Gears: everything you need to know about these sprockets


The Gear They are in a multitude of current mechanisms, from analog clocks, to vehicle engines, gearboxes, through robots, printers, and many other mechatronic systems. Thanks to them, transmission systems can be made and go beyond transmitting movement, they can also alter it.

Therefore, they are very important elements that you should know how they work Correctly. That way, you can use the right gears for your projects and better understand how they operate ...

What is a gear?


There are chain systems, pulley systems, friction wheels, etc. All of them transmission systems with its advantages and disadvantages. But of all of them, the gear system stands out, which are usually favorites for their properties:

  • They can withstand great forces due to their teeth without slipping, as could happen to friction wheels or pulleys.
  • It is a reversible system, capable of transmitting power or movement in both directions.
  • They allow very precise movement control, as can be seen in the stepper motors, Por ejemplo.
  • They allow to create compact transmission systems in front of the chains or pulleys.
  • Different sizes can be combined to interfere with the rotation of each axis. Generally, when two sprockets are used, the larger gear is called the wheel and the small pinion.

Un gear or cogwheel It is nothing more than a type of wheel with a series of teeth carved on its outer or inner edge, depending on the type of gear it is. These sprockets will be in rotary motion to generate torque on the shafts to which they are attached, and they can be grouped together to generate more complex gear systems, fitting their teeth together.

Obviously, for that to be possible, the type and size of the teeth must match. Otherwise they will be incompatible and would not fit. These parameters are those that are discussed in the next section ...

Parts of a gear

gear parts

For two gears to fit together, the diameter and number of teeth could be varied, but they must respect a series of factors that are what make the gear be compatible with each other, such as the type of tooth they use, the dimensions, etc.

As you can see in the previous image, there are several parts in a gear you should know:

  • Septum or arms: it is the part that is in charge of joining the crown and the cube in order to transmit the movement. They can be more or less thick, and its composition and strength will largely depend on strength and weight. Sometimes they are usually pierced to reduce weight, other times a solid partition is chosen.
  • Cube: it is the part where the movement transmission shaft is coupled and which is attached to the partition.
  • Corona: is the area of ​​the gear where the teeth have been cut. It is the most important, since the compatibility, behavior and performance of the gear will depend on it.
  • Tooth: it is one of the teeth or protrusions of the crown. The tooth can be subdivided into several parts:
    • Cresta: is the outer part or tip of the tooth.
    • Face and flank: is the upper and lower part of the side of the tooth, that is, the contact surface between two gear wheels that mesh.
    • Valle: it is the lower part of the tooth or intermediate area between two teeth, where the crest of another toothed wheel with which it meshes will be housed.

All this generates a series of crown geometries that will distinguish the types and properties of gears:

  • Root circumference: marks the valley or bottom of the teeth. That is, it delimits the inside diameter of the gear.
  • Primitive circumference: establishes the division between the two parts of the side of the tooth: face and flank. It is a very important parameter, since all the others are defined based on it. It will divide the tooth into two parts, the dedendum and the addendum.
    • Tooth foot or dedendum: it is the lower area of ​​the tooth that is between the original circumference and the root circumference.
    • Tooth head or addendum: upper area of ​​the tooth, which goes from the original circumference and the outer circumference.
  • Head circumference- will mark the crest of the teeth, that is, the outer diameter of the gear.

As you can imagine, depending on the crown, diameter and types of teeth, you can vary gear according:

  • Number of teeth: it will define the gear ratio and is one of the most determining parameters to determine its behavior in a transmission system.
  • Tooth height: the total height, from the valley to the ridge.
  • Circular step: distance between one part of the tooth and the same part of the next tooth. That is, how far apart the teeth are, which is also related to the number.
  • Thickness:: is the thickness of the gear.

Gear Applications

Companies that gear applications there are many, as I have already commented previously. Some of its practical applications are:

  • Vehicle gearboxes.
  • Stepper motors for turning control.
  • Hydraulic bombs.
  • Engines of all kinds, such as turning or movement transmission elements.
  • Differential mechanisms.
  • Printers to move the heads or rollers.
  • Robots for moving parts.
  • Industrial machinery.
  • Analog clocks.
  • Household appliances with mechanical parts.
  • Electronic devices with moving parts.
  • Door opening motors.
  • Mobile toys.
  • Farm machinery.
  • Aeronautics.
  • Energy production (wind, thermal, ...).
  • etc.

