Zero turn radius without using swivel casters

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troop231
 
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Zero turn radius without using swivel casters

Post by troop231 »

I'm not sure if this question fits here, but I've had trouble finding a good simple physics forum.

I'm trying to think if the below wheel (image below) could allow for my push mower to have a zero or near zero turn radius. The edges of the wheel contour up (from the ground upwards), which should bend the blades of grass over and allow the wheel to glide over them (theoretically). The contact point of the wheel is in the middle due to the contoured edges. I would like to use this wheel instead of a swivel caster as it would still allow the mower to track straight much better than using a swivel caster. Also it would bolt right on with no extensive mods that the swivel caster would require.

Am I thinking right? If there is any risk of tearing the grass (scalping) I will abandon this idea. These are called anti-scalp wheels however.

I appreciate your feedback.

Image

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adafruit_support_mike
 
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Re: Zero turn radius without using swivel casters

Post by adafruit_support_mike »

It wouldn't make much difference.

For the sake of vocabulary, I'll call the region where the surface of a wheel is in contact with the ground the 'contact area'. The part of the contact area toward the direction of travel is the 'leading edge' and the part away from the direction of travel is the 'trailing edge'.

When a wheel is rolling, a point on the surface of the wheel slightly ahead of the leading edge will move down to touch the ground, while a point slightly behind the trailing edge lifts up off the ground. Points in the contact area don't move relative to the ground at all (at least ideally).

That pattern of motion creates very little friction in the direction of motion. The up-and-down motion is perpendicular to the direction of travel, so there's no forward or backward component. There's no friction within the contact area because the wheel surface and ground aren't moving relative to each other.

The reality of a rolling wheel isn't quite so perfect.. there's a small forward/backward component to the motion as points enter and leave the contact area, and some squirming between the wheel surface and the ground in the contact area. Even so, the friction generated by the imperfections is far smaller than the friction that would exist if you dragged the contact area along the ground.

If you mount any set of wheels on fixed axles that allow the base to travel forward and backward, then rotate the base around its center point, the first small increment of motion will basically pull the contact area perpendicular to the direction of forward/backward rolling travel.

That means the contact area has to move relative to the ground in a direction that the wheel can't roll. Any motion in that direction will be pure sliding friction.

Friction is proportional to the force pushing two objects together, but is largely independent of the size of the contact area. Friction is the force per unit area times the size of the contact area (friction = K * F.unit * area), but force per unit area is just the overall force divided by the size of the contact area (F.unit = F.total / area). When you combine those equations, the area term drops out.

The rounded edges of the wheels will have some effect.. they won't dig into soil the way square edges of a regular wheel would, and they'll make it as easy as possible for moisture on the grass to slide between the wheel and the ground to act as a lubricant (and lubricated motion has about the same friction as rolling motion). The basic motion will still be sliding friction though.

troop231
 
Posts: 19
Joined: Fri May 07, 2010 9:28 pm

Re: Zero turn radius without using swivel casters

Post by troop231 »

adafruit_support_mike wrote:It wouldn't make much difference.

The rounded edges of the wheels will have some effect.. they won't dig into soil the way square edges of a regular wheel would, and they'll make it as easy as possible for moisture on the grass to slide between the wheel and the ground to act as a lubricant (and lubricated motion has about the same friction as rolling motion). The basic motion will still be sliding friction though.
Thanks for the reply Mike! So it's not even worth trying out then? I'm trying to get away from using casters as they take up so much room due to the needed bracket support, which in turn means you can't mow as close to obstacles.

I tried these wheels: http://www.andymark.com/product-p/am-0048.htm but they failed on the zero turn test in grass unfortunately, just grabbing blades of grass as I tried to maneuver the mower.

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adafruit_support_mike
 
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Re: Zero turn radius without using swivel casters

Post by adafruit_support_mike »

troop231 wrote:Thanks for the reply Mike! So it's not even worth trying out then?
That's more of an economic decision than a technical one.. I often try stuff thinking, "let's see if this fails the way I expect it to."

If the cost of trying is low, even negative results are worth testing. In this case, I wouldn't expect smooth zero-radius turns though. Wheels with fixed axles have two basic modes of operation, rolling and skidding, and provide no way to steer a skid.

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zener
 
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Re: Zero turn radius without using swivel casters

Post by zener »

If you could drive them in opposite directions then you might get a skid steer effect a la BANNED loader.

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adafruit_support_bill
 
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Re: Zero turn radius without using swivel casters

Post by adafruit_support_bill »

Have you considered a combination of wheels and casters? If you have one wheel on each side you can get a zero turn radius. Then you can add one or two casters in the back to keep it level.

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