Gear
From Combat Robot
A gear wheel is a wheel with teeth around its circumference, the purpose of the teeth being to mesh with similar teeth on another mechanical device -- possibly another gear wheel -- so that force can be transmitted between the two devices in a direction tangential to their surfaces. A non-toothed wheel can transmit some tangential force but will slip if the force is large; teeth prevent slippage and allow the transmission of large forces.
A gear can mesh with any device having teeth compatible with the gear's teeth. Such devices include racks and other non-rotating devices; however, the most common situation is for a gear to be in mesh with another gear. In this case rotation of one of the gears necessarily causes the other gear to rotate. In this way, rotational motion can be transferred from one location to another (that is, from one shaft to another). While gears are sometimes used simply for this reason -- to transmit rotation to another shaft -- perhaps their most important feature is that, if the gears are of unequal sizes (diameters), a mechanical advantage is also achieved, so that the rotational speed, and torque (rotational force), of the second gear are different from that of the first. In this way, gears provide a means of increasing or decreasing a rotational speed, or a torque. This is a highly useful property.
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Mechanical advantage
The interlocking of the teeth in a pair of meshing gears means that their circumferences necessarily move at the same rate of linear motion (eg., metres per second, or feet per minute). Since rotational speed (eg., measured in revolutions per second, revolutions per minute, or radians per second) is proportional to a wheel's circumferential speed divided by its radius, we see that the larger the radius of a gear, the slower will be its rotational speed, when meshed with a gear of given size and speed. The same conclusion can also be reached by a different analytical process: counting teeth. Since the teeth of two meshing gears are locked in a one to one correspondance, when all of the teeth of the smaller gear have passed the point where the gears meet -- ie., when the smaller gear has made one revolution -- not all of the teeth of the larger gear will have passed that point -- the larger gear will have made less than one revolution. The smaller gear makes more revolutions in a given period of time; it turns faster. The speed ratio is simply the ratio of the numbers of teeth on the two gears. (Or, actually, its reciprocal.)
- speed A : speed B : : number of teeth B : number of teeth A
This ratio is known as the gear ratio.
The torque ratio can be determined by considering the force that a tooth of one gear exerts on a tooth of the okeen other gear. Consider two teeth in contact at a point on the line joining the shaft axes of the two gears. In general, the force will have both a radial and a circumferential component. The radial component can be ignored: it merely causes a sideways push on the shaft and does not contribute to turning. The circumferential component causes turning. The torque is equal to the circumferential component of the force times radius. Thus we see that the larger gear experiences greater torque; the smaller gear less. The torque ratio is equal to the ratio of the radii. This is exactly the inverse of the case with the velocity ratio. Higher torque implies lower velocity and vice versa. The fact that the torque ratio is the inverse of the velocity ratio could also be inferred from the law of conservation of energy. Here we have been neglecting the effect of friction on the torque ratio. The velocity ratio is truly given by the tooth or size ratio, but friction will cause the torque ratio to be actually somewhat less than the inverse of the velocity ratio.
A gearbox is not an amplifier. Conservation of energy requires that the amount of power delivered by the output gear or shaft will never exceed the power applied to the input gear, regardless of the gear ratio. Work equals the product of force and distance, therefore the small gear is required to run a longer distance and in the process is able to exert a larger twisting force or torque, than would have been the case if the gears were the same size. There is actually some loss of output power due to friction.
Spur gears
Spur gears are the simplest, and probably most common, type of gear . Their general form is a cylinder or disk (a disk is just a short cylinder). The teeth project radially, and with these "straight-cut gears", the leading edges of the teeth are aligned parallel to the axis of rotation. These gears can only mesh correctly if they are fitted to parallel axles.
Bevel gears
Bevel gears are essentially conically shaped, although the actual gear does not extend all the way to the vertex (tip) of the cone that bounds it. With two bevel gears in mesh, the vertices of their two cones lie on a single point, and the shaft axes also intersect at that point. The angle between the shafts can be anything except zero or 180 degrees. Bevel gears with equal numbers of teeth and shaft axes at 90 degrees are called miter gears.
Crown gear
A crown gear is a gear whose teeth project at right angles to the plane of the wheel; in their orientation the teeth resemble the points on a crown.
Worm gear
A worm is a gear that resembles a screw. It is a species of helical gear, but its helix angle is usually somewhat large(ie., somewhat close to 90 degrees) and its body is usually fairly long in the axial direction; and it is these attributes which give it its screw like qualities. A worm is usually meshed with an ordinary looking, disk-shaped gear, which is called the "gear", the "wheel", the "worm gear", or the "worm wheel". The prime feature of a worm-and-gear set is that it allows the attainment of a high gear ratio with few parts, in a small space. Helical gears are, in practice, limited to gear ratios of 10:1 and under; worm gear sets commonly have gear ratios between 10:1 and 100:1, and occasionally 500:1. In worm-and-gear sets, because the worm's helix angle is large, the sliding action between teeth is considerable, and the resulting frictional loss causes the efficiency of the drive to be usually less than 90 percent, sometimes less than 50 percent.
A worm may have as few as one tooth. If that tooth persists for several turns around the helix, the worm will appear, superficially, to have more than one tooth, but what one in fact sees is the same tooth reappearing at intervals along the length of the worm. The usual screw nomenclature applies: a one-toothed worm is called "single thread" or "single start"; a worm with more than one tooth is called "multiple thread" or "multiple start".
In a worm-and-gear set, the worm can always drive the gear. However, if the gear attempts to drive the worm, it may or may not succeed. Particularly if the lead angle is small, the gear's teeth may simply lock against the worm's teeth, because the force component circumferential to the worm is not sufficient to overcome friction. Whether this will happen depends on a function of several parameters; however, an approximate rule is that if the tangent of the lead angle is greater than the coefficient of friction, the gear will not lock. Worm-and-gear sets that do lock in the above manner are called "self locking". The self locking feature can be an advantage, as for instance when it is desired to set the position af a mechanism by turning the worm and then have the mechanism hold that position. Tuning gears on stringed musical instruments work that way.
Rack and pinion
A rack is a toothed bar or rod that can be thought of as a sector gear with an infinitely large radius of curvature. Torque can be converted to linear force by meshing a rack with a pinion: the pinion turns; the rack moves in a straight line. Such a mechanism is used in automobiles to convert the rotation of the steering wheel into the left-to-right motion of the tie rod(s). Racks also feature in the theory of gear geometry, where, for instance, the tooth shape of an interchangeable set of gears may be specified for the rack (infinite radius), and the tooth shapes for gears of particular actual radii then derived from that.
