Gear - Revision history

Jmdonev: 1 revision imported

2026-08-04T20:43:58Z

1 revision imported

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energy>Jmdonev at 20:21, 4 August 2026

2026-08-04T20:21:34Z

← Older revision		Revision as of 20:21, 4 August 2026
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	[[Category:Done ~~2018~~-05-18]]		[[Category:Done 2026-08-01]]
	[[File:1HZ-timing-gears.jpg\|400px\|thumbnail\|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]		[[File:1HZ-timing-gears.jpg\|400px\|thumbnail\|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]

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	Therefore, if the mechanical advantage of a gear train is 3, that means that the last gear in the train has a radius of 3x that of the first gear. With such a ratio, the input gear can be rotated with 3x less force than is output by the final gear, but in exchange it must be rotating 3x faster than the final gear.		Therefore, if the mechanical advantage of a gear train is 3, that means that the last gear in the train has a radius of 3x that of the first gear. With such a ratio, the input gear can be rotated with 3x less force than is output by the final gear, but in exchange it must be rotating 3x faster than the final gear.

	This relationship for gear trains is fundamentally dependent on the law of [[conservation of energy]]. When analyzing gear trains, this concept is more easily understood by using an analysis of the conserved [[power]] of the system. This analysis relates the [[torque]]s of the gears to their angular velocities~~. A full analysis of this type of exchange can be viewed [http://maelabs.ucsd.edu/mae_guides/machine_design/machine_design_basics/Mech_Ad/mech_ad.htm here] '''BROKEN LINK'''~~.		This relationship for gear trains is fundamentally dependent on the law of [[conservation of energy]]. When analyzing gear trains, this concept is more easily understood by using an analysis of the conserved [[power]] of the system. This analysis relates the [[torque]]s of the gears to their angular velocities.

	==Uses==		==Uses==

Jmdonev: 1 revision imported

2018-05-18T22:53:09Z

1 revision imported

← Older revision	Revision as of 22:53, 18 May 2018
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Jmdonev at 22:47, 11 May 2018

2018-05-11T22:47:57Z

← Older revision		Revision as of 22:47, 11 May 2018
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	[[Category:Done ~~2016~~-04-30]]		[[Category:Done 2018-05-18]]
	[[File:1HZ-timing-gears.jpg\|400px\|thumbnail\|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]		[[File:1HZ-timing-gears.jpg\|400px\|thumbnail\|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]

	<onlyinclude>A '''gear''' is a type of [[simple machine]] that is used to manipulate the magnitude or direction of a [[force]]. Gears are used in combination and are linked together by their teeth - referred to as ''cogs'' - in order to form a "gear train". These gear trains are useful for transferring [[energy]] from one part of a system to another.</onlyinclude> Systems that utilize gears and gear trains include bicycles, cars, electric screwdrivers, and many ~~more~~ common machines.<ref>HowStuffWorks, ''How gear ratios work'' [Online], Available: http://auto.howstuffworks.com/gears3.htm</ref>		<onlyinclude>A '''gear''' (also called a '''cogwheel''') is a type of [[simple machine]] that is used to manipulate the magnitude or direction of a [[force]]. Gears are used in combination and are linked together by their teeth - referred to as ''cogs'' - in order to form a '''"gear train"'''. These gear trains are useful for transferring [[energy]] from one part of a system to another.</onlyinclude> Systems that utilize gears and gear trains include bicycles, cars, electric screwdrivers, and many other common machines.<ref>HowStuffWorks, ''How gear ratios work'' [Online], Available: http://auto.howstuffworks.com/gears3.htm</ref>

	==How they work==		==How they work==
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	[[File:Gears animation.gif\|350px\|thumbnail\|Figure 2: Animation of a gear pair, it can be seen that the smaller gear is spinning faster in order to keep up with the larger number of teeth on the bigger gear.<ref>Wikimedia Commons [Online] Available: http://upload.wikimedia.org/wikipedia/commons/1/14/Gears_animation.gif</ref>]]		[[File:Gears animation.gif\|350px\|thumbnail\|Figure 2: Animation of a gear pair, it can be seen that the smaller gear is spinning faster in order to keep up with the larger number of teeth on the bigger gear.<ref>Wikimedia Commons [Online] Available: http://upload.wikimedia.org/wikipedia/commons/1/14/Gears_animation.gif</ref>]]

	<center><m>MA=\frac{\omega_A}{\omega_B}=\frac{r_B}{r_A}=\frac{N_B}{N_A}</m></center>		<center><math>MA=\frac{\omega_A}{\omega_B}=\frac{r_B}{r_A}=\frac{N_B}{N_A}</math></center>

	where		where
	* <m>N</m> is the number of teeth on the gear,		* <math>N</math> is the number of teeth on the gear,
	* <m>\omega</m> is the angular velocity of the gear and		* <math>\omega</math> is the angular velocity of the gear and
	* <m>r</m> is the radius of the gear.		* <math>r</math> is the radius of the gear.

