# Homework Help: FBD of Segway model

1. Nov 19, 2008

### saltine

This problem is not from a textbook. There is no given problem statement. Please let me know if the problem statement does not make sense.

1. The problem statement, all variables and given/known data
Model a two-wheeled system with DC motors that is meant to self-balance like a Segway if there is control. The input is the voltage to the DC motor. The output is the angle from the vertical axis.

The Body and the Motor together is one rigid piece. The Wheel and the Axle are also rigid. There is friction between the Axle and the Motor such that when the Body is off-balanced, the Wheel would roll with respect to the ground, but not with respect to the Body.

2. Relevant equations
(none)

3. The attempt at a solution
I separate the equations into two groups. The first group is that from the voltage applied to the Motor to the torque acting on the Axle. The second group is that from the applied torque to theta. At the moment I want to focus on the equations of the second group starting from the FBD.

This is the FBD I have now. Is it correct? Does it have enough variables?

For the Body:
I sum the forces in the x and y directions for the Body. This would tell how the center of mass would move in the absolute coordinates. Then I would sum the torques about the center of mass. This would tell me how the body rotates with respect to itself, although in reality, the body is rotating about the Axle. When I combine the movement in the x and y directions and the rotation about the center of mass, the result should show that the Body is in fact attached to the Axle and rotates about the Axle. Is this correct?

For the Wheel:
I would sum the forces in x direction but not y, because I know that the wheel does not move upward. I know that the Wheel should be moving horizontally. So when I sum the horizontal forces, one of the components is from the torque. Here I assume that the wheel rolls without slipping, and relate the torque to the horizontal force. When I combine the results of the angular velocity and the horizontal motion of the wheel, they should show that the wheel is spinning and not slipping.

TBA:
It seems to me that TBA is the sum of the Motor torque and the torque caused by the falling Body. Is TAB simply the negative of TBA?

FBAx:
It seems that this is caused by the falling Body. It is the horizontal force the falling Body would create if the Body is rotating about its center of mass.

FBAy:
This is caused by the weight of the Body. If one snaps the top of the Body forcefully can the wheels leave the ground?

4. A specfic question
How do momentum and moment of inertia come into the picture?