I am working on designing a walking machine, but I needed to know the Center of Mass of the LEGO NXT Motors. When using Newton’s Laws to compute the forces on the system, we can treat the motor as if all of its mass is located at a single point. The Center of Mass is the location of this point.
There are several ways to find the Center of Mass of the motor. The most straightforward way is to hang the motor from an axle placed in one of the holes. The motor will orient itself so that the Center of Mass lies directly below the axle. By hanging a mass on a string from the axle, the Center of Mass must lie somewhere along the line defined by the string.
After performing this experiment, I placed a small piece of Scotch tape over the string so that I can keep track of where that line is. I then cut the string off of the axle.
Now to find the precise point, we simply perform the experiment again, but place the axle through a different hole. This gives us a second line. Since the Center of Mass must be on both the first line and the second line, it is located at the intersection of these two lines.
The Center of Mass is very close to being aligned with the holes on the motor. Below is an MLCAD image of the NXT motor (from Philo). I have overlayed a Cartesian coordinate system that corresponds to that used to define the 3-D image file. The origin of this system is at the center of the axle hole on the motors drive axis. This is perfect for me since I will be rotating the motor and trying to compute the position of the Center of Mass after the motor has rotated through some arbitrary angle.
This image not only helps with identifying the Center of Mass of the NXT motor, but also in understanding the dimensions of the NXT motor overall.