Society of Robots - Robot Forum
Mechanics and Construction => Mechanics and Construction => Topic started by: kennykck on December 17, 2007, 08:47:48 AM
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how do i derive this formula? or is there any website i can refer to?
Torque * rps > = Mass * Acceleration * Velocity / (2 * pi)
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I think this is what you are looking for... http://www.societyofrobots.com/RMF_calculator.shtml
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i mean how do i start derive it until the end of that equation? Coz i need write it into my report of robot design. Can anyone help?
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Torque * rps > = Mass * Acceleration * Velocity / (2 * pi)
(kg*m^2/s^2)* (round/s) = (kg)*(m/s^2)*(m/s)/(2*pi)
Do the units even match up? Given 1 round = 2 pi radians, and assuming the (2 * pi) is in radians, the radians are not on the same side (one is in the numerator, the other in the denominator).
To derive it you would probably start from F = m*a (force = mass * acceleration), T=F*d (torque = force *distance), and some rotational mechanics like Torque = I *alpha (torque = I * angular acceleration), where I= moment of inertia and alpha = a/r where r is radius.
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From this site(http://www.societyofrobots.com/mechanics_dynamics.shtml)
v = 2 * r * PI * rpm or rpm = v / (2 * r * PI)
T = F * r
F = m * a
so, T/r = m * a or T = m * a * r
multiply rpm into the equation,
T * rpm = m * a * r * v / (2 * r * PI)
T * rpm = m * a * v / (2 * PI)
But why the website says
"Torque * rps > = Mass * Acceleration * Velocity / (2 * pi)
RMF = Torque * rps "
I'm confused... ???
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i mess up abit by the unit conversion
Velocity = 2 * radius * pi * rpm
Is my velocity in unit meter per second when using that formula?
I'm confuse whether it's second or minute...
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If you want meters per second, then do this:
Velocity = 2 * radius * pi * rpm / 60
or
Velocity = diameter * pi * rps
So, for example, a 600 RPM gear-motor turning a 2" diameter tire would be:
V = 2" * pi * 10 = 62.8 inches per second
If you wanted it in meters per second, the tire diameter would be 0.0508 m, so the velocity would be:
V = 0.0508 * pi * 10 = 1.6 m/s
- Jon
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rpm is equivalent to rps, just different units of time (minutes vs seconds)
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meaning
rpm / 60 = rps
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Coz i need write it into my report of robot design.
don't forget to reference my site :P
(I lost a lot of braincells and social life to figure out and derive that equation)
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yup of course. I'll give credit to ur website in my report. ;)