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Gears

Basic Terms

Face Width
Pitch Diameter
Face Width is the width of the gear tooth.
Pitch Diameter also known as PD is the invisible line where gear teeth mesh.

Basic Equations

Term
Symbol
Equation
Diametral Pitch
DP
Number of teeth ÷ PD
Outside Diameter
OD
(Number of teeth + 2) ÷ DP
Pitch Diameter
PD
Number of teeth ÷ DP
Number of Teeth
T
(OD x DP) - 2
Gear Ratio
GR
Driven Gear / Driving Gear

Gear Basics

Gears can be used to transfer motion from a spinning object to an object you want to rotate (ex: another shaft, a wheel, an arm, etc.). In addition to transferring motion, gears can be used to change the speed and torque inside a mechanism.
Speed and torque are inversely proportional. This means that as one increases, the other must be reduced. For example, if you decrease speed by 3x then torque will increase by 3x.

Changing Speed & Torque

You can change the speed and torque in a gear train by using different sized gears. The size ratio of two meshed gears will determine how much the speed and torque are changed. If two meshed gears are the same size, then speed and torque will remain the same.

Reducing Speed / Increasing Torque

In order to reduce speed and increase torque you must drive a gear with a smaller gear. For example, a 12T gear is driving an 84T gear. Since the 84T gear is 7x larger than the 12T gear driving it, the speed will be reduced by 7x while the torque will be increased by 7x

Increasing Speed / Reducing Torque

In order to increase speed and reduce torque you must drive a gear with a larger gear. For example, a 48T gear is driving a 24T gear. Since the 24T gear is 2x smaller than the 48T gear driving it, the speed will be increased by 2x while the torque will be reduced by 2x.

Direction Of Rotation

Gears can also be used to change the direction of rotation. Gears spin in the opposite direction of the gear driving it. For example, if you have a gear train with two gears, the direction of rotation will be the opposite of the input. However, if you have three gears in a drivetrain, the direction of rotation at the output will be the same as the input.

When To Use Gears

There are pros and cons to using gears, so it's important to carefully consider your application before electing to use them in your design.
Here are some examples of applications when you should use gears:
  • The items you need to transfer motion to are close together. Generally speaking, gears are better at transferring motion between items that are close together.
  • You need a large speed reduction in a small space. Gears allow you to make a large amount of reduction in a relatively small space compared to timing belts and chain.
  • You need something to spin in opposite directions. Timing belts and chain will always spin in the same direction. So if you need two shafts to spin in opposite directions, gears are one of the easiest ways to do it.

When NOT To Use Gears

  • You need to transfer motion to something far away. Using a long gear train to transfer motion to something far away usually weighs more than just using timing belts or chain.
  • High shock loads. Shock loads are extremely high spikes in torque. These can be caused by a number of things like an arm crashing into something. Shock loads can produce spikes in torque many times higher than the mechanism would normally see. since gears transfer motion through a single tooth, they do not handle shock loads as well as timing belts or chain.

Calculating Center-to-Center Distance

CC=PD12+PD22+ExtraCC=\frac{PD_{1}}{2}+\frac{PD_{2}}{2}+Extra
Use this calculator for finding the correct center to center distance for gears (Gear Distance Calculator).

Extra Spacing

Sometimes you want to add extra spacing to center-to-center distance. The benefit of adding extra spacing to a center-to-center distance is to reduce gear wear and help the gearbox run smoother. However, adding extra spacing does increase backlash in the system.
Extra distance to add for center to center:
  • Exact Spacing: +0.000"
  • Standard Spacing: +.0015-.003"
In the context of gears, backlash is the amount a shaft can rotate before it drives a mating gear. In some applications, like a roller intake or conveyor, backlash doesn't greatly affect the performance of the the system.
However, in some applications like an arm, backlash can be very detrimental since it makes accurate position control much more difficult. A few degrees of backlash can result in inches of variance at the end of a long arm.

