Sprocket Basics

Sprockets are rotating parts that have teeth and can be used with a chain and another sprocket to transmit torque. Sprockets and chain can be used to change the speed, torque or direction of a motor. For sprockets and chain to be compatible with each other, they must have the same thickness and pitch.

Sprocket and chain is a very efficient way to transmit torque over long distances.

Sprockets consist of a disk with straight teeth projecting radially. Sprockets will only work correctly with chain and other sprockets if they are on parallel shafts and the teeth are in the same plane. A chain consists of a continuous set of links that ride on the sprockets to transmit motion. The REV 15mm Build System is designed around #25 Roller Chain (REV-41-1365) using compatible #25 Sprockets.

Anatomy of a Sprocket

The most common and important features of a sprocket are called out in the figure below.

* Number of Teeth* is the total count of the

* Pitch Diameter (PD)* is an imaginary circle which is traced by the center of the chain pins when the sprocket rotates while meshed with a chain. The ratio of the

* Pitch* represents the amount of

* Outside Diameter (OD)* will always be larger than the

* Chain Clearance Diameter* is the outside diameter of a sprocket with chain wrapped around it. The

Anatomy of Chain

Roller chain is used to connect two sprockets together and transfer torque. Roller chain is made up of a series of inner and outer links connected together which forms a flexible strand.

* Outside Links* consist of two outside plates which are connected by two

* Inside Link* consist of two inside plates that are connected by two hollow

* Pitch* is the distance between the centers of two adjacent

Product Specifications

The REV DUO Build System includes both Metal and Plastic Sprockets. The table below covers some of the basic specifications for the different types of Sprockets.

REV DUO sprockets are a #25 pitch. Plastic Sprockets are designed to fit a 5mm hex shaft which eliminates the need for special hubs and setscrews. Most Metal Sprockets use a Locking Motion Hub (REV-41-1719) in order to connect to a Hex Shaft. The REV DUO Metal Sprockets are at less risk for wear than the Plastic Sprockets.

All REV DUO Plastic Sprockets have a M3 bolt hole mounting pattern that is on an 8mm pitch. This makes it easy to directly mount REV DUO Brackets and Extrusion to sprockets. The 8mm pitch is also compatible with many other building systems.

Using Sprockets and Chain as a Powertrain

Transforming the **torque** and **speed** of the motion is accomplished by changing the size of the sprockets.

*Physics concepts, like speed and power, have a lot of applications in the REV 15mm Build System. To learn more about them, check out how they apply to sprockets and chains **here**.*

A** sprocket size ratio** is the relationship between the number of teeth of two sprockets (input and output). In the image below, the input sprocket is a 15 tooth sprocket and the output is a 20 tooth. The sprocket size ratio for the example is 20T:15T. The ratio in size from the **input** (driving) sprocket to the **output **(driven) sprocket determines if the output is **faster** (less torque) or has more **torque** (slower).

To learn more about ratio calculations for sprockets check out the ratio section.

The 15 tooth sprocket outside of the chain loop is known as an** idler**. Idlers do not affect the sprocket size ratio and thus are not part of the calculation. To learn more about idlers check out Idler section on the Advanced Sprockets and Chain page.

Within a chain loop, motion follows the direction set by the input sprocket. In the example, both sprockets inside the chain loop move counter clockwise. Idlers, which sit outside of the chain loop, are pushed in the opposing direction. So, the 15 tooth idler sprocket is moving clockwise.

How to Use REV DUO Sprockets and Chain?

Like with other motion components, REV DUO Sprockets drive motion with the 5mm Hex Shaft. However, in order to use a Hex Shaft with the Metal Sprockets, a Locking Motion Hub will also need to be used. To learn more about using Hex Shafts and proper motion support and constraint visit the pages linked below:

Chain Tension

In order for sprockets to work effectively, it’s important that the** center-to-center distance** is correctly adjusted. The sprocket and chain example with the red 'X', in the image below, may work under very light loads, but they will certainly not work and will skip under any significant loading. The sprockets in this example are too close together so chain is loose enough that it can skip on the sprocket teeth. The sprockets, with the green check mark, are correctly spaced which will provide smooth reliable operation.

