of the nymphs of the planthopper insect Issus coleoptratus.

In spite of the advantages of metal and plastic, wood continued to be used for large gears until a couple of centuries ago, because of cost, weight, tradition, or other considerations.

Metal gears intended for heavy duty operation, such as in the transmissions of cars and trucks, the teeth are heat treated to make them hard and more wear resistant while leaving the core soft but tough.

On the other hand, gears are more expensive to manufacture, may require periodic lubrication, and may have greater mass and rotational inertia than the equivalent pulleys.

For basic analysis purposes, each gear can be idealized as a perfectly rigid body that, in normal operation, turns around a rotation axis that is fixed in space, without sliding along it.

If the gear is meant to transmit or receive torque with a definite sense only (clockwise or counterclockwise with respect to some reference viewpoint), the action surface consists of N separate patches, the tooth faces; which have the same shape and are positioned in the same way relative to the axis, spaced ⁠1/N⁠ turn apart.

For best operation, each wheel then must be a bevel gear, whose overall shape is like a slice (frustum) of a cone whose apex is the meeting point of the two axes.

Independently of the angle between the axes, the larger of two unequal matching bevel gears may be internal or external, depending the desired relative sense of rotation.

Whereas a regular (nonhypoid) ring-and-pinion gear set is suitable for many applications, it is not ideal for vehicle drive trains because it generates more noise and vibration than a hypoid does.

An imaginary pitch surface (cylinder, cone, or hyperboloid, depending on the relative axis positions) intersects each tooth face along an arc of a helix.

In spur gears, teeth suddenly meet at a line contact across their entire width, causing stress and noise.

A second disadvantage of helical gears is a greater degree of sliding friction between the meshing teeth, often addressed with additives in the lubricant.

Worm-and-gear sets are a simple and compact way to achieve a high torque, low speed gear ratio.

The teeth of antique or artisanal gears that were cut by hand from sheet material, like those in the Antikhytera mechanism, generally had simple profiles, such as triangles.

Cage gears are more efficient than solid pinions,[citation needed] and dirt can fall through the rods rather than becoming trapped and increasing wear.

They can be constructed with very simple tools as the teeth are not formed by cutting or milling, but rather by drilling holes and inserting rods.

[citation needed] In most modern gears, the tooth profile is usually not straight or circular, but of special form designed to achieve a constant angular velocity ratio.

However, two constant velocity tooth profiles are the most commonly used in modern times for gears with parallel or crossed axes, based on the cycloid and involute curves.

The cycloid is in some ways the more interesting and flexible shape; however the involute has two advantages: it is easier to manufacture, and it permits the center-to-center spacing of the gears to vary over some range without ruining the constancy of the velocity ratio.

[51] A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature.

Examples are sun and planet gearing (see below), cycloidal drive, automatic transmissions, and mechanical differentials.

In the illustration, the sun is yellow, the planet red, the reciprocating arm is blue, the flywheel is green and the driveshaft is gray.

Most gears are ideally rigid bodies which transmit torque and movement through the lever principle and contact forces between the teeth.

[52] They can be used in configurations that are not possible for gears that must be physically touching and can operate with a non-metallic barrier completely separating the driving force from the load.

A pair of gears could be designed to have zero backlash, but this would presuppose perfection in manufacturing, uniform thermal expansion characteristics throughout the system, and no lubricant.

For instance, the gear can be split along a plane perpendicular to the axis, one half fixed to the shaft in the usual manner, the other half placed alongside it, free to rotate about the shaft, but with springs between the two-halves providing relative torque between them, so that one achieves, in effect, a single gear with expanding teeth.

Pitch is a property associated with linear dimensions and so differs whether the standard values are in the imperial (inch) or metric systems.

In the nineteenth century, James Clerk Maxwell developed a model of electromagnetism in which magnetic field lines were rotating tubes of incompressible fluid.

As a result, the legs move in almost perfect unison, giving the insect more power as the gears rotate to their stopping point and then unlock.