Tooth Spacing

Another way to think about gear spacing is the sum of the teeth in the gear ratio. You can change the gears in any gear ratio, as long as the sum of the two gears remains the same. For example:
Driving Gear
Driven Gear
Sum of Both Gears
Ratio
24T
60T
84T
2.5:1
42T
42T
84T
1:1
12T
72T
84T
6:1
In the table above, you can see some examples of possible gears you can use on a gear ratio with "84 Tooth Spacing". As gear teeth are added or removed from the driving gear, the inverse is added to the driven gear, which keeps the sum at 84T.

20DP Gears

All 20DP WCP gears have a 14.5 degree pressure angle, and have the same 3/8" face width. This means it is easy to change gears in your design to find the perfect gear ratio without having to redesign your gearbox.
The specifications shown in the image below will be standard for all our 20DP Hex Gears.
3/8" Hex Bore Gears
1/2" Hex Bore Gears

Hex Bore, Aluminum Gears (Product Page)

  • 3/8" or 1/2" hex bores for use on hex or rounded hex shafts
  • Made from 7075-T6 aluminum with a Teflon infused ceramic coating
  • Overall width 0.500"
Bore
# of Teeth
3/8" Hex
14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52
1/2" Hex
16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84

Hex Bore, Steel Gears (Product Page)

  • 3/8" or 1/2" hex bores for use on hex or rounded hex shafts
  • Made from 4140 Steel with black nitride coating.
  • Overall width 0.500"
Bore
# of Teeth
3/8" Hex
14, 16, 18, 20, 22, 24
1/2" Hex Rounded
16
1/2" Hex
16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64

SplineXL Bore, Aluminum Gears

  • Compatible bore size for the Spline Tube
  • Made from 7075-T6 aluminum with a Teflon infused ceramic coating
  • Overall width 0.375"
Depending on the size, the Spline XL Gears will now have the Motion Pattern and as many additional holes as possible following the 1" pitch.
Bore
# of Teeth
Spline XL
34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84

SplineXL Bore, Steel Gears

  • Compatible bore size for the Spline Tube
  • Made from 4140 Steel with black oxide coating.
  • Overall width 0.375"
  • Gears bigger than a 46T will be pocketed to a .090" Web Thickness.
Steel gears bigger than a 44T will have the alignment notch on the back side.
Depending on the size, the Spline XL Gears will now have the Motion Pattern and as many additional holes as possible following the 1" pitch.
SplineXL
Hex Bore with MotionX
Pocketed Gear
Material
Bore
# of Teeth
Steel
SplineXL
34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84
Steel
1/2" Hex
58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84

Motor Pinions (Product Page)

Motor Pinions are smaller gears that are design to fit on a motor shaft. These gears use a wider 3/4" face width to help strengthen the gear tooth.
  • Includes gear and mounting hardware
  • 14.5° pressure angle
  • Mounts to various sized FRC motors
  • Mounts to other motors or gearboxes with similar shaft sizes
Bore
# of Teeth
8mm SplineXS
10, 11, 12, 13, 14, 15, 16
Falcon Spline
8, 9, 10, 11, 12, 13, 14
CIM Motor
9, 10, 11, 12, 13, 14
RS550/RS775/BAG Motor
6, 8

Addendum Modified Gears

Addendum modifying gears is when you change the tooth profile to reduce undercut, which strengthens the tooth. When gears are addendum modified, it changes its Pitch Diameter, which changes the gear spacing. For example, an addendum modified 11T gear could be on 12T spacing. This means that the gear acts like an 11T gear when doing ratio calculations, but acts like a 12T gear when doing center-to-center calculations.
WCP sells a number of Motor Pinions that are addendum modified. This allows teams to change the tooth count on a motor pinion without having to change the corresponding gear.
Driving Gear (Spacing)
Driven Gear
Spacing Sum
Ratio
10T (12T)
60T
72T
7.2:1
11T (12T)
60T
72T
6.54:1
12T (12T)
60T
72T
5:1
The table above demonstrates how you can use addendum modified motor pinions to change gear ratios without having to change the Driven Gear.