You can think of a multitude of other applications for your projects with Arduino, robots, etc. You can automate many mechanisms and play with speeds, etc.

Types of gears

According to its teeth and the characteristics of the gear itself, you have different types of gears at your fingertips, each with its advantages and disadvantages, so it is important to choose the right one for each application.

The most common types are:

  • Cylindrical: are used for parallel axes.
    • Straight: they are the most common, used when a simple gear with not very high speeds is needed.
    • Helical: they are a somewhat more advanced version of the previous ones. In them the teeth are arranged in parallel helix paths around a cylinder (single or double). They have a clear advantage over straights, such as being quieter, operating at higher speeds, can transmit more power, and have a more uniform and safe movement.
  • Conical: they are used to transmit movement between axes placed at different angles, even at 90º.
    • Straight: they use straight teeth and share characteristics with the straight cylindrical ones.
    • Spiral: in this case they support higher speeds and forces, as happened to the helical ones.
  • Internal gear: instead of having the teeth or crown carved on the outside, they have it on the inside. They are not as common, but they are also used for certain applications.
  • Planetariums: it is a set of gears used in certain transmission systems where there is a central gear around which other smaller ones rotate. That is why it has that name, since they appear to be orbiting.
  • Endless screw: it is a common gear in some industrial or electronic mechanisms. It uses a gear whose teeth are cut into a spiral shape. They generate a very constant speed and without vibrations or noise. They can drive a straight toothed wheel whose axis is oblique to the worm.
  • Rack and pinion: it is a set of gears that is also common in some mechanisms and that allows to transform a rotary movement of an axis into a linear movement or vice versa.

If you attend to His composition, you can also differentiate between materials such as:

  • MetalsThey are usually made of different types of steel, copper alloys, aluminum alloys, cast iron or gray cast iron, magnesium alloys, etc.
  • Plastics: used in electronics, toys, etc. They are polycarbonate, polyamide or PVC gears, acetal resins, PEEK polyetheretherketone, polytetrafluoroethylene (PTFE), and liquid crystal polymers (LCP).
  • Madera: they are not common, only in old mechanisms or in certain toys.
  • Others: it is likely that for very specific cases other fibers or specific materials are used.

Where to buy gears?

gears buy

You can find different types of gears in many mechanical or electronics stores. For example, here are some examples:

These products are small in size, if you need larger gears it is likely that you will not find them so easily. Also, if you need something very specific, many turner workshops can make it for you. The 3D printers They are also helping makers to create their own gears.

Basic calculations for sprocket systems


As you can see in this GIF, you have to understand that when two gears mesh, both axes will rotate in the opposite direction and not in the same sense. As you can see, if you look at the red jagged rue it is turning to the right, while the blue one is turning to the left.

Thus, for an axis to rotate in the same direction an additional wheel should be added, such as the green one. That way, red and green rotate in the same direction. This is because, as blue rotated to the left, when engaging blue-green, green will reverse the direction of rotation again, synchronizing with red.

Another of the things that can be appreciated in that GIF is turning speed. If all the gears had the same diameter and number of teeth, all the shafts would be rotating at the same speed. On the other hand, when the tooth number / diameter is altered, the speed is also altered. As you can see in this case, red is the one that spins the fastest, as it has a smaller diameter, while blue spins at a medium speed and green is the one that spins the slowest.

In response to this, you can think that by playing with the sizes you can alter the speeds. You are correct, just as a bicycle can do it with the gearshifts or the gearbox does it with the gear ratios of a car. And not only that, you can also make calculations on the turning speed.

When you have two gears meshed, one small (pinion) and another large (wheel), the following could occur:

  • If we imagine that the motor or traction is applied to the pinion and the wheel is driven, although the pinion rotates at high speed, having a larger wheel, it will slow it down, acting as a reducer. Only if they were the same size (pinion = wheel) would both axles rotate at the same speed.
  • On the other hand, if we imagine that it is the wheel that has the traction and a speed is applied to it, even if it is low, the pinion will be turning faster, since its small size acts as multiplier.

