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Robot Dynamics Tutorial- Units query

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timstirling:
I've been trying to find out what sort of motors would be required by my robot in order to carry around a laptop and some cameras. The tutoiral was helpful in revising my physics knowledge but I have a question about the units used.

Specifically with the Robot Motor Factor.
The equation examples have the Torque in lb/in but the acceleration and velocity are in ft/s, i.e there is a mix of inches and feet going on. Is this correct, doesn't seem right to me unless I'm missing something.




These are my numbers:
Mass: 6-8kg/13.2-17.6lbs
Motor Choice 1: 200rpm, 4.6kg/cm = 25.8lb/in
Motor Choice 2: 120rpm, 8.87Kg/cm =  49.7lb/in

Motor 1 RMF = 15.3 kg.... / 86   lb...
Motor 2 RMF = 17.74kg..../ 99.4 lb...


Now, using similar velocities as in the example equations= 3ft/s and 2ft/s^2
~= 90cm/s and 60cm/s.
Metric: 6*90*60/(2Pi)= 4751....
with your imperial equatgion and ft/s: 11.6.......


Why is the velocity in feet and the torque in inches?
 

Admin:
Oops! I wrote inches where I should have written feet in several places. I even had another mechanical engineer check before I posted this and she didnt even notice it . . . I guess I was inspired by NASA  ;)

Anyway it should be corrected now.

I probably should have written this using the metric system . . . its just Im american and although it is easier I believe to calculate in metric, it is easier for me to think in the english system.

As long as you stay consistent with unit use, your RMF will always be:
Torque * rps > = Mass * Acceleration * Velocity / (2 * pi)


So I did the calculations, and I got the same motor RMF's as you:
86 lb in rps
99.4 lb in rps

And finding the minimum RMF required, I got:
english
(13.22lbs * 3ft/s * 2ft/s^2) / (2 * pi) = 1817.88 lb in rps
metric
(6 * 91.44 * 60.96) / (2 * pi) = 5322.95 kg cm rps

Those motors are way below your spec . . . you might just want a velocity of 1 ft/s and accel of 1 ft/s for a minimum RMF of 303 lb in rps. Then find a motor about 3x better RMF than motor 2. The problem you will find is that stronger motors are expensive and weight on your robot means money out of your pocket . . .

Anyway let me know if I pulled a NASA again . . . g'luck!

timstirling:
Ok, thanks. So I haven't gone bad.

This is one time when i wish i was wrong though. Looks like it is going to be very difficult to get hold of motors powerful enough to lug the laptop around. And if I do get motors powerful enough then  the motor controllers I was hoping to use wont be able to take the current.

back to the drawing board!  ;)

Admin:
use a microcontroller <cough>  ;)

timstirling:

--- Quote from: Admin on August 13, 2006, 09:40:28 AM ---use a microcontroller <cough>  ;)

--- End quote ---
i may well use a microcontroller anyway, but the main purpose of the robot is to do some advanced vision processing, sound localisation and recognition and neural-SLAM type stuff.

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