Hex Bore Pocketed Gears (Steel | Aluminum)

Steel Pocketing Aluminum Pocketing
WCP sells pocketed versions of steel and aluminum gears for maximum weight savings. On average each pocketed gear is 50% lighter than the unpocketed version! Pocketed gears have been tested for strength and durability for years on teams such as 254, 973, 1323, and 971. Fun fact, Team 971’s 2016 robot saved about two pounds of weight just by lightening their gears! This was enough for them to add their hanging claw at the Championships!
  • 3/8" or 1/2" hex bores for use on hex shafts
  • 20DP with 14.5 degree pressure angle
  • Overall width 0.500"
  • Pocketed to a .090" Web Thickness
Material
Bore
# of Teeth
Aluminum
1/2" Hex
40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84
Steel
1/2" Hex
30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64

SplineXL Bore Pocketed Gears (Steel)

WCP offers pocketed versions of the steel Spline XL gears for maximum weight savings. On average each pocketed gear is 50% lighter than the unpocketed version!
  • Compatible bore size for the Spline Tube
  • 20DP with 14.5 degree pressure angle
  • Overall width .0375"
  • Pocketed to a .090" Web Thickness
Material
Bore
# of Teeth
Steel
SplineXL
46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84

Bevel Gears (Product Page)

The "standard" swerve drive bevel gear - now with black nitride coating for superior performance.
As time passes and experience grows within the FRC community, previously complicated build techniques are becoming more commonplace. Coaxial swerve drives, once attempted by only the most elite of teams, are now a well documented and accessible solution. Most coaxial swerve drives utilize a bevel gear pair as part of their design. After surveying FRC teams, we found almost everyone is using the same gear.
WCP now offers multiple Bevel Gears that are great for custom swerve modules!

12DP

Bore
# of Teeth
3/8" Hex or 1/2" Hex
15

1.5 Module

Bore
# of Teeth
3/8" Hex
15
1.125" Round
45

Specialty Gears

Dog Gears and Ball Shifter Gears (Product Page)

WestCoast Products offers an assortment of gear sizes, chosen to provide the greatest versatility for gearing options to users. Our sizes were specifically chosen to provide a wide spread of of ratio options useful for FIRST ® Robotics Competition designers. Larger size gears are available so designers can accomplish their entire reduction in a single stage where otherwise they would have used more than one!
Bore
# of Teeth
1/2" Bearing
40, 44, 50
1/2" ThunderHex Bearing
30, 40, 44, 50

10DP Gears (Product Page)

Want to make your own turret and arm gears on your router, but you're struggling to find a gear that'll drive it? Try our 10T 10 DP gear. 10 DP gears have large enough radii that teams can easily manufacture their own 10 DP gears. The 10T 10 DP gear is made of 4140 steel and is meant to drive 10 DP gears teams manufacture on their own.
As an added bonus, you can find STEP files of sample 10 DP gears under the "CAD Files" tab. These models are meant to be a starting point teams can use for their own custom gears. These models feature the true involute gear profile rather than an approximation that many CAD programs generate. This means that your custom manufactured gear will run smoother when meshing with our 10T 10 DP gear.
Material
Bore
# of Teeth
Steel
8mm SplineXS
10
Steel/Aluminum
1/2" Hex
10

32DP Gears (Product Page)

These gears have a Diametral Pitch of 32, which allows for reductions in smaller areas. They are also pocketed for maximum weight savings. Great for lighter load applications and smaller robots!
  • Diametrical Pitch: 32
  • Pressure Angle: 20°
  • Face Width: 7/16"
  • Overall Width: 1/2"
Material
Bore
# of Teeth
Steel
RS775
12
Steel
CIM Motor
20
Aluminum
3/8" Hex
40, 60, 80, 100
Steel
3/8" Hex
20, 40, 60, 80, 100

Gear Rack (Product Page | Manual)

These gear racks are great for powered linear motion! This will give you the positional control that pneumatics can't.
  • Comes in 10DP & 20DP options
  • Made from 6061-T6 Aluminum
  • #10-32 Clearance Holes
  • Both come in 35.5" lengths which allows for infinite stacking
10DP Gear Rack (35.5" L, #10-32 Clearance)
20DP Gear Rack (35.5" L, #10-32 Clearance)