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Gears Selection How To Choose A Gear?
How to Select a gear?  Explanation of gears, guidelines and tips for selecting gears
Background
Gears are round mechanical components with teeth arranged in their perimeter. These teeth are interlocking with the teeth of a second gear or belt and thus transfer power and motion between them. A gear is one of the most important components in a robotic and driving system.
Gears can increase torque while reducing speed and vice versa due to energy conservation laws, gears cannot increase both torque and speed. Gears are not energy source but a means for transferring mechanical energy from one place to the other.
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Gears can also change the direction of rotation and transfer a rotary motion of one axis to another axis.
Gears are used for five main applications:
 Reverse direction of rotation
 Increase or decrease rotation speed
 Increase or decrease torque delivered by the driving system
 Transmit rotary motion of one axis to second axis
 Make sure that there is a synchornized circular motion between axes..
A set of gears called transmission when the ratio of the speed of rotation of the first gear to the last gear is called Gear ratio or Transmission ratio.
The same ratio can be determined by counting the number of teeth on each gear. For example, if one gear has 50 teeth and the other has 25 teeth then the transmission ratio will be 1:2.
Gears can be classified into several criteria:
 The geometric relationship between the axes of motion
 Number of stages
 Enclosure
 Speed of rotation
 Precision of manufacturing
The geometric relationship between the axes of motion
Gears can be divided into 3 groups:
Parallel motion axes
 Spur Gears
 Helical Gears
 Herringbone Gears
 Double Helical Gears
Intersecting motion axes
 Miter Gears
 Face Gears
 Bevel Gears
 Spiral Bevel Gears
 Zero Bevel Gears
nonparallel and nonintersecting motion axes
 Spiral Gears
 Worm Gears
 Hypoid Gears
Number of stages
1 Stage  two gears are combined with each other
2 Stage  three gears are combined with each other
3 Stage, etc.  four or more gears are combined with each other
Enclusre
Open transmission  the gears are not enclosed and without a protective cover and exposed to environmental conditions such as dust, moisture, etc.
Closed transmission  the gears are integrated inside a closed transmission enclosure that protects the gears from dust, moisture, etc.
Speed of rotation
Low speed  the linear rotation speed of the gear is slower than 3 m/s.
Medium speed  the linear rotation speed of the gear is in the range of 3  15 m/s.
High speed  the linear rotation speed of the gear is faster than 15 m/s.
Precision of Manufacturing
Gears quality is measured by an international quality standard that determine 12 quality grades of gear manufacturing when grade 1 indicating the most precise gear (and the most expansive).
Gears  Mathematics and formulas
As stated previously, the transmission ratio between gears can cause a reduction or increase of torque or speed. The transmission ratio can be also calculated by counting the number of teeth in each gear. But what is the relationship between the number of teeth and the increasing of torque and speed?
Suppose two gears. One with a radius of R1 and the other have a radius of R2. On the first gear there is a torque designated as tau1, meaning, the force that the first gear exerting on the other gear in the point of contact between them is equal to F1.
The force is calculated like this:
Meaning,
F2 can be calculated by the same method:
Meaning,
Since those contact force are equal in size but opposite in direction they can be compared like this:
Meaning,
Therefore, the ratio is determined like this:
The ratio of the radius of the two gears is equal to the ratio of the torque between them.
The following equality can be obtained:
With the same principal, the relationship between speed of rotation and gear radius can be calculated:
Suppose two gears. One with a radius of R1 and the other have a radius of R2. The first gear rotates i a speed equal to omega1, meaning, the linear velocity of the two gears in the point of contact between them is equal to V1.
The Linear speed is calculated as follows:
V2 can be calculated with the same principal:
Since the linear speed is the same then they can be compared:
Meaning,
Therefore, the ratio is determined like this:
The ratio of the radius of gears is equal and inversed to the ratio of the gear rotational speed. The following equality can be obtained:
If we compare the ratio of diameters, the ratio of torque and the ratio of speed, the following equation exists:
That is, given a certain transmission ratio (diameter of the gears is fixed and does not change) than any change in speed will cause a change in the torque. Increasing the speed of gear 1 will decrease the torque in gear 2 and vice versa.
