Turning radius of a ZTR vehicle with two different wheel velocitiesby RonnieTheBear Tags: radius, turning, vehicle, velocities, wheel 

#1
Mar608, 08:09 PM

P: 3

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! 



#2
Mar708, 12:53 AM

HW Helper
P: 6,929

Seems like the equation to solve would be:
(V1/R) = (V2/(L+R)) 



#3
Mar708, 04:32 PM

P: 3

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




#4
Mar808, 04:18 AM

PF Gold
P: 8,961

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



#5
Mar808, 04:46 AM

HW Helper
P: 6,929

http://jeffareid.net/misc/lego01.jpg http://jeffareid.net/misc/lego03.jpg 



#6
Mar808, 09:35 AM

P: 3





#7
Mar808, 09:50 AM

PF Gold
P: 8,961

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. 



#8
Mar808, 10:25 AM

PF Gold
P: 701

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. 


Register to reply 
Related Discussions  
What exactly is a zero radius turn vehicle?  Mechanical Engineering  25  
revolutions and radius of wheel  Introductory Physics Homework  1  
Turning a Straight Wire into a wheel with spokes, solve for I  Introductory Physics Homework  3  
supersonic turning radius  Mechanical Engineering  8  
Turning Radius of a floating vehicle in water  Mechanical Engineering  0 