*To learn more about calculating center-to-center distance for sprockets visit the **Advance Sprockets and Chain Page**. *

To ensure proper chain tension it is recommended to create a properly sized chain loop. To learn more about manipulating chain to size check out the Chain Tool page.

The first step to getting ideal chain tension is to manipulate, or cut the chain to the correct size. Using the center-to-center distance calculation is one of the most accurate ways to find the chain size needed. Once sizing is approximated, use the Chain Tool (REV-41-1442) or Master Link (REV-41-1366) to break and reform the chain.

*To learn more about using the Chain Tool and Master Link, check out the **Chain Tool **section*

When using the slots on REV DUO structural elements its is very easy to adjust and tension the chain if the sizing is off. When using the Extended Motion Pattern in conjunction with a chain drive, use Tensioning Bushings (REV-41-1702) and Standoffs (REV-41-1492).

*For an example on how to use the Tensioning Bushings check out the **Drivetrain **guide. *

Sprocket Alignment Mark

Sometimes in a design it may be desirable to stack together multiple of the same sprocket on a shaft. In the cases where the number of teeth on the sprocket is not divisible by six, because of how they are oriented when put onto the hex shaft, the teeth may not be aligned between the two sprockets. To ensure all of the sprockets are clocked the same way, use the alignment shaft notch to put all the gears on the shaft with the same orientation.

Sprocket and Chain Physics

Sprockets are one common way to transmit power and change the output torque or speed of a mechanical system. Understanding these basic concepts is required to make optimized design decisions. This section will briefly cover the definition of these concepts and then explain them in relationship to basic sprocket and chain designs.

* Speed* is the measure of how fast an object is moving. The speed of an object is how far it will travel in a given amount of time. The SI unit for speed is meters per second but speed is also commonly expressed in feet per second.

* Torque* is roughly the measure of the turning force on an object like a sprocket or a wheel. Mathematically, torque is defined as the rate of change of the angular momentum of an object. A common example of torque is a wrench attached to a bolt produces a torque to tighten or loosen it. Torque is commonly expressed in N⋅m or in⋅lbs.

When torque is turning an object, like a sprocket, the sprocket will create a straight line (linear) force at the point where the teeth contact the chain. The magnitude of the torque created is the product of the rotational force applied and the length of the lever arm, which in the case of a sprocket, is half of the pitch diameter (the radius).

* Power (P)* is the rate of work over time. The concept of power includes both a physical change and a time period which the change occurs. This is distinct from the concept of work which only measures a physical change. It takes the same amount of work to carry a brick up a mountain whether you walk or run, but running takes more power because the work is done in a shorter amount of time. The SI unit for power is the watt(W) which is the same as one joule per second (J/s).

Often in competition robotics the total power is fixed by the motors and the batteries available. The maximum speed at which an arm can lift a certain load is dictated by the maximum system power.

Chain Drive

By selecting sprockets with different sizes relative to the input sprocket varies the output speed and the output torque. Total power is not effected through these changes.

Sprocket and chain is a very efficient way to transmit torque over long distances. Modest **reductions **can be accomplished using sprockets and chain, but gears typically provide a more space efficient solution for higher ratio reductions.

Sprocket Ratio

When a larger sprocket drives a smaller one, for one rotation of the larger sprocket the smaller sprocket must complete more revolutions so the output will be faster than the input. If the situation is reversed and a smaller sprocket drives a larger output sprocket, then for one rotation of the input the output will complete less than one revolution resulting in a speed decrease from the input. The **ratio **of the sizes of the two sprockets is proportional to the speed and torque changes between them.

The** ratio** in size from the input (driving) sprocket to the output (driven) sprocket determines if the output is faster (less torque) or has more torque (slower). To calculate exactly how the sprocket size ratio effects the relationship from input to output use the ratio of the number of teeth between the two sprockets.

Idlers

Now lets add a 15 tooth **idler **sprocket into the example on the outside of the chain loop. An** idler** sprocket is any sprocket meshed with the chain which does not drive any shaft or do any work. **Idlers **do not change the system reduction which remains 20T:15T.

