Turning radius of a ZTR vehicle with two different wheel velocities

RonnieTheBear

Hi folks, my first post here, looks like a very helpful website though, so i thought i'd share my problem.

I'm a mechanical engineering student working on a vehicle that has a zero turning radius system, which is to say (for the purposes of this problem) that it's controlled by 2 drivewheels fixed in line with the body (i.e. straight ahead) that can turn at different velocities independent of one another.

So say one wheel is at V1 and the other is at V2 (linear, not rotational). What i'm trying to figure out is the turning radius for the vehicle as a function of V1 and V2. My basic mechanics are a little rusty (so please correct me if i'm wrong), but I had figured if you just approximate the vehicle as a point, it will contain a tangential velocity that's the lesser of the two wheel velocities (say V1), and a rotational velocity [tex]\omega[/tex] that is equal to the difference of the two velocities over the distance between the wheels, L ( or [tex]\stackrel{V1 - V2}{L}[/tex]. I'm not sure how to take those components and find the turning radius from there, though. Any help you guys could give would be greatly appreciated. Also, let me know if i've been way too vague and you need a picture or something for explanation. Thanks in advance!

rcgldr

Seems like the equation to solve would be:

(V1/R) = (V2/(L+R))

RonnieTheBear

setting the angular velocity of one equal to the other, yeah, that'd seem to make sense. Thanks very much!

Danger

I'm deviating from the original question, but still on topic. Why on Earth would you use fixed orientation wheels for this purpose? Steer all 4 of them, and there's no need for calculations.
No offense intended; I really don't understand the reasoning.

rcgldr

Maybe there are only two wheels, like a Segway. Maybe the other two wheels are simply free to pivot. In a legobot competition at my previous company, my group set a speed record (about 40 cm / second on long straights) by simply standing the brick near vertical, which greatly reduced the yaw inertia, allowing the lego bot to quickly turn and follow a track (by sensing changes in light reflected off the edge of the track (brown tape on a white board, black velcro used to issue "commands", uturn or stop). Two driven wheels, with two castered wheels behind. Pictures.

http://jeffareid.net/misc/lego01.jpg

http://jeffareid.net/misc/lego03.jpg

RonnieTheBear

Jeff's exactly right, the two rear drivewheels are fixed, and there are two casters in the front capable of pivoting 360. Here's an early 3D model (real early, ignore that the casters are floating in space and that the one support strut doesn't go anywhere, heheh )

Danger

My bad; I misread the OP.
I somehow got the impression that there were 4 fixed wheels, and my question was based upon that. Two alone, or with castors, would of course be fine. Sorry 'bout that.
Nice Legobot, by the way.

RonL

two examples for study are
1. Commercial mowers, with hydraulic drive, the wheels on each side are controlled independent from each other, with pivot wheels in front.
2. Bobcat skid steer loaders, have two wheels on each side, locked together with sprockets and chain, each side is driven with hydraulic motors controlled by the operator, the ztr is accomplished by one side going forward and the other side going backwards, and the rotation and slide action is split between the four tires.
A good operator can make this a very smooth operation, while someone with less skill will bounce around quite a bit.