But what is the connection between the number of teeth and the transmission ratio?
The teeth are geometry of the gear and affected by its diameter and its pitch. The pitch definition is the distance between one tooth to the other. The link between the number of teeth, the diameter and the pitch is defined as:
When combining two gears, the pitch has to be the same or else the motion transmitted by the gears will not be good and can even damage the gears.
When selecting two gears with the same pitch, the following ratio is obtained:
therefore,
If we compare the ratio of the diameter to the previous ratios we calculated we can get the following relationship:
And here is the simple connection showing the transmission ratio of the gear as function of the number of teeth without the need to calculate or know their diameter.
But what about the transmission ratio of three or more gears or as socalled gear train?
Suppose we have three gears with different teeth numbers: N1, N2, N3. The overall ratio is defined by the first gear (driving gear) and the last gear (driven gear). This ratio is obtained by multiplying the transmission ratio of each pair of gears taking into account the negative sign (the reason for the negative sign is due the change in rotation direction in each pair of gears).
That is, the ratio between the first and the last gear is:
With the same principal we can obtain the transmission ratio of a train gear consists of 8 gears:
or:
therefore:
How to select a gear?  Types of Gears
Spur Gear
The most common and simple gear. Consists of a cylinder with straight teeth in its perimeter. Transmit motion only between parallel axes. These gears are very cheap to manufacture and are used in most of the existing industrial transmissions. Spur gears can be manufactured from a variety of materials such as plastic, metal, copper, steel, aluminum, etc.
Spur gears are used for lower torque and speed than Helical gears.
In spur gears, there are no axial forces acting on the axis of rotation. The forces that the gears generate are radial forces only. When designing driving mechanism one must take this into account when selecting the bearing.
Rack and Pinion
Rack is a linear block with teeth. When a pinion with teeth attached to it they interlock with each other and convert rotary motion to linear motion. Rack can be treated as round gear with infinite radius.
By the way, if we try to prove mathematically it seems that the relationship between the radius of the pinion and the rack aims to 0. This is because the denominator of the ratio (rack radius) set to infinity. Distribution at infinity gives us zero. We can therefore conclude that the angular velocity of the rack is zero – which is really true. The rack has no angular velocity but linear velocity only.
Internal Ring Gear
Internal ring gear is ringshaped gear where the teeth arrange in the inner circumference of the ring. When a gear interlocks with the internal ring gear, there is more surface area contact between the teeth of the two gears – this increased the life span of the gear and reduces loads and stresses acting between the gears. These gears are used in planetary transmissions delivering a high gear ratio.
When selecting the appropriate gear for the internal ring gear the difference between the teeth number should be higher than 15.
Internal ring gears transmit motion between parallel axes.
©gimpdome.com By Shawn Evans
Helical Gear
Helical gear provides more subtle features than a spur gear. The teeth arranged at an angle to the rotation axis. Since there is an angle between the rotation axis to the teeth a pair of helical gears can be arranged together in parallel or crossed orientation. When interlocked in parallel orientation, the gears transmit motion between parallel axes. When arranged in cross orientation, the gears transmit motion between nonparallel axes and the angle depends on the angle of the helical teeth and their sum.
For example, the teeth of one gear are arranged in an angle of 30 degrees and in the 2^{nd} gear are in 10 degrees. This gives us a 40 degrees difference between two axes of rotation.
The special teeth arrangement causing the teeth to interlock gradually with each other. The first contact between the teeth is localized and as the gear spins, more surface contact is made (as opposed to spur gears which all of the tooth area is in contact immediately when interlocked with 2^{nd} gear). This feature produces more smooth and quite motion.
Helical gears are made for higher speed and torque application than spur gears and other application where noise reduction is important. A high speed of helical gears defined when the linear velocity of a point in the circumference of the gear is faster than 25m/s.