	Therefore if the mechanical advantage of a gear train is 3, that means that the last gear in the train has a radius of 3x that of the first gear. With such a ratio, the input gear can be rotated with 3x less force than is output by the final gear, but in exchange it must be rotating 3x faster than the final gear.		Therefore, if the mechanical advantage of a gear train is 3, that means that the last gear in the train has a radius of 3x that of the first gear. With such a ratio, the input gear can be rotated with 3x less force than is output by the final gear, but in exchange it must be rotating 3x faster than the final gear.

	This relationship for gear trains is fundamentally dependent on the law of [[conservation of energy]]. When analyzing gear trains, this concept is more easily understood by using an analysis of the conserved [[power]] of the system. This analysis relates the [[torque]]s of the gears to their angular velocities. A full analysis of this type of exchange can be viewed [http://maelabs.ucsd.edu/mae_guides/machine_design/machine_design_basics/Mech_Ad/mech_ad.htm here].		This relationship for gear trains is fundamentally dependent on the law of [[conservation of energy]]. When analyzing gear trains, this concept is more easily understood by using an analysis of the conserved [[power]] of the system. This analysis relates the [[torque]]s of the gears to their angular velocities. A full analysis of this type of exchange can be viewed [http://maelabs.ucsd.edu/mae_guides/machine_design/machine_design_basics/Mech_Ad/mech_ad.htm here] '''BROKEN LINK'''.

	==Uses==		==Uses==
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	The same principle of gears applies to bicycles; going uphill requires lower gears in order to supply more force to counter the force of [[gravity]], and once the rider is back on flat land, they can switch to higher gears in order to generate more speed for their bicycle.		The same principle of gears applies to bicycles; going uphill requires lower gears in order to supply more force to counter the force of [[gravity]], and once the rider is back on flat land, they can switch to higher gears in order to generate more speed for their bicycle.

			== For Further Reading ==
			For further information please see the related pages below:
			*[[Mechanical advantage]]
			*[[Simple machine]]
			*[[Inclined plane]]
			*[[Pulley]]
			*[[Lever]]
			*[[Wheel and axle]]
			*[[Special:Random\|A random page]]

	==References==		==References==
	{{reflist}}		{{reflist}}
	[[Category:Uploaded]]		[[Category:Uploaded]]

Jmdonev: 1 revision imported: From the summer

2016-09-17T22:29:28Z

1 revision imported: From the summer

← Older revision	Revision as of 22:29, 17 September 2016
(No difference)

Jmdonev at 01:12, 23 July 2016

2016-07-23T01:12:28Z

← Older revision		Revision as of 01:12, 23 July 2016
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	[[Category:Done ~~2015~~-06-01]]		[[Category:Done 2016-04-30]]
	[[File:1HZ-timing-gears.jpg\|400px\|thumbnail\|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]		[[File:1HZ-timing-gears.jpg\|400px\|thumbnail\|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]

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	Gears serve two main purposes: increasing '''speed''' or increasing '''force'''. In order to increase one of these, compromises must me made. For example, to increase the speed of a bicycle's wheels the force applied to the pedals must be increased. Similarly, to increase the force on the wheels the pedals must be turned faster. This technique is used when a rider is trying to climb a hill on a bike. This is all related to the conservation laws of energy and power.		Gears serve two main purposes: increasing '''speed''' or increasing '''force'''. In order to increase one of these, compromises must me made. For example, to increase the speed of a bicycle's wheels the force applied to the pedals must be increased. Similarly, to increase the force on the wheels the pedals must be turned faster. This technique is used when a rider is trying to climb a hill on a bike. This is all related to the conservation laws of energy and power.

	Gears are of common use in many systems, but can most easily be recognized in everyday life in the cars we drive. Cars must make use of gears in order to transfer energy from the [[engine]] to the wheels efficiently and safely. An idling engine operates at about 1000 [[rpm]] - if the engine was connected directly to the wheels, this would mean the car must be moving approximately 120 [[kph]]. This means if a car's engine is turned on, it would immediately accelerate to this speed. When the engine moved into ranges with high rpm's - around 7000 - the car would be going 840 kph! Although this seems very fun, it is highly impractical. This is impractical due to the fact that a car requires a large amount of energy to get moving, so an engine trying to go full speed just as it started up wouldn't generate enough force to move the car. Therefore the car makes use of gears in a "gearbox", which starts off by using lower gears that generate more force in order to get the car moving, eventually moving up to higher gears that focus on speed.<ref name=ets/>		Gears are of common use in many systems, but can most easily be recognized in everyday life in the cars we drive. Cars must make use of gears in order to transfer energy from the [[engine]] to the wheels efficiently and safely. An idling engine operates at about 1000 [[rpm]] - if the engine was connected directly to the wheels, this would mean the car must be moving approximately 120 [[kph]]. This means if a car's engine is turned on, it would immediately accelerate to this speed. When the engine moved into ranges with high rpm's - around 7000 - the car would be going 840 kph! Although this seems very fun, it is highly impractical. This is impractical due to the fact that a car requires a large amount of energy to get moving, so an engine trying to go full speed just as it started up wouldn't generate enough force to move the car. Therefore the car makes use of gears in a transmission, or alternatively a "gearbox", which starts off by using lower gears that generate more force in order to get the car moving, eventually moving up to higher gears that focus on speed.<ref name=ets/>

	The same principle of gears applies to bicycles; going uphill requires lower gears in order to supply more force to counter the force of [[gravity]], and once the rider is back on flat land, they can switch to higher gears in order to generate more speed for their bicycle.		The same principle of gears applies to bicycles; going uphill requires lower gears in order to supply more force to counter the force of [[gravity]], and once the rider is back on flat land, they can switch to higher gears in order to generate more speed for their bicycle.

