what wheel diameter for a mecanum drive

We recommend choosing mecanum wheels with a diameter between 3 and 4 inches (approximately 75mm to 100mm). According to Game Manual 0, larger options like 6-inch wheels are generally more expensive and fail to provide any meaningful performance benefits. The gold standard wheels highlighted by Game Manual 0 fit right into this recommended range, including the 96mm goBILDA v2 wheels and the smaller 75mm REV Robotics wheels.

Your specific choice within this 3-to-4-inch range depends on your drivetrain's torque, speed, and clearance needs. As explained in Telemark's guide on wheel diameter, wheel size acts as a transmission choice; a smaller wheel provides an additional gear reduction that is highly beneficial if your motors are short on torque. Conversely, you should opt for a larger wheel in this range if your robot needs to cross field seams, clear small obstacles, or achieve a higher top speed at a given motor RPM.

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Holonomic Drivetrains > Mecanum Drive > Mecanum Wheels Miniguide

Game Manual 0·CC BY-NC 4.0

One of the most important features of a mecanum wheel is the mechanism that allows the roller to spin---either bushings or ball bearings. Mecanums which use ball bearings strafe better than those which use bushings, as the rollers can spin with less friction.

Note: In the past, some teams have invested in 6 inch diameter mecanum wheels. These are generally much more expensive and generally do not provide significant performance benefits. We highly recommend sticking with wheels that are between 3 and 4 inches in diameter.

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Holonomic Drivetrains > Mecanum Drive > Mecanum Wheels Miniguide > Recommended

Game Manual 0·CC BY-NC 4.0

These wheels are the gold standard of mecanum wheels, if you are buying new mecanum wheels there is very little reason to buy any mecanum wheels not from this section.

goBILDA Mecanum Wheels v2 (https://www.gobilda.com/96mm-mecanum-wheel-set-70a-durometer-bearing-supported-rollers/) ($127.49 with team discount): The goBILDA v2 Mecanum Wheels are the gold standard for teams wanting a quality design in all aspects. They feature a 96mm diameter and a thickness of 38mm, with ball bearing supported, 70A durometer rollers that provide excellent strafing performance. With the use of recessed 16x16mm and 32x32mm holes, these wheels have the largest amount of mounting options and can fit all shaft styles commonly used in FTC®.
REV Robotics Mecanum Wheels (https://www.revrobotics.com/rev-45-1655/) ($127.50 with team discount): The REV Robotics Mecanum Wheels come in at only 75mm in diameter, providing a smaller mecanum wheel option to FTC teams; however, they are not the thinnest option at 40.8mm thick. They feature ball bearing supported rollers that provide exceptional strafing capabilities and traction. The hole pattern featured on these wheels is compatible with Andymark Nubs as well as the REV Robotics Universal Hex Adapter v2 (which is included); however, in order to use other shaft options the use of an adapter or physical modification will likely be required.

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Holonomic Drivetrains > Mecanum Drive > Mecanum Wheels Miniguide > Viable

Game Manual 0·CC BY-NC 4.0

These mecanums have acceptable performance but there is very little reason to buy them at this point, as they have been superseded by better ones. If you already own them, they are a viable option, but consider looking at some of the mecanums from the Recommended section.

Nexus Ball Bearing Mecanum Wheels (https://www.robotshop.com/en/100mm-mecanum-wheel-set.html) ($134.00): These wheels are 100 mm in diameter and 59 mm wide. They strafe excellently because of the use of ball bearings. However, they are more expensive, take up more space, have less traction, and are harder to mount to than the recommended wheels.
goBILDA Mecanum Wheels v1 (https://www.gobilda.com/96mm-mecanum-wheel-set-70a-durometer-bearing-supported-rollers/) (discontinued): These wheels are very similar to the Nexus Ball Bearing Mecanum Wheels, but with a different color scheme and better mounting options.
Andymark Heavy Duty Mecanum Wheels (https://andymark.com/products/4-in-hd-mecanum-wheels) ($225): These are easily the most expensive mecanums on the list. These wheels are 4" in diameter and 1.65" wide. These are bushing based mecanums, so while they strafe decently they still perform worse than bearing based ones. They have a good amount of traction, more than the Nexus bearing or bushing wheels.
Nexus Bushing Mecanum Wheels (https://www.robotshop.com/en/100mm-aluminum-mecanum-wheel-set.html) ($80.00): This is the Nexus Ball Bearing Mecanum Wheel with bushings instead of ball bearings. There is not much to say about them except that they strafe decently but worse than the ball bearing based equivalent.

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The Three Families

Telemark·Team owned

Tank drive has wheels that only roll forward and backward. The robot turns by driving the sides at different speeds. Simple, efficient, strong in a pushing match, and it cannot move sideways.

Mecanum drive uses four wheels with angled rollers around the circumference. By combining wheel directions the robot translates in any direction and rotates independently. Excellent maneuverability, and it pays for it in traction and efficiency.

Swerve drive puts each wheel on a module that can rotate to any heading. It has the maneuverability of mecanum with the traction of tank, and it costs substantially more in complexity, parts, weight, and programming.