Helical gears produces both radial and axial forces. The combination of these forces caused by the angle of the teeth. When designing driving mechanism, one should take into account these forces when selecting bearing for the application.
Screw Gear / Crossed Helical Gear
Screw gear (or Crossed helical gear) is identical to the structure of the normal helical gear. The “crossed” definition refers to the arrangement of two helical gears together. The meaning is the gears are not mounted on the same rotation plane but at angle to one another.
Helical Rack Gear
Helical rack gear is a linear block with helical teeth. When a helical pinion is interlocked with the rack the rotary motion is converted to linear motion.
The difference between a spur rack and a helical rack is the same difference between the spur and helical gears: it is used for high speed and torque application and applications where noise reduction is important.
The same mathematical formula to prove that the angular velocity equals zero is relevant in this type of rack.
Double Helical Gear / Herringbone Gear
Double helical gears (or Herringbone gear) is a gear with special teeth arrangement that cancels the axial forces exerted by the gears. Although it is one gear produced as one part, it can be treated as two opposing helical gears attached backtoback. The axial force generated by one gear is canceled by the other.
This type of gear is also used for smoother motion and high torque application. Nevertheless, it is very expensive to manufacture due to the complicated geometry of the teeth.
Another disadvantage is that these gears are designed to work towards a specific rotation direction and not bidirectional. This is because the axial forces generated by the gear. It is true that the sum of the axial forces in this gear equals zero, but the value that do changes and depends on the rotation direction is the compressive and tensile stresses. When the gear spins to a certain direction, two opposing forces directed outwards. This is a nonbalanced arrangement that can lead to dismantling the transmission gears when the rotation axes are nonparallel or unbalanced. When the gear turns to the other side, the forces are directed inwards and stability is maintained. Therefore, when integrating a double helical gear, one should take into account the expected rotation direction. If the application involves a moving back and forth, then consider using different gear.
Straight Bevel Gear / Miter Gear
Straight bevel gear is based on the same principal of all bevel gears – the motion and torque transmission is between nonparallel axes of rotation. It is shaped like a truncated cone with teeth arranged on the surface. When two bevel gears are interlocked, the rotation axes are intersected in a certain point.
Miter gears are actually straight bevel gears with identical teeth number which produces a transmission ratio of 1:1 and the axes of rotation are in 90 degrees.
Straight bevel gears have straight teeth (exactly as spur gears). It is built for relative low speed an torque transmission than the helical bevel gears.
These gears come in two configurations: standard type and Gleason type. In the Gleason type configuration, the teeth are slightly raised from the surface of the gear compared to a normal type configuration where the teeth are machined on the surface of the cone. In the image below, the upper gear is in normal type configuration and the bottom gear is in Gleason type configuration.
Straight bevel gears generate radial and axial forces. One should take this into account when designing driving mechanism that supports the two gears.
Spiral Bevel Gear
Spiral Bevel Gear is based on the same principle as straight bevel gears – the motion and torque transmission is made between two nonparallel rotation axes. It is shaped like a truncated cone. When two gears are interlocked, there is an intersection point between their rotation axes.
Spiral bevel gears made from teeth arranged in angle to the rotation axis (just as helical gears). It is built to deliver higher speed and torque and for noise reduction application.
These gears generate both axial and radial forces. The axial forces generated in spiral bevel gears are greater than the axial forces in the straight bevel gears. This must be taken into account when selecting bearings for the driving mechanism.
Face Gear
Cylkro® face gear set of ASSAG, Switzerland ASSAG, Switzerland, Switzerland
Face gear is actually a ring which the teeth are machined on the face of the gear and not on the circumference. The teeth transmits motion to another compatible gear which its rotation axis is in 90 degrees to the rotation axis of the face gear.
Face gears are usually characterized by a high transmission ratio and can deliver high torque and great accuracy. Face gears can increase system accuracy and rigidity of the transmission box.
