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Mechanical Design
Written by David Giessel

While I still haven't written up a formal bit on mechanical design, I'll leave a list of guidelines to follow.

Lighter is better
Smaller is better (to a point)
Lower center of gravity is better
Lower inertia is better
Lower polar moment is better
Lower wheel inertia is better

Remember the words of the great Colin Chapman, "To add speed, add lightness."

When you write a software algorithm that simply turns a motor on or off, you assume the limiting case of zero inertia and instantaneous acceleration. The lighter your robot is and the stickier the tires are, the easier it is to approach this limiting case. Obviously the proper way to control your mouse isn't with discrete on and off events but with PID loops that provide "second order" controls, but even these rather flexible PID loops are easier to tune when inertias and moments are minimized.

Remember that with a wheelchair design you want your weight very nearly centered so that neither the front nor rear skid touches the ground when the robot is stationary. You also want to space the skids as far as possible from the wheel centerline as this will minimize mass transfer under braking and acceleration. You want mass over the wheels to maximize traction (something that's tricky when you only have two wheels). Low center of gravity also minimizes mass transfer and is a fundamental key for acceleration and deceleration. It's much easier to control accel and decel with a robot that isn't tipping back and fourth.

Polar moment is the rotational inertia of the entire robot about its "center of rotation" (which is exactly in the center for two wheel turns, and slightly offset to the left or right for one wheel turns). Mass centralization is how one minimizes polar moment. Think for a second about a meter stick (or yard stick) with a 1 kilo (or two pound) weight on it. First imagine holding the stick in the center with the weight resting in the palm of your hand (centered mass). Now twist the stick clockwise and anti-clockwise. It's very easy to change the direction of rotation. Now attach the same weight to the end of the stick and try to rotate it back and fourth. Notice how much harder it is to change direction? The stick is still the same length and the mass is still the same, but it is no longer centered about the axis of rotation. In your micromice, you'll notice "overshoot" when you first start tuning your turn algorithms (your encoder counts will spill over a bit from what you want them to be). A mouse with a high polar moment will overturn significantly whereas one with low polar moment will be much more responsive and may only overturn a degree or less for a 90 deg turn making it much easier to tune.

Wheel inertia and tire tread width is the last thing I'll ramble about here. Notice in the competition photos of our 2008 robot that I've cut the tires in half (from 1 cm width down to 5 mm). This provided two benefits with only one minor tradeoff. Firstly, the rotational inertia was reduced and acceleration and deceleration became more consistent (our PID loops had an easier time homing in on a target speed). Secondly, with a 1 cm tread width, the part of the tire which the robot was pivoting on was somewhat uncertain. For example, in one corner the robot might rotate on the inside edge of the tread making it 5 mm narrower than our mathematical model whereas in another corner it might rotate on the outside edge of the tread making it 5 mm wider. By turning the tires into "O" rings, much of this uncertainty was eliminated and the turns became much more deterministic. The one tradeoff was that the overall traction was reduced very slightly, primarily because the tread had more pressure on it and was therefore more prone to collecting dirt. While a physicist will tell you that tire width does not affect µS or µK (lower surface area = higher ground pressure ... so they cancel), equations for "traction" do not linearly follow those for coefficient of friction, so in most cases a wider tire will have a bit more "bite" than a narrower one under the same conditions.