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kaos116
02-03-2009, 03:47 PM
Hello everyone,
I spent a little time searching the forum for the information, but I came up empty handed. This is really a mathematics question. I want to know the maximum diameter wheel I can use on a continuous rotation servo. The servo I am looking at is http://www.trossenrobotics.com/store/p/5385-Parallax-Futaba-Continuous-Rotation-Servo.aspx

Quick Specs : 60RPM(no [email protected]); 47oz/in

There will be four of them, one for each wheel in a differential drive configuration.

The robot max weight will be 5 lbs and I like it to drive up a 15 degree incline.

The reason I am wondering this is ultimately speed. At ~60rpm and 3" diameter it's about 9.5"/s, not very quick. If I use 6" wheels, I am looking at ~18.5"/s. That is the upper end of what I would like (15"-20"/s).

But what kind of torque am I getting? Will this be able to drive a 5# robot up a 15degree incline?

Thanks in advance,

Todd

Adrenalynn
02-03-2009, 04:11 PM
Hi Todd,

Just doing some off-the-cuff numbers, if we figure the robot weighs a total of 5lbs and needs to climb a 15deg angle, and has 6" wheels, and that each servo is putting out 0.25lb-ft of torque, I'd expect our max velocity to be about 0.12ft/sec with a 0.12ft/sec^2 acceleration (assuming 4 powered wheels)

Turning is going to be a bit of a challenge like that though. I'd say you're under-sized by quite a fair bit.

kaos116
02-03-2009, 05:30 PM
Thanks Adrenalynn. Is there a formular to do this calculation?

If I have a known weight - 5lbs.
A specific incline - 15 degrees
A known motor torque - 47oz/in X 4 (can we assume this is stall?)

How do I solve for max wheel diameter (or radius) at stall?

A bit more background information. I am trying to create a good, stable drive platform to work off of. I have used servos before in my simple robots and I am familiar with them. They are also inexpensive when compared to gearhead motors and a motor controller. What I didn't like about the servos, was the speed. My obstacle avoidance robot is using 3.25" tires and it is a bit slow. I might just make the jump to gearhead motors and controller. I could create a much faster, stronger drive platform. But I would like to explore all avenues with the Servos, if for nothing else, the knowledge of it.

Adrenalynn
02-03-2009, 06:00 PM
I'd go with gearhead motors... (and do, although I might build a little AX-12 desktop 'bot just 'cause I have two of 'em now. ;) )

It's hard to directly solve for, you kinda have to run some "what if" iteration.

Torque = Distance * Force
Distance = Wheel Radius
Force = Torque / Wheel Radius
acceleration for inclines = 32 ft/s^2 * sin((angle_of_incline * pi) / 180)

You can pick-up some additional pointers here: http://www.societyofrobots.com/mechanics_dynamics.shtml

Adrenalynn
02-07-2009, 01:26 PM
I think it would take a very very long time to accelerate the 'bot as you approached your stalled max, right? Momentum = Mass * Velocity?

You're also looking at a theoretical 100% efficient motor and gearbox. I'm not sure how many gears are in the servos you're wanting to use, but if we did - we'd probably calculate it at something like 65-70%, I'd guess.

Probably a few more things we haven't taken into account yet - but I'm all for the "get the numbers close, then bench test, where "close" equals "same zip-code" " ;)

Adrenalynn
02-08-2009, 08:28 PM
Moderator Note:
Metaform3D's excellent motor/wheel size paper relocated to: http://forums.trossenrobotics.com/showthread.php?t=2900 (http://forums.trossenrobotics.com/showthread.php?t=2900) and stickied in Mechanics/Construction (http://forums.trossenrobotics.com/forumdisplay.php?f=52).