Hello, this is for an individual project.

The car can only move forward, i.e. wheels are not allowed to have a negative motion in any case. Wheels are approximately 10 cm apart from each other. I am trying to figure out how the car will turn when the wheels are not turning at the same amount. Obviously car will turn in a circular motion but i need a mathematical equation to model the movement. The midpoint, lets say M, will move circularly around a point in 2D space. I need to find the radius of this circle. What should I research on?

I have a feeling that this is a topic which is widely researched, but I couldn’t find the required material for this problem.

Thanks in advance

 

The outside wheels travel where the r=M+5cm the inside wheels make a circle where r=M-5cm.
r=radius
5cm comes from 10cm/2

 

The outside wheels travel where the r=M+5cm the inside wheels make a circle where r=M-5cm.
r=radius
5cm comes from 10cm/2

Yes that is true, if M is the distance between the center of curvature and midpoint M. But I am asking for the distance M. I couldn't see it in your answer

 

The steering mechanism you are referring to commonly used in Skid-steers. There are two motors which separately drive the left and right wheels. It works like this:

1) If the left and right wheels are spinning at the same speed the vehicle moves forward.

2) If the left wheels are spinning while the right is stopped the vehicle turns hard right.

3) If the right wheels are spinning while the left is stopped the vehicle turns hard left.

These vehicles get their name because the wheel's often "skid" at low speeds due to friction and the response time of the machine.

As for your problem, I would solve it like this:

For cases 2 & 3, the turning arc will be the distance between the left and right wheels (the track). Create an expression to reflect this.

For case 1, there will be no turning arc. Create an expression to reflect this.

For all other cases, the turning arc will be a function of the track distance plus the speed at which the left wheels are turning relative to the right. It would be convenient for your expressions to assign full speed as "1" and half speed as "0.5".

The reason for this is because if the left is moving at 1 and the right at 0.5, the turning arc will be X.

But, if the left is moving at 0.5 and the right 0.25, the turning arc will be the same value of X due to the mechanics of the machine (recall case #1). Now all you have to do is combine expressions to solve for the turning arc for a given left and right wheel speed.

I'm not really sure what you are trying to determine but this should be enough for you to get started.

 

The steering mechanism you are referring to commonly used in Skid-steers. There are two motors which separately drive the left and right wheels.

You're referring to differential steering but I'm not sure that's what TS means. It sounds to me like he's asking for the equation for turning radius of a vehicle with traditional Ackerman steering

@Tayyare10.5 there were two pieces of Google fodder there:
Differential steering
Ackerman steering
Whatever you're asking about should be answer by looking at those.

 

Hello, this is for an individual project.

The car can only move forward, i.e. wheels are not allowed to have a negative motion in any case. Wheels are approximately 10 cm apart from each other. I am trying to figure out how the car will turn when the wheels are not turning at the same amount. Obviously car will turn in a circular motion but i need a mathematical equation to model the movement. The midpoint, lets say M, will move circularly around a point in 2D space. I need to find the radius of this circle. What should I research on?

I have a feeling that this is a topic which is widely researched, but I couldn’t find the required material for this problem.

Thanks in advance

You can only make an estimate because both wheels are going to skid and you don't know by how much. That will depend on a host of constantly changing factors, including the specifics of the material that the car is on, the nature of the tires (which will vary not only from one tire to the other, but also at different points around the same tire, the speed of the car, the weight and balance, and the radius of the turn itself (plus a bunch of others).

What is it that you are controlling on this care -- the rotational rate of each wheel?

Assuming (and it's a big assumption) that the wheels don't slip tangentially, then figure out how fast each wheel is moving over the surface. Then just find the radius that results in those two speeds for the two wheels.

 

Here is a partial proof for a 1 axle system already in motion under ideal circumstances. It says nothing about the path the wheels draw out on the ground but rather what I'm calling the bearing (the instantaneous direction relative to north). If you want to know the path, that will take some calculus.

The equation below is a decent starting point if you want to program a microcontroller to turn hard left or just a bit (notice the trends in the table).

You're referring to differential steering but I'm not sure that's what TS means. It sounds to me like he's asking for the equation for turning radius of a vehicle with traditional Ackerman steering

@Tayyare10.5 there were two pieces of Google fodder there:
Differential steering
Ackerman steering
Whatever you're asking about should be answer by looking at those.

Good point but I suspect TS is making a remote control since each wheel has a motor. I thought Ackerman used either front wheel or rear wheel drive but I don't know my auto terms.

 

If the wheel speeds are V1 and V2 then the respective wheels W1 and W2 will move in circles with respective radii given by R1/V1 = R2/V2. Your case where the inside wheel is not turning needs to be thought of as the limit as the speed tends to zero rather than dividing by zero. Solve for either R1 or R2 knowing that R2 = 10 + R1

 

Just yesterday I went to the local peasant market to carry potatoes for my wife and before us staid the Ukrainian woman with both feet and one hand amputated. War is war, so sad! She sat in very modern made invalid wheelchair model I never seen before. I highly interested watch the construction - titanium frame, four small wheels about 12 or 14 inches, and two separate 400 W 36 V BLDC - mounted on left and right back-wheels. That was just surprise how waggy was she in operation with this machine. Just like perfectly healthy me when I put all the efforts. So... the two motor system is highly turnable as well may go well straight if one want, and 800W is more than enough to have jump-like dynamics.

 

Respect. There are some amazing wheelchairs these days, but the concept of steering motorised wheelchairs with the rear wheels driven by two motors running at different speeds has been the norm for many years.

We seem to have lost the thread starter, but for completeness, where R1 and R2 are the radii of travel and R1=M+5 and R2=M-5 then (M+5) x V2 = (M-5) x V1 so M x (V1 - V2) = 5 x (V1+V2) so M = 5 x (V1+V2)/(V1-V2). With V2 = 0 the value of M is 5 as expected.

 

Differential steering is not often as exactly predictable because the rear wheels will also need to slip a bit, depending on the distance behind the differentially driven set. So the exact radius will depend also on the ground traction. Thus in many cases a feedback system is required to provide steering on an exact course.