# Turning radius of a ZTR vehicle with two different wheel velocities

• RonnieTheBear
In summary, according to this expert, a vehicle with zero turning radius has two fixed, straight-ahead orientation wheels that can turn at different velocities. The turning radius for the vehicle is a function of the lesser of the two 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 $$\omega$$ that is equal to the difference of the two velocities over the distance between the wheels, L ( or $$\stackrel{V1 - V2}{L}$$. 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!

Seems like the equation to solve would be:

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

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

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.

Danger said:
I'm deviating from the original question, but still on topic. Why on Earth would you use fixed orientation wheels for this purpose?
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

Jeff Reid said:
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

Jeff's exactly right, the two rear drivewheels are fixed, and there are two casters in the front capable of pivoting 360. Here's http://img401.imageshack.us/img401/7127/74589885ds7.jpg" (real early, ignore that the casters are floating in space and that the one support strut doesn't go anywhere, heheh )

Last edited by a moderator:
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.

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.

## 1. What is a ZTR vehicle?

A ZTR (Zero Turn Radius) vehicle is a type of riding lawn mower or small tractor that has the ability to make a 360-degree turn without moving forward or backward. This is achieved by controlling the speed of the two rear wheels independently.

## 2. How is the turning radius of a ZTR vehicle measured?

The turning radius of a ZTR vehicle is typically measured by the diameter of the smallest circle that the vehicle can make without moving forward or backward. This is also known as the zero turn radius.

## 3. How does the turning radius of a ZTR vehicle with two different wheel velocities compare to one with equal wheel velocities?

A ZTR vehicle with two different wheel velocities will have a smaller turning radius than one with equal wheel velocities. This is because the difference in wheel speeds allows for tighter turns and greater maneuverability.

## 4. What factors affect the turning radius of a ZTR vehicle?

The turning radius of a ZTR vehicle can be affected by several factors, including the size and weight of the vehicle, the condition of the tires, the terrain, and the speed of the vehicle.

## 5. How can I improve the turning radius of my ZTR vehicle?

To improve the turning radius of your ZTR vehicle, you can adjust the speed of the two rear wheels, ensure that the tires are properly inflated and in good condition, and avoid rough or uneven terrain. You can also consult the manufacturer's instructions for any specific recommendations for your particular vehicle.

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