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[DPRG] DC motor requirements??

Subject: [DPRG] DC motor requirements??
From: DeltaGraph at aol.com DeltaGraph at aol.com
Date: Sat Jul 16 09:43:59 CDT 2005

Re: Balancing Robot Motor Requirements

I am not going to give you a real answer, but maybe this will give you some 
ideas for doing research...

My mechanical engineering skills are sketchy at best.

A few years ago I dug out my physics and dynamics texts and  wrote a 
simulation program (probably full of flaws) then later built a balancing robot almost 
as good as nbot.

For your consideration would be the moment of inertia of the wheels and the 
inertial properties of the robot body which I recall modeling as two point 
masses. One mass fixed at the axis of rotation (which I believe I included the 
mass of the wheels)  and another at center of mass of the robot body. I 
considered inertial properties of the wheels separately 

To simplify the problem start by fixing the wheels to the ground where they 
cannot roll. Your problem is now a torque problem except your as your robot 
center of mass starts rotating it now has inertial kinetic energy which will 
require motor torque to restore so you now have a nice dynamics problem deciding 
how fast you will recover from the "fall" from balance.

It gets a bit trickier when you let go of the wheels. Now the wheels tend to 
accelerate when you apply torque which causes a combination of things to 
happen: 1) Energy is stored in the wheels (rotational moment of inertia -- correct 
term?) and 2) as the wheels move the base of the robot moves which creates 
forces acting along a line of action to the body center of mass. 

I hope this makes some sense. A ball and stick model of the robot might help. 

Keep in mind. You can make almost anything balance, but how well will be 
determined by several factors, so I say:

Robot Mass
Location of Mass from Rotational Axis
Wheel Moment of Inertia
Wheel Torque
Wheel Max Speed
Control Algorithm
Speed of Control Loop 
Tilt Sensor Accuracy
Rotational Velocity Sensor Accuracy
Wheel Encoder Accuracy
Your Patients

- Ron Grant

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