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Engineering Mechanisms: Gears

What Are Gears:

Gears are mechanisms that mesh together via teeth and are used to transmit rotary motion from one shaft to another. Gears are defined by two important items: radius and number of teeth. They are typically mounted, or connected to other parts, via a shaft or base. 

1. Radius: The gear radius is defined differently depending on the particular section of the gear being discussed. The two most relevant measurements, however, are the root radius and the addendum radius. The root radius is the distance from the center of the gear to the base of the teeth while the addendum radius (also called the "pitch" radius) is the distance from the center of the gear to the outside of the teeth (as circumscribed by the addendum circle below). 


"Root circle" by GearHeads at the English language Wikipedia. Licensed under CC BY-SA 3.0 via Commons.

2. Teeth: The teeth are the portion of the gear that makes contact with another gear. In order for two gears to mesh together the pitch must be the same for all mating pairs. The pitch of a gear is the distance between equivalent points of adjacent teeth. When the teeth of gears mesh properly they prevent slipping and can exhibit efficiencies of up to 98%.

What Are Gears Used For:

Gears can serve as an efficient means to reverse the direction of motion, change rotational speed, or to change which axis the rotary motion is occurring on. The sizes of the gears usually depend on the desired gear ratio and the shaft upon which the gears will be mated.

How Do Gears Work:

1. Reversing Direction of Motion: Any two gears that come into contact with one another will naturally produce an equal and opposite force in the other gear. For example, as the smaller gear pictured below moves clockwise, the larger gear will naturally move counter-clockwise. Any shaft attached to the respective gear will rotate in the direction of the gear it is attached to. 


2. Changing Rotational Speed: Rotational speed is adjusted through the use of a "gear ratio." The gear ratio is the ratio of the radius of the drive or "input" gear (the one that is powering the interaction between the two gears) to the radius of the "output" gear. It can also commonly defined as the number of teeth on the input gear to the number of teeth on the output gear. The larger the gear ratio the more the output rotation will slow. The smaller the gear ratio the more the output rotation's angular velocity will increase. Gear ratios farther from "1" means that the disparity between the gear sizes will be greater. Read more on gear ratios below. 


When discussing a pair of gears, the smaller gear is considered the pinion while the larger is considered the "gear." When two or more gears are linked together it is considered a gear train. The gear being turned by the motor is referred to as the “driver” gear while the last gear, often the output gear, in the system is referred to as the “driven” gear.  Any additional gears in the drive train are “idler” gears.

3. Changing The Axis of Rotation: Perhaps the most common gear for changing rotational axis is the bevel gear (seen below). The bevel gear is commonly used in vehicle differentials to rotate the motion provided by the engine 90 degrees in order to drive the wheels along their proper axis. 


Where Are Gears Used:

Gears can be seen in a variety of applications such as automobile transmissions, clocks, winches, remote control cars, and most other mechanisms that feature some sort of motor. 


Figure 1. Gear train

Changing Speed And Torque With Gears:

Gear ratios are an important aspect of gears defined by the number of teeth on each gear. For example, if a driven gear with 60 teeth is mated to a driver gear with 20 teeth, the gear ratio will be 3:1 and thus the driven gear will rotate once for every three rotations of the driver gear. Torque is also affected by gear ratios. In a simple two-gear gear train, when the driven gear has more teeth than driver gear, the output shaft will rotate slower, but with more torque. The opposite is true when the driver gear has more teeth. The ratio of torque between the gears is the same as the gear ratio which is found by the number of teeth of the driven gear divided by the number of teeth of the driver gear. When using standard gears, like those shown in the picture above, idler gears will have no effect on the overall gear ratio of the gear train. The gear ratio of a gear train is set by the ratio of the number of teeth on the driver gear to the driven gear. However, the introduction of a compound gear in a gear train will have an effect on the overall gear ratio. Compound gears pair dissimilarly sized gears together so they rotate as one. These gears can increase the gear ratio of a gear train significantly, while also not taking up much space.


Figure 2. Compound gear

Types of Gears:

Several different types of gears exist in order to serve different purposes.

1. Spur Gear: The most common type of gear is a spur gear. Spur gears have teeth that protrude outward from the perimeter of the gear. They are mounted on parallel axes and can be used to create a wide range of gear ratios. One drawback of this mechanism is that the collisions between each tooth cause a potentially objectionable noise since the entirety of each tooth meshes at once.


Figure 3. Spur gear

2. Helical Gears: In an effort to reduce the noise from spur gears, helical gears can be utilized. The teeth of helical gears are cut at an angle to the face of the gear so that the tooth engagement begins at one end and gradually transfers to the rest of the tooth as the gear rotates. This design leads to noise reduction and an overall smoother system. The helical pattern of the gears creates a thrust load as the gear teeth come into contact with each other at an angle that is not perpendicular to the shaft axis. Bearings are often incorporated into mechanisms with helical gears in order to support that thrust load.




Figure 4. Helical gear

3. Bevel Gears: Bevel gears can be used in mechanisms to change the axis of rotation. Although they can be designed to work at other angles, they are most often used to change the axis of rotation by 90 degrees. Similar to spur gears, bevel gears may also feature straight or helical teeth. Additionally, hypoid bevel gears can be used when the input and output shafts’ axes do not intersect.


Figure 5. Bevel gears


4. Worm Gears: In mechanisms where large gear reductions are needed, worm gears can be used to achieve gear ratios of greater than 300:1 if necessary. Worm gears also possess a natural locking feature in that the worm can easily turn the gear, but the gear cannot turn the worm due to the shallow angle of the worm causing high friction between the gears. These mechanisms also change the axis of rotation by 90 degrees, but in a different manner than bevel gears. Unlike other gears where the teeth are cut parallel, worm gear teeth are cut almost perpendicular to the shaft’s axis of rotation while mating with a more traditional gear profile.



Figure 6. Guitar tuning keys are worm gears.

 5. Rack & Pinion Gears: Rack and pinion gears are used to convert rotation into linear motion. The circular gear, or pinion, meshes with the rack and the rotation of the pinion causes the rack to translate. The steering mechanism in automobiles utilizes a rack and pinion system. As the pinion rotates, it forces the rack to move linearly. Since the length of the rack is not infinite, these mechanisms are not used in applications that have continuous rotation.


Figure 7. Rack and pinion gear

6. Planetary Gears: Planetary gear sets may be the most interesting mechanism in the gear world. These mechanisms have three main components:  the sun gear, the planet gears and carrier, and the ring gear. Each of these components can serve as the input, output, or can be held stationary. The functional designation of each component determines the gear ratio of the entire system. A set of bands or clutches is often used in order to lock different parts of the device. The direction of rotation can even be reversed by having the sun gear as the input, the ring gear as the output, and the planet gears stationary. Additionally, locking any two components of the mechanisms will lock the whole system into a 1:1 gear ratio. This one set of gears can produce several gear ratios and the most common application for this mechanism is in the transmission of automatic cars. The following equation can be used to compute the different gear ratios of planetary gear sets:


Where N is the number of teeth, ω is angular velocity, and the subscripts R, S, and C, represent the ring, sun, and carrier gears respectively.


Figure 8. Planetary gear set


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