## Introduction: Basic Gear Mechanisms

Cars, clocks, and can openers, along with many other devices, use gears in their mechanisms to transmit power through rotation. Gears are a type of circular mechanical device with teeth that mesh to transmit rotation across axes, and they are a very valuable mechanism to know about as their applications range far and wide. In this Instructable I'll go over some basic gear concepts and interesting mechanisms, and hopefully you'll be able to design your own gear systems and make stuff like this!

## Step 1: What Are Gears?

A gear is a wheel with teeth around its circumference. Gears are usually found in sets of two or more, used to transmit rotation from the axis of one gear to the axis of another. The teeth of a gear one one axis mesh with the teeth of a gear on another, thus creating a relationship between the rotation of the two axes. When one axis is spun, the other will too. Two gears of different sizes will make their two axes spin at different speeds, which you'll learn about, along with different types of gears and places they're used.

## Step 2: Why Use Gears?

Gears are a very useful type of transmission mechanism used to transmit rotation from one axis to another. As I mentioned previously, you can use gears to change the output speed of a shaft. Say you have a motor that spins at 100 rotations per minute, and you only want it to spin at 50 rotations per minute. You can use a system of gears to reduce the speed (and likewise increase the torque) so that the output shaft spins at half the speed of the motor. Gears are commonly used in high load situations because The teeth of a gear allow for more fine, discrete control over movement of a shaft, which is one advantage gears have over most pulley systems. Gears can be used to transmit rotation from one axis to another, and special types of gears can allow for the transfer of motion to non-parallel axes.

## Step 3: Parts of a Gear

There are a few different terms that you'll need to know if you're just getting started with gears, as listed below. In order for gears to mesh, the diametral pitch and the pressure angle need to be the same.

**Axis: **The axis of revolution of the gear, where the shaft passes through

**Teeth: **The jagged faces projecting outward from the circumference of the gear, used to transmit rotation to other gears. The number of teeth on a gear must be an integer. Gears will only transmit rotation if their teeth mesh and have the same profile.

**Pitch Circle: **The circle that defines the "size" of the gear. The pitch circles of two meshing gears need to be tangent for them to mesh. If the two gears were instead two discs that drove by friction, the perimeter of those discs would be the pitch circle.

**Pitch Diameter:** The pitch diameter refers to the working diameter of the gear, a.k.a., the diameter of the pitch circle. You can use the pitch diameter to calculate how far away two gears should be: the sum of the two pitch diameters divided by 2 is equal to the distance between the two axes.

**Diametral Pitch: **The ratio of the number of teeth to the pitch diameter. Two gears must have the same diametral pitch to mesh.

**Circular Pitch: **The distance from a point on one tooth to the same point on the adjacent tooth, measured along the pitch circle. (so that the length is the length of the arc rather than a line).

**Module: **The module of a gear is simply the circular pitch divided by pi. This value is much easier to handle than the circular pitch, because it is a rational number.

**Pressure Angle: **The pressure angle of a gear is the angle between the line defining the radius of the pitch circle to the point where the pitch circle intersects a tooth, and the tangent line to that tooth at that point. Standard pressure angles are 14.5, 20, and 25 degrees. The pressure angle affects how the gears contact each other, and thus how the force is distributed along the tooth. Two gears must have the same pressure angle to mesh.

## Step 4: Calculating Gear Ratios

As I mentioned previously, gears can be used to decrease or increase the speed or torque of a drive shaft. In order to drive an output shaft at a desired speed, you need to use a gear system with a specific gear ratio to output that speed.

The **gear ratio** of a system is the ratio between the rotational speed of the input shaft to the rotational speed of the output shaft. There are a number of ways to calculate this in a two gear system. The first is via the number of teeth (N) on each gear. To calculate the gear ratio (R), the equation is as follows:

R = ^{N2}⁄_{N1}

Where N2 refers to the number of teeth on the gear linked to the output shaft, and N1 refers to the same on the input shaft. The left gear in the first image above has 16 teeth, and the right gear has 32 teeth. If the left gear is the input shaft. then the ratio is 32:16, which can be simplified to 2:1. This means that for every 2 rotations of the left gear, the right gear rotates once.