Regardless of the number or size of idler sprockets, only the input and output sprocket determine the reduction.

All sprockets on the same side of a chain have the same rotation. The driving and driven sprocket are inside the chain and are rotating counter clockwise while the idler sprocket is outside of the chain loop and is rotating clockwise. This property is useful sometime when it is desirable to have two shafts powered from the same source, but with opposite rotations. Common examples of this on robots are intakes and dual wheeled shooters.

Idlers can be used to tension chain or increase the amount of chain wrap around a sprocket. From the figure below, all power transmission sprockets should have chain wrapped approximately 180° around the circumference of the sprocket. This amount of wrap is necessary so that there are sufficient teeth engaged with the chain to transmit the torque. Too little wrap (<120°) and the chain will skip under heavy load, while excessive wrap (>200°) can decrease system efficiency. The sprocket outside of the chain is noted with a warning because it has a chain wrap of <90°. If this sprocket is an idler, then it is unpowered and minimal chain wrap is acceptable, however if this sprocket will be driving a shaft which is doing work, this amount of wrap would be insufficient.

Sprocket and chain is an efficient way to transmit torque long distances in a robot. A common example of this is a sprocket and chain drivetrain. In this example the sprockets on the ends are linked to the drive wheels and the center sprocket would be driven by a motor (not shown). Because the driving and driven sprockets are all inside the chain, they all have the same rotation direction. The smaller sprockets on the outside of the chain loop are used to increase the amount of chain wrap on the center driving sprocket.

Compound Gearing

Some designs may require more reduction than is practical in a single stage. The ratio from the smallest sprocket available to the largest is 54:15, so if a greater reduction then 3.6x is required, multiple reduction stages can be used in the same mechanism which is called a compound gear reduction. There are multiple gear or sprocket pairs in a compound reduction with each pair linked by a shared axle. When using sprockets and chain in a multi stage reduction, it’s very common to use gears for the first stage and then use sprockets and chain for the last stage. The figure below is an example of a two-stage reduction using all gears, but one of the pairs could be replaced with sprockets and chain. The driving gear (input) of each pair is highlighted in orange.

Reduction is calculated the same for gears and sprockets based on the ratio of the number of teeth. To calculate the total reduction of a compound reduction, identify the reduction of each stage and then multiply each reduction together.

**Where:**

CR is the total Compound Reduction

Rn is the total reduction of each stage

Using the image above as an example the compound reduction is 12:1.

For any gear system there are a limited number of gear and sprocket sizes available so in addition to being able to create greater reductions using compound reductions it is also possible to create a wider range of reduction values or the same reduction of a single stage, but with smaller diameter motion components.

Each additional compound stage will result in a decrease in efficiency of the system.

Spacing and Center to Center Distances

When REV Robotics Sprockets are used in conjunction with the slots on Extrusion or Channel, the **center to center distance **between axles is completely adjustable. Slide and retighten the shaft mounting plates anywhere along the slots to adjust chain tension. This system allows any combination of compatible REV Robotics Sprocket to be used together, allowing for a high level of flexibility. When adjusting the reduction of a system, just a single sprocket can be replaced reducing the amount of reassembly time.

When using the pitch featured on the Extended Motion Pattern a similar level of flexibility can be achieved in sprocket spacing by using Tensioning Bushings (REV-41-1702) with M3 Standoffs (REV-41-1492).

Spacing

In order for sprockets to work effectively, it’s important that the** center-to-center distance** is correctly adjusted. The sprocket and chain example with the red 'X;, in the image below, may work under very light loads, but they will certainly not work and will skip under any significant loading. The sprockets in this example are too close together so chain is loose enough that it can skip on the sprocket teeth. The sprockets, with the green check mark, are correctly spaced which will provide smooth reliable operation.

**To correctly space REV Robotics Sprockets along slots, use the following procedure:**

Securely fix the axle of either the input or output sprocket. In the case of a gear train with multiple idlers or a compound reduction, consider which axle makes the most sense to fix such as the very first input gear or the very last gear.

