Designing Around the Gyroscopic Effect
- Adam Wrigley
Last updated - September 2006


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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


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)

You don't need to use meters for length here, but make sure that L and D are 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]

If tip is >1, the robot will raise a wheel when turning. If tip stays <1, your robot will never have a wheel lift, but if tip is near 1 one side of your drive train will have little traction when turning sharply, slowing your turn.

Tip should 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

Drive Train Width mm
Drive Motor Speed RPM
Wheel Diameter mm
Robot Mass kilograms
Weapon Mass Moment of Inertia kg·m²
Weapon Speed RPM
Max Robot Spin Rate Second per revolution
Force on Raising Wheel Newtons @ Max Spin Rate
Max Flat Turn Rate Second per revolution


'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.

'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.

For a more in depth description of the gyro effect, visit: http://www.gyroscopes.org/math.asp

 

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