The gear ratio can also be calculated with the pitch diameter (or even the radius) with basically the same equation:

R = ^{D2}⁄_{D1}

Where D2 is the pitch diameter of the output gear, and D1 is the pitch diameter of the input gear.

The gear ratio can also be used to determine the output torque of the system. Torque is defined as the tendency of an object to rotate about its axis; basically, the turning power of a shaft. A shaft with more torque can turn larger things. The gear ratio R is also equal to the ratio between the torque of the output shaft and that of the input shaft. In the example above, although the 32 tooth gear spins more slowly, it outputs twice the turning power as the input shaft.

In a larger system of gears with multiple gears and shafts, the overall ratio of the system is still the ratio of the speeds of the input and output shafts, there are just more shafts in between. To calculate the overall ratio, it is easiest to start by identifying the gear ratio of each set. Then, starting with the set driving the output shaft and working backward, you can multiply the first value in the ratio (the input shaft's speed) by the values corresponding to the ratio of the next gear set, and use the value obtained from the input shaft's speed after the multiplication as your new input speed for a net ratio. This may be a bit confusing, so an example is provided below.

Say you had a gear train consisting of three sets of gears, one set coming from a motor with a 2:1 ratio, and another set stemming off the output shaft of the first set with a 3:2 ratio, and the next set driving the output of the system, with another 2:1 ratio. To calculate the gear ratio of the overall system, you would start with the last ratio, 2:1. Because the smaller gear on the 3:2 set and the larger gear on the 2:1 set are currently "equal" because of the ratios, the ratio of the input shaft of the second set of gears to the overall system output shaft is 3:1. We do that again, multiplying the ratio of the first gear set by 3 (to get 6:3), and combining it with our net ratio (currently 3:1), to get the overall ratio of the system, 6:1.

## Step 5: Types of Gears

There are a handful of different types of gears and gear mechanisms, and this Instructable definitely doesn't cover all of them. I hope that this guide will give you a sense for how you can use gears to improve your mechanical design techniques. In the next few steps I'll be starting with some of the simplest types of gears and gear mechanisms and going into some of the more complicated, interesting ones as well. If you're really interested in learning more, I would suggest you check out this book, 507 Mechanical Movements, as it comes with a lot of really neat mechanisms!

## Step 6: Spur Gears

Spur gears are the most common and simplest type of gear. Spur gears are used to transfer motion from one shaft to a parallel shaft. The teeth are cut straight up and down, parallel to the axis of rotation. When two adjacent spur gears mesh, they spin in opposite directions. These gears are most commonly used because they can be easily cut on a 3 axis machine like a laser cutter, waterjet, or router. Other types of gears require more precise and more complicated machining procedures.

## Step 7: Gearboxes

Before I go any further, I first want to introduce the gearbox. Gearboxes take the rotation of an input shaft, usually the axle of a motor, and through a series of gears alter the speed and power coming from the input shaft to turn an output shaft at a desired speed or torque. Gearboxes are usually classified in terms of their overall speed ratio, the ratio of the speed of the input shaft to the speed of the output shaft.

## Step 8: Bevel Gears

Bevel gears are a type of gear used to transmit power from one axis to another non-parallel axis. Bevel gears have slanted teeth, which actually makes the shape of their "pitch diameter" a cone. This is why most bevel gears are classified based on the distance from the rear face of the gear to the imaginary tip of the cone that the gear would form if its teeth extended out. In order for two bevel gears to mesh, the tips of each imaginary cone should meet at the same vertex. When two bevel gears are the same size and turn shafts at 90 degree angles, they are called **mitre gears**.

## Step 9: Rack and Pinion

The rack and pinion converts the rotational motion of a gear (the pinion) to the linear motion of a rack. The pinion is just like any other spur gear, and it meshes with the rack, which is a rail with teeth. The rack slides continuously as the gear rotates.

## Step 10: Internal Gears

An internal gear is simply a gear with teeth on the inside rather than the outside. Internal gears can be used to reduce the amount of space a drive train takes up, or allow something to pass through the center of the axis as the gear is turning. Unlike normal spur gears, an internal gear rotates in the same direction as the normal spur gear spinning it. For the most part, internal gears are used for planetary gearboxes, which I'll talk about next.