Starting with the fixed axle, then identify all the driving and driven sprockets for any sprockets on that axle. One by one loosen these axles, slide them until the chain is tensioned and then retighten the axle mounts.

Continue the procedure from Step 2 for each fixed axle until all the chains are tight and all the axles have been retightened.

The process highlighted above works with the slots but the process with the Extended Motion Pattern may require center to center distance calculations.

Center to Center Distance

It is possible to mathematically calculate the number of links needed between two sprockets or the correct center to center distances for two sprockets for a given chain length. These methods are appropriate for robot planning purposes, but assembling your robot using these measurement is typically impractical. The details of these calculations are included for completeness, but most modern CAD packages or numerous free online calculators can also generate the correct values.

Center to center distance in inches

Chain length in pitches

**Where:**

C= Center to Center Distance

L= Chain Length in Pitches

P= Pitch of Chain

N= Number of Teeth on Large Sprocket

n= Number of Teeth on Small Sprocket

Calculate center to center distance

Calculate center to center distance using the 'center to center distance in inches' formula and the chain drive example in the above image.

**Where:**

L = 48

P = 0.25

N = 20

n = 15

After running calculations, the center to center distance for the example is** 3.807 inches**

Calculate chain length

In most design cases the chain length is not known ahead of time, but the two sprockets in the reduction and an approximate center-to-center distance to fit the reduction is known. For this example, a 20:15 reduction is needed, and the whole solution must fit in a space of five inches or less.

In this example the whole solutions must fit into a five-inch space, so in addition to the center to center distance, the chain clearance radius for both sprockets must be accounted for. Use Sprocket Measurement Details to look up the chain clearance diameter (A) for both the 15 tooth and 20 tooth sprocket and subtract the radius of each from the total given solution size to get the maximum center to center distance available.

**Where:**

Using the center to center distance of 3.371 inches as the maximum spacing for this reduction to fit into a five-inch space, solve the chain length in pitches equation.

**Where:**

C= 3.35

P= 0.25

N= 20

n= 15

Since it is **not possible to have a fraction of a pitch length in the chain, the number obtained by solving the formula must be rounded to a whole even number**. In this example because the center to center distance used was the maximum allowed, the exact pitch length should be rounded down to 44 to meet the design requirements.

Now that the maximum even pitch lengths in the chain has been calculated, this value can be plugged back into center to center distance formula to find the exact center to center distance using a 44 link chain:

**Where: **

L = 44

P = 0.25

N = 20

n = 15

For a 15T:20T reduction the longest chain which will fit in under 5-inches using a 44 link chain which gives a center-to-center distance is 3.307 inches and the total solution width of 4.957 inches.

Sprocket Measurements

Plastic Sprockets

The** Motion Interface Pattern** is a circular M3 hole pattern on a 16mm diameter that interfaces with certain REV Brackets and the UltraPlanetary 5mm Hex Output (REV-41-1604).

The 10 tooth #25 sprocket does not have a motion pattern due to size constraints. However, the 10 Tooth Sprocket shares features of the other Plastic Sprockets, like compatibility with #25 Chain. The table below provides the outer diameter and pitch diameter of the 10 Tooth Sprocket.

Metal Sprockets

The 10 Tooth Metal #25 Sprocket (REV-41-1716) while still being #25 Chain compatible differs from the other metal sprockets significantly. See the drawing for relevant information for the 10 Tooth Metal #25 Sprocket.

Creating a loop of chain requires breaking off the correct number of links by removing a specific chain pin and joining the ends together. Chain can be broken using many methods, including a Chain Tool or various steel cutting blades, like a dremel. Once you have counted the number of links necessary for your application, the chain can be joined using a master link or by replacing the chain pin.

#25 Chain Tool Basics

Kit Contents

1 Chain tool block

2 set screw mandrels

1 depth guide screw

1 cup point set screw

1 4mm Allen Wrench

Before using the #25 Chain Tool for the first time, remove the thread pin screw and use WD-40 or compressed air to remove any shavings left in the tool from the manufacturing process. This will ensure the chain break works smoothly and efficiently breaks your chain. Reinstall the thread pin screw. Once this is complete the chain break is ready for use.