Worm Gear
Worm gear is a gear that allows motion transmission between two perpendicular rotation axes placed on two different planes. The worm gear is made of worm (cylinder shaped with machined spiral teeth) and a spiral gear (worm gear) adjusted to the same pitch of the worm.
Worm gear is characterized by a high speed and torque application and high transmission ratio.
The transmission ratio of a worm gear is determined by the number of teeth of the worm gear (assuming that the worm cylinder has 1 tooth in contact each time). For example, for a 1:60 transmission ratio of a worm gear, the worm gear will have 60 teeth.
A very important feature of worm gear is selflocking. When you turn the worm, the worm gear will start to rotate. But when you try to rotate the worm gear, the worm won’t move. This fact is related to the relatively flat angle of the worm teeth. Because of the flat angle, the force that the worm gear exerting on the worm can’t overcome the friction and therefore the worm won’t spin.
In mechanical mechanism, machines and robots, the selflocking feature can save production costs of breaking systems or other mechanical restrainers. By selecting the appropriate transmission ratio, you can create a braking mechanism based only on the worm gear without adding additional mechanical or electromechanical components such as brakes.
An example for the selflocking mechanism of the worm gear:
Suppose a robot was designed to lift a certain part using a motor and a transmission gearbox.
Let’s assume a first case that the transmission gearbox is based on spur gears only. When the motor starts to turn, the gearbox transmits the torque and lifts the part. When the motor is turned off, the weight of the part overcome the internal friction of the gear and it starting to drop down. In order to keep in place the part after it was being lifted, a brake should be added to the application or the motor has to be kept turned on in with a constant torque (unnecessary power consumption).
To overcome this, we replace the spur gearbox with a worm gearbox with high transmission ratio. The motor attached to the worm gearbox and starts to rotate thus lifting the part. When the motor is turned on, the part exerts its weight on the worm gearbox. Because of the structure and the flat angle of the worm teeth, the worm gearbox opposes the part gravitational force and prevents it from falling.
Double Enveloping Worm Gear
©rmhoffman.com
Double envelope worm gear is based on the same principle as standard worm gear. The difference is that the structure of the worm cylinder is curved and concave.
This allows a greater contact area and grip between the worm and the worm gear. By that we increase system rigidity and durability to higher loads and torques.
Face Worm Gear
Face worm gear is a gear that combines the principle of a face gear and a worm gear. The motion and torques are transmitted between two nonparallel rotation axes in different planes. The worm gear is replaced with a face gear with special spiral teeth that interlocks with the worm.
Hypoid Gear
Hypoid gear is very similar to a helical gear except that there the axis of rotation are not intersects (not parallel and not in the same plane). Hypoid gears are always designed to work perpendicular to each other (90 degrees).
Hypoid gears are very common in differential gearbox.
Sprocket Gear
Sprocket Gear has teeth in its circumference with a special shape that designed to interlock with a chain of links (like a bicycle chain). The gear is built to interlock only with that special chain and not build to interlock with other sprocket gears.
The creation of such transmission ratio is made by using two or more sprocket gear when a chain is connected between two gears. For example, when a sprocket with 25 teeth is rotating, the motion is transmitted through that chain to a 2^{nd} sprocket gear with 50 teeth, hence the transmission ratio is 1:2.
When connecting three gears or more there can be a problem of loosening of the chain therefore additional sprocket gear with the only purpose of tensioning the chain should be used.
A sprocket gears is usually made of metals (cast iron, aluminum, steel, etc.).
This type of gear have a relatively high erosion and need attention regarding their maintenance.
Timing Gear
Timing gears are gears designed to transmit motion and torque similar to the sprocket gear. The difference is that with timing gears, timing belts are used and not chain of links. A timing belt is a teethed belt as in the following images:
The teeth in the belt interlock with the teeth in the timing gear and this is how the motion is transferred. Also in this case a large quantity of gears can be used to increase or decrease the transmission ratio.