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Holonomic Drivetrains > Mecanum Drive > Mecanum Wheels Miniguide > Not Recommended

Game Manual 0·CC BY-NC 4.0

There is almost no reason to use these mecanum wheels---they perform very poorly and are not much cheaper than those in the Recommended section. We cannot recommend the use of these on an FTC robot, if at all possible replace them with mecanums from the Recommended section.

TETRIX Mecanum Wheels (https://www.pitsco.com/TETRIX-MAX-Mecanum-Wheels) ($149.00): These mecanums are designed with a bushing based, hard plastic roller which in turn creates poor strafing performance. The integrated hub is a set screw based design with a round bore, causing unreliability as well as taking up extra space.
Andymark Standard Duty Mecanum Wheels (https://andymark.com/products/4-in-sd-mecanum-wheel) ($77.00): These wheels barely strafe and are super fragile.

(Figure: 8103 Null Robotics, Rover Ruckus, using Nexus mecanum bearing)

(Figure: 731 Wannabee Strange, Rover Ruckus, using AndyMark HD mecanum wheels)

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Mecanum TeleOp

Game Manual 0·CC BY-NC 4.0

Note: Some common COTS mecanum drivetrain kits are the goBILDA Strafer Chassis Kit (https://www.gobilda.com/strafer-chassis-kit-v5/) and the REV Mecanum Drivetrain Kit (https://www.revrobotics.com/rev-45-2470/).

A standard mecanum drive configuration possesses 4 mecanum wheels oriented in an "X" shape. This means that the rollers are angled towards the center when looking at it from above. This configuration allows one to add up the force vectors generated by the offset rollers and derive movement in any direction. It is important to note that because of friction, perfect movement isn't possible in every direction, so a mecanum drivetrain will be able to drive slightly faster forwards/backwards than any other directions. Combining translation and rotation will also result in slower movement.

In the image above, vectors 1, 2, 3, and 4 are the force vectors created by the mecanum wheels when the chassis is instructed to drive towards the top of the image. All motors are driving forward. The blue and red lines are their X and Y components, respectively. Here are a few examples of how the wheels must be driven to achieve different movements:

Attention: It is strongly advised to not hardcode these movements in; there is a much better way described below that allows for true holonomic movement and is much more elegant.

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Chief Delphi > FTC > FTC 8-Wheel Mecanum Drive - NX PowerPlay

Chief Delphi·Community forum posts — not openly licensed

This source does not publish a licence, so its text is not reproduced here. Open the source to read it.

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Holonomic Drivetrains > Mecanum Drive > Advantages

Game Manual 0·CC BY-NC 4.0

Fantastic maneuverability and agility due to strafing, can avoid defense very well
Good acceleration, can have high top speed
Very versatile drivetrain for nearly any game

Suffers in traction, as mecanum rollers have a lower coefficient of friction than traction wheels; cannot traverse terrain
Able to be pushed around on defense
Wheels must be powered independently, so there is no redundancy

CAD Examples of Mecanum Drive (Click to expand) goBILDA COTS Click here to explore this model in OnShape online CAD (https://cad.onshape.com/documents/45549489f570f3694569a2df/w/85ff26b9fca4988ebc4df3b4/e/df9bcea72fcdd7e4aee4134b)

REV COTS Click here to explore this model in OnShape online CAD (https://cad.onshape.com/documents/45549489f570f3694569a2df/w/85ff26b9fca4988ebc4df3b4/e/b8d4a6cfe4f26c5170f40a6c)

goBILDA Custom Click here to explore this model in OnShape online CAD (https://cad.onshape.com/documents/45549489f570f3694569a2df/w/85ff26b9fca4988ebc4df3b4/e/cc2df2fbce0e9ca393696b54)

REV Custom Click here to explore this model in OnShape online CAD (https://cad.onshape.com/documents/45549489f570f3694569a2df/w/85ff26b9fca4988ebc4df3b4/e/40c3266dab2e444011cce79c)

(Figure: Configuration for mecanum wheels, courtesy goBILDA)

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Holonomic Drivetrains > X-Drive

Game Manual 0·CC BY-NC 4.0

X-Drive is a holonomic omni-wheel based drivetrain. This type of drive involves mounting 4 omni wheels at the corner of the robot at a 45 degree angle.

One notable difference between X-Drive and mecanum is strafe speed. While, as mentioned in the mecanum section, the ratio of strafe speed to forward speed is noticeably less than 1, the ratio on an X-Drive is exactly 1 due to the rotational symmetry of the wheel placement. This means that an X-Drive bot's strafe speed and forward speed are equivalent. The drivetrains are slower, however, when strafing at 45° (approximately frac{sqrt{2}}{2} of its forward speed).

Even though X-drive has good turning and acceleration, the main downside to the drive is packaging/form factor. Packaging refers to how easy/convenient the drivetrain fits into the overall design of the robot.

Ideally, the drivetrain should take up as little space as possible to make it easier to design mechanisms around. Because the omni wheels are offset, packaging a X-Drive is more difficult than other types of holonomic drive like mecanum or H-Drive. Also because of the strange packaging, it is relatively difficult to cleanly transfer power from the motors to wheels, meaning that most X-Drives end up being direct-driven, which is bad for the lifespan of the motor gearbox.