Manipulating Chain

In almost all applications, chain links are connected to form a loop. While chain can sometimes be purchased in specific length loops, it is more common and economical to buy chain by the foot and make custom loop lengths to fit the application. It’s recommend to use a specialized tool, a chain breaker, to cut chain into desired lengths to prevent accidental damage.

Chain breakers do not actually cut the chain, instead they are used to press out the pins from an outer link. After the pins have been removed the chain can be separated leaving inner links on both ends of the break.

Chain Tools have two methods for resetting chain. Using Master Links and resetting the chain pin. Resetting the pin is results in a stronger chain than using a master link.

Master Links

Roller chain is typically connected into a continuous loop. This can be done using a special tool to press the pins in and out of the desired outer link as described in the Custom Length Chain section, or if the chain is already the correct length a common roller chain accessory called a master link, or quick-release link, can be used to connect two ends of the chain.

Master links allow for easy chain assembly/disassembly without any special chain tools. Master links can typically be reused many times, but can become bent with multiple uses. At the point that master links become bent they should be discarded.

Steps to using a master link

Place the loose outer plate onto the two pins pressed into the other outer plate.

Ensure the outer plate is inserted onto the pins far enough that the grooves on the pins are fully exposed past the outer plate.

Align the widest gap near the middle of the clip with one of the pins.

The gap in the clip should allow the clip to slip over the pin and sit flush against the outer plate and aligned with the groove in the pins.

Use pliers or another tool to slide the clip towards the other pin until the clip is securely engaged with the grooves on both pins.

Installing the clip as shown in Steps 4 and Step 5 can be sometimes difficult.

There are a number of approaches that may work for these steps, but a common method is to use a pair of needle nose pliers to grip between the back of the clip and the nearest pin to slide the clip.

Using the Chain Tool

Resetting Chain Pins

In the image below, the ratio of the number of teeth from the input sprocket to the output sprocket is 20T:15T which means the input needs to turn 1.3 rotations for the output to complete one rotation $20T/15T =1.3$.

$\text{CR}=\text{R}_1×\text{R}_2 ×\text{…} ×\text{R}_n$

$\text{CR}=\text{R}_1× \text{R}_2 =\frac{60}{30}× \frac{90}{15}=2 ×6=12$

$\text{CDC} = \frac{P}{8}\left[2L - (N+n) + \sqrt{(2L-(N+n))^2-\frac{8}{\pi^2}\times(N - n)^2} \right]$

$L = \frac{2C}{P} + \frac{N+n}{2} + \frac{P(\frac{N -n}{2\pi})^2}{C}$

$\text{CDC} = \frac{0.25}{8}\left[2(48) - (20+15) + \sqrt{(2(48)-(20+15))^2-\frac{8}{\pi^2}\times(20 - 15)^2} \right]\newline= \frac{0.25}{8}\left[ 96 - 35 +\sqrt{(96-35)^2 - \frac{8}{\pi^2} \times (5)^2} \right]\newline=\frac{0.25}{8} \left[ 61 + \sqrt{(61)^2 - \frac{8}{\pi^2}\times25}\right]\newline = \frac{0.25}{8}\left[ 61 + \sqrt{3721 - \frac{200}{\pi^2}}\right]\newline\frac{0.25}{8}\left[61+\sqrt{3721-20.24642}\right]\newline = 0.03125\left[61+60.833\right]\newline = 3.807$

$\text{Maximum CDC} = \text{Total Solution Width} - \text{Clearance Radius 1}-\text{Clearance Radius 2}$

$\text{Total Solution Width} = 5 \text {inches}\newline\text{Clearance Radius 1}\,=15T_{chain\, clearance\, diameter(A)} = 1.45\,\text{inches}\newline\text{Clearance Radius 2} =20T_{chain\, clearance\, diameter(A)} = 1.85\,\text{inches}$

$\text{Maximum CDC Available} = 5 - \frac{1.45}{2} - \frac{1.85}{2}\newline\text{Maximum CDC Available} = 3.35 \text{inches}$