Timing belts and timing gears are very common in the automotive industry and the industrial machines, automation and robotics industry.
If using 3 timing gears or more make sure that the all the belts between each pair of gears are in tension. If necessary, timing belt tensioners or idlers must be used. It is also possible to use fixed rods placed near the belt to keep it tensioned (but this method can cause friction in the belt and belt degradation – use it for prototyping only).
Ratchet Gear
Ratchet gear is a gear that allows motion in only one direction. The ratchet transmits motion and torque only in one direction and acts as a brake in the other direction. Ratchet gears usually made of metal and the teeth shape is convex on one side and straight on the other side. In order to implement the principle of selflocking of the ratchet, a special pin is used. When the ratchet gear spins in certain direction, the pin slips on the teeth (this is the ticking noise you can hear) and nothing interferes with the motion. But when the gear rotates in the other direction, the pin collide with the straight side of the tooth and prevent the gear from moving.
In order to release the pin and allow the ratchet gear to rotate both directions, a special release mechanism must be constructed that pulls the pin away.
Ratchet gear is characterized by backlash. It can prevent the rotation back only if the pin is in contact with the straight side of the tooth.
By Georg Wiora (Dr. Schorsch) [CCBYSA2.0, GFDL or CCBYSA3.0], via Wikimedia Commons
How to select gears  Understanding the tehnical data form the datasheet.
Module / Diametral Pitch
A Module (or Diametral Pitch) describes the size of the tooth. A gear with smaller diametral pitch will have smaller teeth. The diametral pitch is directly related to the circumference of the gear, that is the larger the diametral pitch the larger the circumference of the gear.
Tip: select gears with higher module when higher torques is expected.
Number of Teeth
Number of teeth indicated the… number of teeth in the gear (amazing!!!). the number of teeth parameter can help to calculate the final transmission ratio between the first gear and the last.
Gear Ratio / Reduction Ratio

Transmission ratio (or reduction ratio or gear ratio) describes the ratio:
 Between the torque exerted on the driving gear and the torque the driven gear exerts.
 Between the rotational speed of the driving and driven gear.
 Between the number of teeth of the driving and driven gear.
 Between the diameter of the driving and driven gear.
When purchasing a single gear, this parameter is irrelevant. This parameter only refers to pair of gears (or more) or a gearbox.
Material
Indicates the material from which the gear is made of. Most of the gears in robotics and automation machines are made of metal. But there are some applications where plastic gears are also common (where low loads and torques are expected). Examples of such plastics are: rugged rubber, nylon, delerin, acetyl, etc.
Tooth Form
Straight, Helical or spiral? This parameter indicates the shape of the gear tooth.
Direction
In helical gears, the rotation direction is important. This parameter usually comes with two values: right and left. When matching two helical and spiral gears note this important parameter.
Pressure Angle
Pressure angle indicates the angle in which contact between teeth of two gears occurs.
By Claudio Rocchini [GFDL, CCBYSA3.0 or CCBY2.5], via Wikimedia Commons
Common values for pressure angles are: 14.5°, 20° and 25°.
Inner Bore Diameter
Inner Bore diameter describes the diameter of the shaft that the gear should be mounted on. It is possible to purchase a gear with smaller bore and perform additional machining to fit in special shaft diameter.
Mounting Feature
Mounting feature describes the assembly method of the gear to the driving shaft.
Hub / Hubless – A smaller circular shoulder protruding from the gear face and allows placing components that fix the gear to the shaft using keys, setscrews, pins, clamping rings, etc.
© omni components corp
Keyway – A slot in the inner diameter of the gear is used for placing keys. This type of mounting is usually used for high torque applications.
Setscrew – A bolt screwed through a threaded hole located on the bore of the gear. It can be bolt or setscrew. In this type of mounting, the friction between the bolt end and the shaft delivers the torque. Setscrews are usually used for locating the gear on the shaft rather than transmitting torque. In very low torque application, setscrew can be used.
