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Designing Around the Gyroscopic Effect
**- Adam Wrigley

Last updated - September 2006

**DISCLAIMER:** Combat robotics is a dangerous sport by it's nature. Extreme caution should be taken when performing ** any** operation explained on this site.

Build Responsibly

The gyroscopic effect is what causes robots with vertically spinning weapons to tip up when turning. This tutorial will describe how to design your robot so that your spinning weapon won't cause your robot to tip while turning.

If you don't wish to look over all the equations, go to the bottom of the page for a calculator that will do the math for you.

There is actually a very simple formula to figure out what the forces are:

M = I × w1 × w2

Iis the mass moment of inertia of the spinning weapon system, measured inkg⋅mClick Here to find the mass moment of inertia for your weapon.^{2}

w1andw2are the rotational velocities of the weapon and the turning robot in the units ofradians/second. It does not matter which label you use for which speed. To convert the RPM of your weapon to radians/second, use this formula:w = (RPM × Pi) ÷ 30

Mis the resulting moment applied to the chassis measured inNewton-meters. With a standard vertically spinning weapon, when turning left, the right wheel will raise. When turning right, the left wheel will raise.

To figure out how fast the robot is rotating when you have one side of your drive in forward, and one in reverse(maximum turning), use this formula:

w = ( RPM × D × Pi ) ÷ ( 30 × L )

Lis the width of your robot's drive train.

Dis the diameter of your wheels.

RPMis the RPM of your drive motors.

wis the how fast your robot is rotating, inradians/second.You don't need to use meters for length here, but make sure that

LandDare in the same units, they will cancel.

The ideal robot, when turning at max speed, will not have either of it's wheels raise. To figure out if your robot's wheels will lift when turning, use the following formula:

Tip = M ÷ ( L^{2}× Weight )

Weightis the weight of your robot inNewtons(kilograms*9.8).

Lmust be inmeters.

- If you will turn by simply stopping one wheel while powering the other, divide
Tipby 2.If

Tipis >1, the robot will raise a wheel when turning. IfTipstays <1, your robot will never have a wheel lift, but ifTipis near 1 one side of your drive train will have little traction when turning sharply, slowing your turn.

Tipshould be minimized. The easiest way to minimize this number is to increase the width of your robot (notice that it is squared in the denominator of the equation).

To figure out the force on the raising wheel (this would normally be a positive number equal to half your robots weight) use this formula:

Force = ( Weight × L ÷ 2 ) - ( M ÷ 2 )If this force is negative the wheel will lift. If the arena surface is magnetic, the lifting force may be countered by chassis magnets located near the wheels. The magnetic force must equal or exceed the gyroscopic lifting force to be effective.

Now that you know how to do it by hand, here's a calculator to save you the trouble...

Gyroscopic Effect Calculator (requires javascript)If you need help converting units, download this program: Convert

'Max Robot Spin Rate'is the quickest the robot can rotate 360 degrees, spining in place with negligable turning friction.

'Force on Raising Wheel'with no gyro effect would be half the weight of your robot.

- If the value is positive the robot can spin at full speed without wheel lift.
- If the value is close to zero one wheel will have very little traction in a high-rate turn.
- If the value is negative one wheel may lift off the floor in a full-speed spin.
For a more in depth description of the gyro effect, visit: http://www.gyroscopes.org/math.asp

'Max Flat Turn Rate'is the quickest the robot is able to rotate 360 degrees without wheel lift. You may restrict the turning rate of your robot by setting a 'Dual Rate', 'ATV', or 'Travel Adjust' on your R/C transmitter. Consult your radio manual for details.

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