Design to 3D print RC car - Steering

[Juanda]

TL;DR Summary

I plan to design and print an RC car as a learning experience.

I am planning to design an RC car to 3D print it and have some fun. It will mostly be a learning experience with the by-product of having a hopefully fun RC car by the end of it. That will probably force some decisions that might be overengineered and negatively impact performance but building the very best 3D-printed RC car in the world is out of the scope anyway. Again, learning and having fun is the focus here.

So, to make it more approachable, I would like to design a few iterations growing in complexity. The main parameters for the first iteration would be:

• As many 3D printed parts as possible.
• Only elements commonly found in hardware stores (DIN and ISO standards) can be added except for some key elements such as bearings among others.
• 3D printed gears. They will need to be bulkier but I want to learn to design and print them.
• M3 will be the usual thread size for all joints. Bigger sizes might be considered.
• Rear-wheel drive.
• Solid rear axle.
• No suspension.
• Front-wheel steering.

So the steering is where I drew the line in terms of complexity. I could make it without steering but then the car is no fun at all. Could it even be considered a car at that point?
Steering can be quite a complex topic so I would like to keep it as simple as possible. As I read about it, many terms such as slip angle, camber, toe, and bump steer among others came up. For this first and simple iteration, I like to just focus on Ackerman steering and other similar alternatives such as Bell-crank steering.

The following is the typical picture of Ackerman steering geometry. As shown in it, the center of the turning circle is crystal clear in the picture.

My problem with such a solution is that the shown situation only happens at a particular steering angle. Is that right? I tried some drawings and it's what I seem to obtain from them. For all other angles, the intersection of those three lines will not be at the same point.
In the case of an Ackerman geometry, the mechanism is just a 4-bar linkage. I wrote some equations to find out if it's possible to design it with such a size ratio so that the intersection happens as in the picture independently of the steering angle but solving the equations is turning out more difficult than initially expected.

Can you confirm if it's possible to design it in such a way as to guarantee the three lines always intersect at one point?
If it's not possible, what's the best approach? To design it so that at full steering angle that condition is fulfilled? Or maybe at half the steering angle because it will occur more frequently?

By the way, I will most likely use a Bell-crank steering because it seems more compatible with a servo but I initially focused the point on the Ackerman mechanism because it's simpler so I'd like to try to understand that one first.

 

[jack action]

Design and choice of geometry

A simple approximation to perfect Ackermann steering geometry may be generated by moving the steering pivot points inward so as to lie on a line drawn between the steering kingpins, which is the pivot point, and the centre of the rear axle. The steering pivot points are joined by a rigid bar called the tie rod, which can also be part of the steering mechanism, in the form of a rack and pinion for instance. With perfect Ackermann, at any angle of steering, the centre point of all of the circles traced by all wheels will lie at a common point.

Modern cars do not use pure Ackermann steering, partly because it ignores important dynamic and compliant effects, but the principle is sound for low-speed maneuvers. Some racing cars use reverse Ackermann geometry to compensate for the large difference in slip angle between the inner and outer front tires while cornering at high speed. The use of such geometry helps reduce tire temperatures during high-speed cornering but compromises performance in low-speed maneuvers.

 

[Juanda]

I did read that page and tried drawing it but then the mechanism didn't do as promised. Or at least, I didn't see it doing as promised.

In the following pictures, you can see how the vertical distance is not preserved for different steering angles. Therefore, it doesn't matter at which distance I place the rear axle, only at a particular steering angle I will have the 3 lines intersecting at a common point.

If that vertical distance was preserved, I could place the rear axle there so turning shouldn't require slipping (or as much slipping). But I don't see how that's the case.
I then wrote the equations that describe that vertical distance (206 and 246 in the previous pictures) to see if it's possible to size the bodies so that it's independent of the steering angle but I haven't solved the system yet. I would need to code something to solve it and I'm not even sure if there exists a solution independent of the angle.

Either I am misinterpreting Wikipedia here or that part of the article is not accurate.

 

[Baluncore]

Can you confirm if it's possible to design it in such a way as to guarantee the three lines always intersect at one point?

Ackerman steering is not exact, but it is a good enough approximation for real vehicles.

 

[Juanda]

Ackerman steering is not exact, but it is a good enough approximation for real vehicles.

So is the Wiki page just wrong in this instance? I love Wikipedia but I am aware it can be wrong sometimes. I am referring to this segment as Jack brought up.

A simple approximation to perfect Ackermann steering geometry may be generated by moving the steering pivot points inward so as to lie on a line drawn between the steering kingpins, which is the pivot point, and the center of the rear axle. The steering pivot points are joined by a rigid bar called the tie rod, which can also be part of the steering mechanism, in the form of a rack and pinion for instance. With perfect Ackermann, at any angle of steering, the center point of all of the circles traced by all wheels will lie at a common point.

Does a Bell-crank steering have the same limitations?

Is there a better mechanism that can really guarantee that, at any angle of steering, the center point of all of the circles traced by all wheels will lie at a common point?

 

[jack action]

see if it's possible to size the bodies so that it's independent of the steering angle but I haven't solved the system yet. I would need to code something to solve it and I'm not even sure if there exists a solution independent of the angle.

Is there a better mechanism that can really guarantee that, at any angle of steering, the center point of all of the circles traced by all wheels will lie at a common point?

By reducing the distance between the two wheel pivots, you will be closer and closer to the "turntable" steering which is essentially the Ackermann geometry where the distance between the wheel pivots is zero.

But this will introduce whole new problems that the Ackermann geometry was created to eliminate:

Rather than the preceding "turntable" steering, where both front wheels turned around a common pivot, each wheel gained its own pivot, close to its own hub. While more complex, this arrangement enhances controllability by avoiding large inputs from road surface variations being applied to the end of a long lever arm, as well as greatly reducing the fore-and-aft travel of the steered wheels.

Don't forget that at high steering angles, your vehicle will necessarily be at slower speeds where precision might not be as worrisome.

 

[Juanda]

I would initially be aiming for an Ackerman geometry (or bell crank or similar) but trying to accomplish a true coincidence of the 3 lines within some tolerance due to manufacturing for any steering angle.

An interesting alternative I found is to independently feed each wheel with a servo and calculate the angle they'd need to be turned. You can see the extract starting at 7:05 in this video.

However, I'd love to simply have a mechanism that does that by itself without needing to implement some control software. Having only one servo to feed the whole steering.
I just haven't come up with such a mechanism yet if it even exists.

 

[Baluncore]

However, I'd love to implement a mechanism that does that by itself without needing to implement some control software.

That is the engineer's dilemma. You need to finish your project, then go back to improve on the prototype, if it justifies the time.

You do not need to independently control the two steering wheels. Only a correction to the Ackerman geometry needs to be implemented. If it is needed, that can be done later with a cam profile or a miniature servo that changes the length of the tie-rod.

 

[Juanda]

You're right. I should focus on the big picture before tackling these details if there isn't a quick and easy solution.
I will make a bell crank steering mechanism so that at half the steering angle the condition of the 3 lines intersecting is fulfilled. I will try to make it in a way that keeps the intersection somewhat close to the right point at a full steering angle.

I didn't think in a cam profile to change the length of the tie-rod. I don't know how I'd do it yet but it seems a pretty interesting concept. I'll try to apply it if the time is justified as you said. Thanks!