Split – Clamp – A grooved shoulder with a very small wall thickness protruding out of the gear face. On top the shoulder, a clamp is placed. When the clamp is tightened, the gear is rotating with the shaft based on friction only.
© omni components corp
Anti Backlash
A gear manufactured in a special way that prevents him from moving back and forth in the backlash range. These types of gears are usually more expensive but more accurate and used for applications where precision and delicate movements are important.
Maximum Allowed Torque
This property specifies the maximum torque that the gear can withstand before the teeth will break.
Maximum Allowed Speed
This property specifies the maximum speed that the gear can withstand before the teeth will break or the inertial moment can cause vibrations in the gear motion.
Dimensions
The geometric dimensions defining the size and shape of the gear: inner diameter, outer diameter, diametrical diameter, bore length, gear length, weight and more.
How to choose a gear? So how do you choose a gear?
To select a gear for your robotics application, you should ask the following questions first:
 Is there a gap between the required torque and the torque deliveredby the motor?
 Is there a gap between the required speed and the available speed of the motor?
 Do i need to change the directino of moion?
 What is the maximum torque can be exerted on the first driving gear?
 Does backlash matters?
 Is Selflocking required?
 Is there a limitation in geometry and space?
 How the gear connects to the shaft?
 How much money to invest on gears?
Is There a gap between the required torque and the torque delivered by the motor?
An example: a torque of 100Nm is has to be exerted on a rotary mechanism. But the existing motor can give only 10Nm. Where to obtain more 90Nm?
Through the transmission gears in the right transmission ratio we can increase the torque that the motor generates from 10Nm (in the driving gear) to 100Nm (in the driven gear).
The required transmission ratio is 1:10. That is, you can take a gear with 20 teeth and another one with 200 teeth. If there is a limitation in space (a gear with 200 teeth is pretty large) so it is possible to select 3 gears. The first pair will generate a transmission ratio of 1:2 and the second pair will generate a transmission ratio of 1:5. Meaning, the first gear can have 10 teeth, the second gear can have 20 teeth and the third gear can have 100 teeth. And so on.
It is important to remember 3 important notes:
1) Torque comes at the expense of speed. Increasing the torque decreases the speed. In the example, if we increased the output torque by 10, the output speed is reduced by 10.
2) Efficiency is a given parameter that characterizes transmission gears like any other mechanical mechanism. Friction in the gears causes loss of energy. Meaning, in real life, if we choose a transmission ratio of 1:10, but the efficiency of the transmission is 90% then the final output torque will be 90Nm (not 100Nm). That why it is important to select the right transmission ratio and add to it as compensation for the loss of efficiency.
3) A gear teeth is made of different materials. Every material has its own strength characteristics. Every part that subjected to loads and stresses larger than its strength characteristics will break. It’s impossible to increase the torque of the motor with unlimited transmission ratio. If too much torque will be exerted on the gear teeth (usually the first smaller driving gears) they will break. It is important to consider the maximum allowable torque applied to each gear in the transmission.
Is there a gap between the required speed and the available speed of the motor?
An example: a speed of 30,000rpm is needed in a rotary mechanism. But the existing motor can give only 3,000rpm. Where to obtain more 27,000rpm
Through the transmission gears in the right transmission ratio we can increase the speed that the motor generates from 3,000Nm (in the driving gear) to 30,000Nm (in the driven gear).
The required transmission ratio is 1:10. That is, you can take a gear with 20 teeth and another one with 200 teeth. If there is a limitation in space (a gear with 200 teeth is pretty large) so it is possible to select 3 gears. The first pair will generate a transmission ratio of 1:2 and the second pair will generate a transmission ratio of 1:5. Meaning, the first gear can have 10 teeth, the second gear can have 20 teeth and the third gear can have 100 teeth. And so on.
The previous three notes are applied in this case too.
Do i need to change the direction of motion?