## Step 11: Planetary Gearboxes

A planetary gearbox is a specific type of gearbox that uses internal gears. The main components of a planetary gearbox include the sun gear, which is in the center of the gearbox, usually connected to the input shaft of the system. The sun gear rotates a few planet gears, which all simultaneously rotate a large internal gear, called the ring or annular gear. The planet gears are usually constrained by a carrier to keep them from spinning around the sun gear. Planetary gearboxes can take on higher laods than most gearboxes because the load is distributed among all of the planet gears, as opposed to just one spur gear. These gearboxes are great for large gear reductions in small spaces, but can be costly and need to be well lubricated because of their design complexity.

## Step 12: Worm Gears

A worm gear is a gear driven by a worm, which is a small, screw-like piece that meshes with the gear. The gear rotates on an axis perpendicular, but on a different plane than, the worm. With each rotation of the worm, the gear rotates by one tooth. This means that the gear ratio of a worm gear is always N:1, where N is the number of teeth the gear has. While most gears have circular pitch, a worm has linear pitch, which is the distance from one turn in the spiral to the next.

Worm gears can thus be used to drastically reduce the speed and increase the torque of a system in only one step in a small amount of space. A worm gear mechanism could create a gear ratio of 40:1 with just a 40 tooth gear and a worm, while when using spur gears to do the same, you would need a small gear meshing wit another 40 times its size.

Because the worm is a spiral, worm gears are almost impossible to back-drive. What this means is that if you tried spinning the system by its output shaft (on the worm gear) instead of its input shaft (on the worm), then you would not be able to. When a worm gear drives, the spiral spins and slowly inches each tooth forward. If you back-drove the system, the gear would be pushing against the side of the threads without actually turning them. This makes worm gears very valuable in mechanical systems because the axle cannot be manipulated by an external force, and it reduces the backlash and the play in the system.

## Step 13: Helical and Herringbone Gears

Helical gears are a more efficient type of spur gear. The teeth are set at an angle to the axis of rotation, so they end up curving around the gear instead of straight up and down like spur gears. Helical gears can be mounted between parallel axes, but can also be used to drive non-parallel axes as long as the angled teeth mesh.

While the teeth on spur gears engage all at once, in that the entire face of a tooth on one gear fully contacts the face of a tooth on an adjacent gear as soon as they mesh, the teeth on helical gears gradually slide into each other. Because of this, helical gears are much better suited for high load and high speed situations. The disadvantage of helical gears is that they require thrust bearings, because when the teeth of a helical gear mesh, they produce an axial thrust pushing the gear along its axis of rotation.

This problem can be fixed with **herringbone gears**, which are basically two helical gears joined together, with their teeth angled in opposite directions. This eliminates the sideways force that helical gears produce because the axial force from one side of the herringbone gear cancels out the force on the other side. Herringbone gears, because of their geometry, are harder to manufacture than helical gears.

## Step 14: Cage and Peg Gears

Cage and peg gears are a certain style of gear mechanisms that are much easier to make, because they can be made cheaply out of wooden boards and dowels. However, they are not very good for high speed or high load situations because they are usually made with a lot of backlash and wiggle-room. Cage and peg gears are mostly used to transmit rotation between perpendicular axes. A peg gear is basically a disc with short pegs sticking out from it around its circumference (to form a spur gear), or on its face parallel to the axis of rotation (to form a bevel gear). The pegs in these gears act as the teeth, and contact one another to spin each of the gears. A cage consists of two discs with pegs running between them parallel to the axis of rotation. A cage gear can be used like a worm gear, as each of the dowels on the gear contact the pegs on a normal peg gear. However, this system can be driven from either end.