Gear transmission calculations

Once you have understood this, you can perform the calculations of a simple transmission system between two gears by applying the formula:

N1 Z1 = N2 Z2

Where Z is the number of teeth of gears 1 and 2 that are meshed and N is the rotation speed of the shafts in RPM (revolutions per minute or revolutions per minute). For example, imagine that in the GIF above, to simplify:

  • Red (drive) = 4 teeth and the motor is applying a rotation speed to its shaft of 7 RPM.
  • Blue = 8 teeth
  • Green = 16 teeth

If you want to calculate the turn in this system, you must first calculate the speed of the blue:

4 7 = 8 z

z = 4 7/8

z = 3.5 RPM

That is, the blue axis would be turning at 3.5 RPM, somewhat slower than the 4 RPM of the red one. If you wanted to calculate the turn of green, now that you know the speed of blue:

8 3.5 = 16 z

z = 8 3.5/16

z = 1.75

As you can see, green would spin at 1.75 RPM, which is slower than blue and green. And what would happen if the motor is located on the green axis and the driving wheel is rotating at 4 RPM, then the rotation would be 8 RPM for blue, 16 RPM for red.

It thus follows that, when the drive wheel is small, a lower speed is achieved on the final shaft, but greater force. In the event that it is the large wheel that carries the traction, the small wheel achieves greater speed, but less force. Because there powers or torque different? Look at this formula:

P = T ω

Where P is the power transmitted by the shaft in watts (W), T is the developed torque (Nm), ω the angular velocity at which the shaft rotates (rad / s). If the power of the motor is maintained and the rotational speed is multiplied or reduced, then T. is also altered. The same happens if T is kept constant and the speed is varied, then P is altered.

You will probably also want to calculate if an axis rotates at X RPM, how much it would advance linearly, that is, the linear velocity. For example, imagine that in the red one you have a DC motor and on the green axis you have placed a wheel so that a motor travels on a surface. How fast would it go?

To do this, you just have to calculate the circumference of the tire you have installed. To do this, multiply the diameter by Pi and it will give you the circumference. Knowing how much the wheel can advance with each turn and taking into account what turns each minute, the linear speed can be obtained ...

Here I show you a video so you can understand this in a better way:

Calculations for worm gear and sprocket

As to worm gear and sprocket, can be calculated with the formula:

i = 1 / Z

This is so because the screw is considered in this system as a single tooth sprocket that has been helically cut. So if you have a 60 tooth sprocket, for example, then it will be 1/60 (this means that the screw would have to turn 60 times for the sprocket to complete 1 turn). In addition, it is a mechanism that is not reversible like others, that is, the sprocket cannot be turned so that the worm rotates, only the worm can be the drive shaft here.

Rack and pinion calculations

For the system Rack and pinion, the calculations change again, in this case they are:

V = (p · Z · N) / 60

That is, multiply the pitch of the pinion teeth (in meters), by the number of pinion teeth, and by the number of pinion turns (in RPM). And that's divided by 60. For example, imagine you have a system with a 30 tooth pinion, a 0.025m pitch, and a 40 RPM spin speed:

V = (0.025) / 30

V = 0.5 m / s

That is, it would advance half a meter every second. And, in this case, yes it is reversibleThat is, if the rack is moved longitudinally, the pinion can be made to rotate.

You could even calculate how long it would take to travel a distance by considering the formula for uniform line movement (v = d / t), that is, if the velocity is equal to the distance divided by time, then time is cleared:

t = d / v

Therefore, already knowing the speed and distance that you want to calculate, for example, imagine that you want to calculate how long it would take to travel 1 meter:

t = 1 / 0.5

t = 2 seconds

I hope I have helped you gain at least the most essential knowledge about gears, so that you understand how they work and how you can use them to your advantage in your future projects.

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  1.   Ramon said

    For a maker like me (happily retired) it is great to have clear, concise and complete information on how to design gears and be able to print them. Congratulations