Note: When using X-Drive, the robot moves forwards/backwards/straight side-to-side sqrt{2} times faster than a drivetrain with wheels in the normal orientation (with the same gear ratio and wheel size).

For an explanation of why exactly this is, see this analysis (https://www.chiefdelphi.com/t/paper-mecanum-and-omni-kinematic-and-force-analysis/106153).

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Variants Worth Knowing

Telemark·Team owned

Six wheel tank with a dropped center. The center wheels sit slightly lower than the outer ones, so the robot pivots about the center rather than dragging four contact patches through the turn. This substantially reduces turning scrub. Common and effective.

Tank with omni wheels on one end. Replacing two of the four wheels with omni wheels cuts turning resistance dramatically while keeping full traction on the driven pair. It also reduces pushing force somewhat and makes the robot easier to push sideways.

H-drive. A tank drive with one additional wheel mounted transversely for strafing. It gives limited sideways motion without paying mecanum's full traction cost.

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Fill-in-the-Blank Practice

Telemark·Team owned

Mecanum wheels have lower effective traction than tank wheels because the angled __________ direct only part of the contact force along the direction of travel.
A six wheel tank drive with a dropped __________ wheel reduces scrub during turns.
The drivetrain choice should be derived from the team's __________ rather than from what a successful robot used last season.

Show answers

rollers
center
strategy (requirements)

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Open Telemark

Dead Wheels > Drive Encoder Localization

Game Manual 0·CC BY-NC 4.0

Pros:

Cheap (the motors you're using most likely already have encoders built in)
Accessible
Very little configuration necessary
Cons:

Drive encoder localization on mecanum drive can be quite inaccurate due to lack on traction on mecanum wheels.
Will drift on high acceleration on mecanum drive. Accuracy will be good enough for basic autonomous modes if acceleration is limited

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Drivetrains > Drivetrain Options

Game Manual 0·CC BY-NC 4.0

Omni Wheel — Omni(directional) wheels, sold by many different vendors, are a special type of wheel that prioritizes mobility and strafing (moving laterally) over traction or front-back movement. They are similar to mecanum wheels in that omni wheels have rubber rollers that rotate perpendicular to the plane of the wheel.

Thus, the robot can move sideways (although the robot is not powered in the sideways direction). It is also utilized as a low-friction wheel in 4 wheel, 6 wheel, and 8 wheel drivetrains instead of having corner traction wheels.

Furthermore, X-drive utilizes four omni wheels, though traction is at a minimum.

A mecanum wheel is technically an omnidirectional wheel, but when generally referred to, an "omni wheel" has rollers rotated 90 degrees to the rotation of the wheel, where a mecanum wheel is generally 45 degrees.

Traction wheel — A traction or grip wheel is a wheel designed for maximum grip. It has an outer ring made of rubber, and its wide track ensures a larger contact patch with the ground. Traction wheels are commonly found in tank drivetrains. They are sold in different sizes and thicknesses by different manufacturers.

Strafing — Strafing is the act of moving sideways or laterally (somewhat similar to drifting). It is possible with omni or mecanum wheels, and not possible with traction wheels.

Parallel Plate Drivetrain — A parallel plate drivetrain is a drivetrain that has drive pods that consist of 2 plates spread apart with wheels and drive transmission in between them.

These plates can be anywhere from 1" to 5" apart, depending on the space requirements of the wheels and drive system. Generally, a pod width of 3" or less is desired to maximize the space between the drive pods for mechanisms such as an intake.

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Kinematics > Mecanum Drive > Forward Kinematics

Game Manual 0·CC BY-NC 4.0

The forward kinematics of a mecanum drive relate the velocity of the wheels to the forward, strafe, and rotational velocities of the robot, relative to itself. These are as follows:

vf = frac{v_fr + v_fl + v_br + v_bl}{4}

vs = frac{v_bl + v_fr - v_fl - v_br}{4}

ω = frac{v_br + v_fr - v_fl - v_bl}{4*2r_b}

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Kinematics > Mecanum Drive > Inverse Kinematics

Game Manual 0·CC BY-NC 4.0

The inverse kinematics of a mecanum drive relate the desired velocity of the robot to the velocity required on the wheels. These are as follows:

vfl = vf - vs - (2r_b · ω)

vbl = vf + vs - (2r_b · ω)

vbr = vf - vs + (2r_b · ω)

vfr = vf + vs + (2r_b · ω)

Open Game Manual 0

Wheel Diameter

Telemark·Team owned

Diameter is a transmission choice as much as a traction choice. For a given wheel RPM, a larger wheel travels faster and delivers less force at the ground, exactly as if you had reduced the gear ratio.

speed = wheel_rpm * pi * diameter
force = wheel_torque / wheel_radius

Practical implications: a smaller wheel is effectively an extra reduction, useful when torque is short; a larger wheel crosses field seams and small obstacles better and gives more ground clearance. Lesson 7.3 puts both into one calculation.

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