Society of Robots - Robot Forum
Mechanics and Construction => Mechanics and Construction => Topic started by: wrinewind on February 29, 2008, 10:38:59 AM
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I'm in the process of designing a simple 2 link robotic arm, akin pretty much identical to what is shown in the Robotic Arm Designer excel sheet. While I'm always for finding fun and easy systems which will do calculations for me, I decided to check what I was getting from the sheet, and I found something which doesn't make sense. The equation used to determine the torque requirements consists of the two general parts:
Eq 1) mass * Radius <- Makes sense, it's the moment generated by the various elements when you consider the mass is in lbm, which numerically converts directly to lbf.
Eq 2) mass * radius * radius * angular velocity <- kinda lost on this one.
The units should end up as Force * distance , however for the second equation, the units end up as Kg * m* m / s, which is not quite Force * distance, which would be (kg * m / s^2) * m. So, if the angular velocity term were squared, this would work, all else being the same. Basically, that equation 2 should be:
mass * (radius * angular velocity)^2
Did I miss something in the units, or am I on to something here?
Thanks.
P.S. I love this site :D
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On closer inspection, I found the part of the site referring to a "Robot Motor Factor," and realized that this is what the calculation is referencing. Thinking some more about this, it looks to be an approximation for (Moment of Inertia * angular acceleration), though I wonder about how accurate it is. Either way, I'm still curious about what others think of this.
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can you post a link to the calculator? or the page with a link to the calculator (sorry I'm new here and don't know what calculator your talking about.)
I'd love to help though.
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http://www.societyofrobots.com/robot_arm_calculator.shtml (http://www.societyofrobots.com/robot_arm_calculator.shtml)
At that site, it sends a link to an excel spreadsheet. If you pick apart equation in the resulting "torque requirements" you'll see what I'm talking about. The units don't quite match. The author made up the second value (The "Robot Motor Factor"), as discussed in the dynamics section, linked below.
http://www.societyofrobots.com/mechanics_dynamics.shtml (http://www.societyofrobots.com/mechanics_dynamics.shtml)
I'm just curious on how this accurate relates to the torque requirements, and if I'm missing something >< Thanks for your help though :D
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You might be on to something.
When looking at newtons law in a rotational perspective, you have
sum of moments = mass moment of inertia * angular acceleration
mass moment of inertia for a point mass is m*r^2 (or as you put it mass*radius*radius, which is what is used). Notice how the spreadsheet asks for a center of gravity location which acts as the point mass.
However, the calculations ask for angular velocity, not angular acceleration. So there is a mistake there.
If you are ok with 50 degrees per second of angular acceleration (default value) then it shouldn't be a problem. (that's a decent rate and unless you really have a need to meet an exact requirement it will be fine)
There will also be a slight error by finding the mass moment of inertia of the arm with the assumption that it is a point mass (once again, it's not that important unless you need to know an exact value for some reason). To get the exact value you would have to use CAD software to compute it (you have to integrate over the volume). You could also experiment with using equations for the mass moment of inertia of a slender rod (no one ever defines slender though).
These equations assume that you are picking the object up and the arm is rotating through the point where it is perpendicular to the ground (this point takes the most torque to pass through). If for some reason you will not be rotating through this point you could get away with a less powerful servo.
I looked at the robot motor factor and I have no idea what's going on there, but I'm pretty sure it's not used in the arm calculation. I think that calculation is supposed to be for robot top speed and acceleration.
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Thank you for your input :D
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However, the calculations ask for angular velocity, not angular acceleration. So there is a mistake there.
Yeap, its supposed to say angular acceleration. Oops. I made the changes.
But for some reason the results concerning the angular acceleration still don't look right, at least for the java version of the calculator. It wasn't immediately obvious to me, and I don't have time to look into it much more right now unfortunately . . . Let me know if you get more strange results.
I looked at the robot motor factor and I have no idea what's going on there, but I'm pretty sure it's not used in the arm calculation.
yeap, RMF is not used in the arm calculation
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Horray! I'm not crazy! Thank you for your response, and for this awesome site! :D