J.williams: 1 revision imported

2015-08-26T21:31:08Z

1 revision imported

← Older revision	Revision as of 21:31, 26 August 2015
(No difference)

J.williams at 16:54, 12 August 2015

2015-08-12T16:54:34Z

New page

[[Category:Done 2015-06-01]]
[[File:1HZ-timing-gears.jpg|400px|thumbnail|Figure 1: A gear train <ref>Wikimedia Commons [Online], Available: http://upload.wikimedia.org/wikipedia/commons/3/3e/1HZ-timing-gears.jpg</ref>]]

<onlyinclude>A '''gear''' is a type of [[simple machine]] that is used to manipulate the magnitude or direction of a [[force]]. Gears are used in combination and are linked together by their teeth - referred to as ''cogs'' - in order to form a "gear train". These gear trains are useful for transferring [[energy]] from one part of a system to another.</onlyinclude> Systems that utilize gears and gear trains include bicycles, cars, electric screwdrivers, and many more common machines.<ref>HowStuffWorks, ''How gear ratios work'' [Online], Available: http://auto.howstuffworks.com/gears3.htm</ref>

==How they work==
Gears use the principle of [[mechanical advantage]], which is the ratio of output force to input force in a system. For gears, the mechanical advantage is given by the ''gear ratio'', which is the ratio of the final gear's speed to the initial gear's speed in a gear train.<ref name=ets>Explain that stuff!, ''Gears'' [Online], Available: http://www.explainthatstuff.com/gears.html</ref> The gear ratio is given by the equation:<ref name=ma>UCSD, ''Gear Ratios and Mechanical Advantage'' [Online], Available: http://maelabs.ucsd.edu/mae_guides/machine_design/machine_design_basics/Mech_Ad/mech_ad.htm</ref>
[[File:Gears animation.gif|350px|thumbnail|Figure 2: Animation of a gear pair, it can be seen that the smaller gear is spinning faster in order to keep up with the larger number of teeth on the bigger gear.<ref>Wikimedia Commons [Online] Available: http://upload.wikimedia.org/wikipedia/commons/1/14/Gears_animation.gif</ref>]]

<center><m>MA=\frac{\omega_A}{\omega_B}=\frac{r_B}{r_A}=\frac{N_B}{N_A}</m></center>

where
* <m>N</m> is the number of teeth on the gear,
* <m>\omega</m> is the angular velocity of the gear and
* <m>r</m> is the radius of the gear.

Therefore if the mechanical advantage of a gear train is 3, that means that the last gear in the train has a radius of 3x that of the first gear. With such a ratio, the input gear can be rotated with 3x less force than is output by the final gear, but in exchange it must be rotating 3x faster than the final gear.

This relationship for gear trains is fundamentally dependent on the law of [[conservation of energy]]. When analyzing gear trains, this concept is more easily understood by using an analysis of the conserved [[power]] of the system. This analysis relates the [[torque]]s of the gears to their angular velocities. A full analysis of this type of exchange can be viewed [http://maelabs.ucsd.edu/mae_guides/machine_design/machine_design_basics/Mech_Ad/mech_ad.htm here].

==Uses==
Gears serve two main purposes: increasing '''speed''' or increasing '''force'''. In order to increase one of these, compromises must me made. For example, to increase the speed of a bicycle's wheels the force applied to the pedals must be increased. Similarly, to increase the force on the wheels the pedals must be turned faster. This technique is used when a rider is trying to climb a hill on a bike. This is all related to the conservation laws of energy and power.

Gears are of common use in many systems, but can most easily be recognized in everyday life in the cars we drive. Cars must make use of gears in order to transfer energy from the [[engine]] to the wheels efficiently and safely. An idling engine operates at about 1000 [[rpm]] - if the engine was connected directly to the wheels, this would mean the car must be moving approximately 120 [[kph]]. This means if a car's engine is turned on, it would immediately accelerate to this speed. When the engine moved into ranges with high rpm's - around 7000 - the car would be going 840 kph! Although this seems very fun, it is highly impractical. This is impractical due to the fact that a car requires a large amount of energy to get moving, so an engine trying to go full speed just as it started up wouldn't generate enough force to move the car. Therefore the car makes use of gears in a "gearbox", which starts off by using lower gears that generate more force in order to get the car moving, eventually moving up to higher gears that focus on speed.<ref name=ets/>

The same principle of gears applies to bicycles; going uphill requires lower gears in order to supply more force to counter the force of [[gravity]], and once the rider is back on flat land, they can switch to higher gears in order to generate more speed for their bicycle.

==References==
{{reflist}}
[[Category:Uploaded]]