Society of Robots - Robot Forum

Mechanics and Construction => Mechanics and Construction => Topic started by: kennykck on December 17, 2007, 08:47:48 AM

Title: robot motor factor
Post by: kennykck on December 17, 2007, 08:47:48 AM

how do i derive this formula? or is there any website i can refer to?

Torque * rps > = Mass * Acceleration * Velocity / (2 * pi)

Title: Re: robot motor factor
Post by: Steve Joblin on December 17, 2007, 09:26:41 AM

I think this is what you are looking for... http://www.societyofrobots.com/RMF_calculator.shtml

Title: Re: robot motor factor
Post by: kennykck on December 17, 2007, 09:34:08 AM

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?

Title: Re: robot motor factor
Post by: bulkhead on December 18, 2007, 02:02:44 AM

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.

Title: Re: robot motor factor
Post by: kennykck on December 19, 2007, 08:27:02 AM

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... ???

Title: Re: robot motor factor
Post by: kennykck on December 19, 2007, 12:17:00 PM

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...

Title: Re: robot motor factor
Post by: JonHylands on December 19, 2007, 12:44:01 PM

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

Title: Re: robot motor factor
Post by: bulkhead on December 19, 2007, 01:54:25 PM

rpm is equivalent to rps, just different units of time (minutes vs seconds)

Title: Re: robot motor factor
Post by: airman00 on December 19, 2007, 02:39:32 PM

meaning
rpm / 60 = rps

Title: Re: robot motor factor
Post by: Admin on December 19, 2007, 05:39:25 PM

Quote

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)

Title: Re: robot motor factor
Post by: kennykck on December 20, 2007, 02:49:13 AM

yup of course. I'll give credit to ur website in my report. ;)