Is the motion has to be maintained in the same direction? Is it necessary to reverse the direction of rotation? Do I need to transmit rotary motion to linear motion and vice versa? Do I need the transmit motion from one axis or plane to another one?
Part of the process of selecting gears is determining what type of gear to be used. There are gears capable of changing the direction of rotation (Helical gears, Spur gears, etc.), change the angle of rotation axis (Bevel gear, Worm gear, etc.) and even transmit rotary motion to linear motion (Worm rack, Rack and pinion, etc.).
What is the maximum torque can be exerted on the first driving gear?
As described earlier, you can’t get all the torque you want by simply increasing transmission ratio. Theoretically you can increase torque almost to unlimited value. For example, take a motor generates 1Nm, attach to its shaft a transmission with a ratio of 1:1,000,000 and you can receive an output torque of 1,000,000Nm. But it’s only theoretical. In practice, there is a critical consideration that determines the maximum value we can get and it depends on the material and shape of the gears.
There can be a situation where transmission ratio of 1:300 is needed. While spur gears might not achieve this output torque, helical gears might achieve this goal.
When selecting gears, it is important to notice the value of the maximum allowable input torque. Deviating from this value can cause breakage of the teeth and yield of the entire mechanism. Usually, the first gears that have impact like this are the driving gears.
Does backlash matters?
Certain machine (usually precise robotics and automation machines) needs to move a part from a certain point to another while maintaining a precise motion. In this type of application, gears with zero backlashes should be used. There can be a situation where a gear with a small backlash can be selected and the robot will move a part a distance of 4.95mm instead of 5.00mm due to this backlash.
These gears are usually more expansive than normal gears because of the manufacturing process.
On the other hand, if there is an application where precision is not needed, for example, a motor spins a fan using axes, than a normal gear with a small backlash can be selected.
Is Selflocking required?
A robot lifting a heavy weight and powered by a motor and transmission of spur gears will drop the load it lifts as soon the motor will shut down unless the following will be performed:
 The motor will not be shut down and keep suppling a constant torque.
 Integrating a braking mechanism which hold the mechanism in place.
 Switching transmission from spur gears to worm gear with a large transmission ratio.
 Adding a ratchet gear to the mechanism (can complicate the mechanism because another ratchet release mechanism might be added as well).
To conclude:
Two mechanisms are known based no their selflocking feature: Worm gears and ratchet.
Self=locking of gears occurs only where a condition of the pressure angle of the gears is met. You can use the following formula:
– Coefficient of friciton between the worm gear and the gear.
– Pressure Angle
– Worm Helix Angle
You can use also a rule of thumb for selflocking. When selecting worm transmission, try to select a gear with transmission ratio of 1:50 and bigger. It is possible to maintain self=locking in smaller transmission ratio worm gears but more complex calculation is needed to find this minimal transmission ratio.
Just for quick reference, below are the coefficients of friction between hard metals:
0.11 (using Oleic acid or Lard oil)
0.23 (using Light mineral oil)
0.15 (using Castor oil)
Is there a limitation in geometry and space?
In the first example, I mentioned that the first gear can be 20 teeth and the second can be 200 teeth. There is situations where tight spaced are inevitable. That’s why we’ll try to select 3 gears with smaller diameter that still maintain the desired transmission ratio.
How the gear connects to the shaft?
For this questions, it is important to address two issues: how to attach the gear to the shaft and how to transmit torque from the shaft to the gear.
To locate the gear on the shaft, it is possible to use a simple retaining ring. But if there is a gear with expected high torque, a retaining ring won’t stand the high torque and might break. A key is the part we need for higher torque applications.
On the other hand, manufacturing keys and key waves concludes additional financial cost.
Here are some examples of different gears connection:
How much money to invest on gears?
The answer is simple  buy the best gear at the cheapest price. Everyone have their financial limitations. After all questions are answered, perform market research from several different suppliers and look for the gear that match your requirements and choose the cheapest. Simple, right?
Written by Eran Cenciper (RobotandMachinesDesign Webmaster)
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