## Step 15: Mutilated Gears

A mutilated gear is a gear whose tooth profile does not extend all the way around its pitch circle. Mutilated gears can be useful for many different purposes. In some cases, you may not need the entire tooth profile of a gear because the gear may never need to rotate 360 degrees, and you could have a linkage, beam, or other mechanism as part of the mutilated side of the gear. In other cases, you may want the mutilated gear to rotate 360 degrees, but you may not want it to be turning another gear all the time. If you rotate a mutilated gear with half its teeth missing, whose teeth mesh with a full spur gear at one rotation every 30 seconds, the spur gear will turn for 15 seconds, and then stay put for 15 seconds. In this way you can turn continuous rotational motion into discrete rotational motion, meaning that the input shaft turns continuously and the output shaft turns a little, and then stops, then turns again, then stops again, repeatedly.

## Step 16: Non-Circular Gears

Although rare in industry, non-circular gears are pretty interesting mechanisms. The diameter of the gears where they are contacting each other change as the gears rotate, so the output speed of the system oscillates as the gears rotate. Non-circular gears can take almost any shape. If the two axes constraining the gears are fixed, then the sum of the radii of the gears at the point where they mesh should always be equal to the distance between the two axes.

## Step 17: Ratchets

A ratchet is a fairly simple mechanism that only allows a gear to turn in one direction. A ratchet system consists of a gear (sometimes the teeth are different than the standard profile) with a small lever or latch that rotates about a pivot point and catches in the teeth of the gear. The latch is designed and oriented such that if the gear were to turn in one direction, the gear could spin freely and the latch would be pushed up by the teeth, but if the gear were to spin in the other direction, the latch would catch in the teeth of the gear and prevent it from moving.

Ratchets are useful in a variety of applications, because they allow force to be applied in one direction but not the other. These systems are common on bikes (how you can pedal forward to turn the wheels, but if you pedal backward the wheel will spin freely), some wrenches, and large winches that reel in loads.

## Step 18: Clutches

Clutches are mechanisms found primarily in cars and other road vehicles, and they are used to change the speed of the output shaft, as well as disengage or engage the turning of the output shaft. A clutch mechanism involves at least two shafts, the input shaft, driven by a power source, and the output shaft, which drives the final mechanism. As an example, I'll explain a simple 2 gear clutch mechanism, referencing the image above. The input shaft would have two gears on it of different sizes (the two blue gears on the top shaft), and the output shaft contains two gears that mesh with the gears on the input shaft (the red and green gears), but can rotate freely around the output shaft, so they do not drive it. A clutch disc (the blue grooved piece in the middle) sits between the two gears, rotates with the output shaft, and can slide along it. If the clutch disc is pressed against the red gear, the output shaft would engage and turn at the speed defined by the gear ratio of that set of gears (3:2). If the clutch disc presses against the green gear, the output shaft drives at a different gear ratio, defined by that gear set (2:3). If the clutch disc sits between the two gears, then the output shaft is in neutral and is not being driven.

The clutch disc can engage with the gears in a few different ways. Some clutch discs engage via friction, and have friction pads mounted to their sides as well as the sides of the gears. Other clutch discs, like the one in the image above, are toothed, and they mesh with specific teeth on the faces of the gears.

## Step 19: Differentials

A gear differential is a pretty interesting mechanism involving a ring bevel gear and four smaller bevel gears (two sun gears and two planet gears that orbit around them), acting sort of like a planetary gearbox. It is used mostly on cars and other vehicles, because it has one input shaft that drives two output shafts (which would connect to the wheels), and allows for the two output shafts to spin at different velocity if they need to. It ends up that the average of the rotational velocities of each output shaft always has to equal the rotational velocity of the ring gear.

I'll explain how a differential works using the images above. The input shaft spins the yellow bevel gear, which spins the green bevel ring gear. A carriage is fixed to the ring gear that spins with it. Both the carriage and the ring gear rotate around (but do not directly turn) the axis of the red output shafts. The two blue bevel gears turn in big circles around the central axis, the axis the output shafts go through. Lets imagine this differential sits with the output shafts connected to the back two wheels of a car. If the car is going straight, the two blue bevel gears will spin around the output shafts, because of the rotation of the carriage, without rotating about their own axis. Their teeth will push the two red gears at the same speed, each connected to their respective output shafts. Thus, the wheels spin at the same speed and the car goes straight. You'll notice the blue gears have the ability to spin about their axis though, which is important to the mechanism. Keep reading!

