metaform3d

02-06-2009, 04:05 AM

It helps to draw a picture.

http://forums.trossenrobotics.com/attachment.php?attachmentid=1123&stc=1&d=1233910760

When you do this type of analysis it also helps to pick a unit system. I like MKS -- meters, kilograms, seconds -- just cause I'm an old physicist. The forward force on a wheel on a bot is equal to the torque (t) of the motor divided by the radius (r) of the wheel. The bigger the wheel the smaller the force. In MKS units the torque is in Newton-meters and the radius is in meters. Go here (http://www.onlineconversion.com/torque.htm) to convert.

For ascending an incline, we set the force of gravity equal to the force of the wheels. This gives us the maximum radius -- the wheel size that results in stalling going uphill. Naturally if you want to actually climb the hill you need a smaller wheel. But this is the upper limit.

The force of gravity on the bot is the mass of the bot times the gravitational acceleration. In this case 2 (Kg) times 9.8 (m/s^2). But it's on an incline, so the force that contributes to pushing the bot backward is the component of gravity in opposition to forward motion. That would be the sine of the angle from vertical times the force. It works out to roughly 5 Newtons.

Putting it all together and solving for the radius:

r = t / (g * m * sin (theta))

So, given 47 oz-in of torque with four motors (1.3 Newton-meters), mass of 2 Kg and an angle of 15 degrees, the answer is:

r = 1.3 / (9.8 * 2 * 0.26) = 0.26 m

For stalled motors 26cm radius (52cm diameter) wheels are your limit. Smaller wheels will give you more force and will move your bot rather than standing still. This is the absolute lower limit and gives you an idea about how to calculate a wheel size that will move your bot.

Boy, I hope my numbers are right. Those are giant wheels. Looking forward to corrections.

http://forums.trossenrobotics.com/attachment.php?attachmentid=1123&stc=1&d=1233910760

When you do this type of analysis it also helps to pick a unit system. I like MKS -- meters, kilograms, seconds -- just cause I'm an old physicist. The forward force on a wheel on a bot is equal to the torque (t) of the motor divided by the radius (r) of the wheel. The bigger the wheel the smaller the force. In MKS units the torque is in Newton-meters and the radius is in meters. Go here (http://www.onlineconversion.com/torque.htm) to convert.

For ascending an incline, we set the force of gravity equal to the force of the wheels. This gives us the maximum radius -- the wheel size that results in stalling going uphill. Naturally if you want to actually climb the hill you need a smaller wheel. But this is the upper limit.

The force of gravity on the bot is the mass of the bot times the gravitational acceleration. In this case 2 (Kg) times 9.8 (m/s^2). But it's on an incline, so the force that contributes to pushing the bot backward is the component of gravity in opposition to forward motion. That would be the sine of the angle from vertical times the force. It works out to roughly 5 Newtons.

Putting it all together and solving for the radius:

r = t / (g * m * sin (theta))

So, given 47 oz-in of torque with four motors (1.3 Newton-meters), mass of 2 Kg and an angle of 15 degrees, the answer is:

r = 1.3 / (9.8 * 2 * 0.26) = 0.26 m

For stalled motors 26cm radius (52cm diameter) wheels are your limit. Smaller wheels will give you more force and will move your bot rather than standing still. This is the absolute lower limit and gives you an idea about how to calculate a wheel size that will move your bot.

Boy, I hope my numbers are right. Those are giant wheels. Looking forward to corrections.