Designing Around the Gyroscopic Effect - Veteran
- Adam Wrigley
Last updated - September 2006
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The gyroscopic effect is what causes robots with vertically spinning weapons to tip over 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 figure it all out for you.
There is actually a very simple formula to figure out what the forces are:
M = I * w1 * w2
The easiest way to use this formula is with the SI unit system.
I is the mass moment of inertia of the spinning weapon system, measured in Kilogram*meters^2 Click Here to find out the mass moment of inertia for your weapon.
w1 and w2 are the rotational velocities of the weapon, and the turning robot in the units of radians/second. It does not matter which label you use for which speed.
M is the resulting moment applied to the chassis measured in Newton*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)
L is the width of your robot's drive train.
D is the diameter of your wheels.
RPM is the RPM of your drive motors.
w is the how fast your robot is rotating, in radians/second.
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.
To convert the RPM of your weapon to radians/second, use this formula:
w = (RPM * Pi)/30
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 it <1, then it will stay on the ground. This number should be minimized as much as possible. 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). Other methods to reduce tip are magnets, or with suction. These methods however are very hard to predict and less effective.
Weight is the mass of your robot in kilograms*9.8 (the result of this will be the robot's weight in Newtons).
L must be in meters.
If you plan to turn by simply stopping one wheel, while powering the other, simply divide tip by 2, and the same rules apply.
Also of concern is that if tip is near 1, then one side of your robot's drive train will have almost no force placed on it. This may cause you to loose traction on that drive side, slowing your turn. However, if tip stays <1, your robot will never have a wheel lift.
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.
Gyroscopic Effect Calculator(requires javascript)
If you need help converting units, download this program: Convert
For a more in depth description of this effect, visit this website:
http://www.gyroscopes.org/math.asp