Should the car turn, then the two wheels will want to spin at different speeds. The inner wheel will want spin at a velocity slower than the outer one because it is closer to the center point of the car's turn. If the two wheels were connected on the same shaft, then the car would have a difficult time turning: one wheel would want to spin slower than the other, so it would drag. With the differential gear mechanism, the two shafts not only allow the wheels to spin at their own speeds, but also are still powered by the input shaft. If one wheel is spinning faster than the other, the blue planetary bevel gears just rotate about their axes instead of staying fixed. Now, the planetary gears are both rotating about their axes and about the output shafts (because of the carriage), thus powering both wheels, but allowing one to spin faster than the other.

This is a pretty tricky mechanism to explain. If you're still confused, I encourage you to check out this video, also shown above, which shows the process visually very well.

## Step 20: Gear Design Software

While you can purchase gears of specific sizes from vendors, there are also situations in which you may want to design your own gears for a specific purpose or so that you can modify them to create non-standard gear parts. Here's some software to help you get started. If you know of any more, let me know and I'll add them!:

**Autodesk Inventor (Free for Students):**Has a gear design feature for spur and helical gears, worm gears, and bevel gears

**RushGears:**Contains a customizeable online gear template that allows you to download 3D CAD files of your designed gears.

**Gearotic:**Online gear mechanism design software.

**DelGear:**Gear design software package.

**WoodGears:**Gear design software for designing laser cut and wood gear profiles.

## Step 21: Make Something With Gears!

Now its your turn to make something cool with gears! I made this simple GearBot to go along with this Instructable, but there are many other directions to go in from here. Use what you've learned and don't forget to share it!

If you have some more gear advice or ideas to share, or have any questions about mechanisms, please do so in the comments.

## 45 Discussions

i want to greate gearbox the allows bike pedals to go in opposing directions. the pedal is in a back and forth motion opposed to continuous circular motion-no chain needed, when one pedal is pushed down the other pedal goes up and vice versa. Seems that the pedal axis needs to be joined by some combination of gears in a gear box. . any ideas, drawings?

i want to greate gearbox the allows bike pedals to go in opposing directions. the pedal is in a back and forth motion opposed to continuous circular motion-no chain needed, when one pedal is pushed down the other pedal goes up and vice versa. Seems that the pedal axis needs to be joined by some combination of gears in a gear box. . any ideas, drawings?

How to find pitch diameter of the gear

der kha .. good job

Hi. You may want to include http://geargenerator.com. Altough it's not a design software is a very neat tool for generatin gear train online.

Thanks for the great write up. I was really hoping to see more on how to calculate and design a simple spur gear setup using a 2d draft. It would make a great follow up. Thanks

Thanks for the advice! What kind of design would you be looking for apart from the gear ratio and terminology? Are you looking to design gears from scratch, or more how to use the software well to create the gears?

very good stuff... I'm thinking on kinetic art, and this is a great introduction to the subject (which I'm sure can go as far as you want to follow it) for a non 'gear head'.

I think there's a minor mistake in the text though... You say both gear ratios with the clutch in either position are 3:2, and I'm sure one is 2:3.

Whoops! The second gear set is 2:3, I guess I mistyped! That's been fixed!

Great write up with some nice links for more info.

Please double check your math in step 4. A 3:2 combined with a 2:1 ends up with a 3:1, doesn't it? And combining that with another 2:1 makes for a 6:1, right? Not a 12:1 as you stated.

Whoops! You are totally right! I'll fix that right away!!

Thank you!

Very nice instructable!

Only thing I would add is Harmonic Drive. It's not overly popular but has properties like no other gear mechanism.

I've been trying to figure out gears for a while now, and your 'ible is amazingly easy to understand. The link to the differential gear box is a real gem, too.

Would love to see how to make non-round gears, as well as show how to figure an assembly of them. Like, how the thought process would be for making something - which goes first, what the ratios are, etc. Thank you!

That was great, thanks!

Hey everybody, WATCH that vid on the differential, it actually makes sense now!

Totally! I love that it was done in the 1930s, too!

great write up, thanks! yup, the diff. video made sense to me :)

Awesome - very coprehensive!

very interesting :)

This is some great information to have. It will reside on my kindle until the end of time.