The Wii board is cool and I want to use it for some physics-stuff. If you are not familiar with the Wii board, basically it is a platform you stand on. Four sensors in the board determine your center of mass. By shifting your weight and stuff, you can interact with a game. First thing - can I use the measurements from the board to find out where the 4 sensors are?
I am going to make some measurements, but first some theory. Suppose you have some mass at some location on the Wii board. If you know the readings from the 4 sensors, how would you find out where the center of mass of the object is? Diagram time.
So what do I need here. First, I labeled the four sensors R1 through R4. I assume that the board is symmetrical so that the sensors on the left are a distance xA from the origin and the ones on the right are the same distance. The vertical distance of the sensors from the center are yy. The red cap represents the center of mass of some object. It has a location of (x,y) with respect to the center of the board. A few more things. W is the weight of the object. K is the weight of the Wii board and n is some constant that relates the Wii sensor readings to real force values (in Newtons).
Now for the physics. If the object on the Wii board is in equilibrium, then the following should be true:
- The sum of the forces in the vertical direction (for the board) must add up to zero.
- The sum of torques about the x-axis must be zero.
- The sum of torques about the y-axis must be zero.
Note: I am assuming that the Wii sensor readings are the same values as the force the floor pushes up on the Wii board. I am also going to assume that the center of mass of the Wii board itself is in the center. Maybe I should include one side view diagram of the Wii board. This is looking down the 'x-axis'
I left some stuff off, but hopefully that will help. With that, the three equations represent the above conditions:
Forgive me, but I have to re-write those last two equations.
Great, but now what? Well, my goal is essentially to find xA and yA. I will place a weight on the Wii board at different locations and record the sensor readings. Using a small modifications to EarthSurfer (an app to let you move around google maps with the Wii board) I can get the data.
If I plot (R2 + R4 - R1 - R3) vs. x (x-value for the weight), I should get a straight line. The slope should be related to the x-location of the sensors. I can do a similar thing for the y values. Here is that graph. I made this with google docs just to be different, but I don't know how to add a trendline. You can determine the slope and intercept for some data though.
According to the expression above, the slope from google docs should be:
The unit "Wii" is whatever units the wii board gives. No clue what that should be. At least this data is linear, even though I can't get a value for xA (because I don't know W or n). Ok, here is a similar plot for the changes in the y value of the mass on the board.
With a slope of:
I still don't know W or n. So, what are the readings when there is no weight added to the board? I get:
Since there is no weight (at least no extra weight) I can assume that K = 0. Great. For the cases where there is weight on the board, I get an average sum of readings of 7.225 Wiis. This gives me:
Now I have a value for W/n. Solving for xA and yA:
Well? Is that correct? Who knows. My first assumption was that the sensors in the Wii board at the same location as the four "feet" on the board. Here is an image of the bottom of the board.
I used Tracker Video to measure the location of the feet. From this, half the distance between the feet in the 'x-direction' is 0.217 meters and 0.119 meters for the y-direction. I think I win.
I still don't know the value of 'n' so that I can't get any real weights from this Wii board. The one way to fix that would be to put some known weight on there. In my case, I just had a hand full of scuba weights and wasn't too sure of the value. Oh well, I can do that later.
