Linkage Design Problem

[Andrew Blair]

I'm thinking about a revision on the crab design, but I have a problem. I need a rather complex linkage, but I have no knowledge in vector calculus. The linkage needs to transform a linear force into a 90* arc. Anyone versed in 37 bar linkages?




(Sorry, about the horrible illustration, but Paint isn't my forte')

[Tristan Lall]

A lot of these sorts of mechanisms will have sinusoidal motion—the path can be anything, but the timing between points is sinusoidal. So, in general, are there any timing requirements? (This also doesn't account for the actual behaviour of the actuator, since it also needs time to accelerate; this assumes that the thing is operating without regard to dynamic effects.)

Also, what's following the arc; can you put a pivot at the centre of the arc, for example?

One simple example of this kind of motion would be a flexible rod attached to a piston and a pulley. Start with the rod wrapped around the pulley, and pull it to go one way. Push on it (so you can't use chain or string) to go the other way.

If you don't mind pivoting the piston, and don't mind rather uneven forces, you can also just attach an arm from the rod of the piston to the centre of the arc, and pin the tail of the piston in place. When the rod extends, the change in length causes the centre joint to move along an arc determined by the arm length.

Another idea would be to take a section of a gear, and a piece of rack. Just design it so that one extension of the piston corresponds to 90° of rotation. (Are the given direction arrows critical? Because if so, you'd need to actually reverse the piston output as part of the linkage—that seems like a waste.)

Lots more possibilities exist; a better idea of the application would help. Are you trying to move the drive modules with this, and if so, why only 90°? Also, what level of complexity and cost do you want?

[Madison]

Perhaps I'm misunderstanding the design problem, but why not apply the same design used as a steam locomotive driver to this circumstance? It's quite like one of the solutions Tristan mentions above, but you can fix the piston or screw in position.

[Andrew Blair]

Basically, the concept is to simply slam the drive module around a pivot 90*, so as to afford a sort of reversable drive- in one position, you drive length-wise, slam it the other ways and you drive long-wise. The problem with the locomotive type linkage is that you basically cannot complete the entire turn in such a way. Either you straighten out the piston and it locks itself from further motion in the opposite direction, or you stop it prior to locking, and you don't get the full 90* turn.

This full angle is crucial to keeping full driving ability once the modules are turned: If the wheels aren't parallel, especially with a high traction wheel like we use, you grind your wheels and get horrible efficiency.

And Tristan, the arrows aren't really important, the linkage will need to go back and forth, but the piston may pull or push either way- no problem.

If such a linkage is possible, it would allow for a very quick reacting, smooth, "slam steer" type drivetrain. Push a button, and you're going sideways, almost instantly. And you get to keep the full traction of a four wheel drive.

[KenWittlief]

Since you only care about the end positions, all you need is a piston and a lever. The piston does not need to go to its stops, put mechanical stops on the lever that can be adjusted to set the alignment for each wheel.

if fact, it could be spring loaded in one direction, so the robot will default to one direction if your pnuematics fail (or simplify your pnuematics so they are only driven in one direction.

[AdamHeard]

I think you're trying to make what is known as a crab (aka swerve) drive. There are many post / half completed designs you could find.

[Andrew Blair]

Originally Posted by KenWittlief

Since you only care about the end positions, all you need is a piston and a lever. The piston does not need to go to its stops, put mechanical stops on the lever that can be adjusted to set the alignment for each wheel.

if fact, it could be spring loaded in one direction, so the robot will default to one direction if your pnuematics fail (or simplify your pnuematics so they are only driven in one direction.

The more I think about it and get frustrated, the more I think this will be my only option. What I'm worried about is in the retracted position, your piston should end up directly in line with both the lever arm and the pivot, and when you try to extend, the piston will jam. However, with some tension springs you could alleviate this by pulling perpendicularly to the piston, so that when it extended, it would be drawn over. I just wanted a nice, smooth linkage that would afford me a one mechanism, no-worry solution, but I'm beginning to think it can't be done easily.

Originally Posted by cromat44

I think you're trying to make what is known as a crab (aka swerve) drive. There are many post / half completed designs you could find.

Well, it's more of a variation on the crab/swerve. The problem with crab/swerve drives is that because of their go-anywhere design, they require that their modules be turned by motors. This results in, generally speaking, a slow direction change, and long lengths of chain/ belt, or an elaborate gearbox- linkage mechanism.

The advantage of simply choosing two module angles is twofold. First of all, you can more easily achieve near instantaneous direction change. (i.e push against a robot, and in 1 second be ten feet away sideways). Secondly, pnuematics in this circumstance offer a nice reliability factor. They are light, easily mounted, offer simple changeout, and if you jam a module somehow, they won't burn up trying to move that single module.

Another benefit to this design is that you may stray away from traditional crab construction, which subject the bottom of the module to high levered loads. They are normally supported only by a teflon ring at the bottom of the module. If you only try to move the module 90 degrees however, you can move the pivot from the top of the module to the side, sort of like a heavy duty door hinge.

In this way, you may make the hinge as beefy as you like to support the robot's weight loads, while the hinge's structure can more easily withstand horizontal impulses, the type most likely to see during a match.

[KenWittlief]

Originally Posted by Andrew Blair

What I'm worried about is in the retracted position, your piston should end up directly in line with both the lever arm and the pivot, and when you try to extend, the piston will jam.

I dont understand your concern? Can you reference it to the drawing in my last post?

Keep in mind the piston linkage pivots at both ends (connected with bushings). As the piston in my drawing extends the piston will angle to the left. When the piston is at the center of its travel it is perpendicular to the lever.

As the piston extends all the way it pivots back to the right, to end up in line with its starting position. At no point in its travel is the piston parallel to the lever.

At the end points the piston is 45 degrees to the lever, which will give you 70% of the applied force holding the level against its mechanical stops.

[Aren_Hill]

i think the simplest idea would be a rack and pinion set up with the piston linked solid to the rack and the pinion would be at the rotation point

[Andrew Blair]

Ha! I misunderstood your picture! That really is a good idea- I hadn't realized that you shifted the 90* movement 45*! Thanks! Evidently I can't use or understand Paint!

[Madison]

Originally Posted by Andrew Blair

Ha! I misunderstood your picture! That really is a good idea- I hadn't realized that you shifted the 90* movement 45*! Thanks! Evidently I can't use or understand Paint!

For the record, that's exactly how a locomotive driver works.

[Al Skierkiewicz]

Blair,
I think you are getting close to understanding why crab systems have evolved to where they are now. With the system that Ken has suggested (which I think is exactly the solution you were looking for) the side loads and frictional loads remain the same as a traditional crab drive without the ability to change directions incrementally. With only the 90 degree motion, you are limiting yourself to a defensive move that may not accomplish what you want. A true crab drive needs to back away before "exiting stage right" in order to break the friction with the robot it is pushing against. The side loads of an instantaneous change are significantly higher than a motor driven steering system.

[dlavery]

Originally Posted by M. Krass

For the record, that's exactly how a locomotive driver works.

Actually, it is not, but it is close. Ken's description maps directly to how a wobbler engine works. On a steam locomotive, the piston is in a fixed orientation and does not rotate relative to the wheel. The motion of the piston is transferred to the driver by an intermediate drive rod (attached to the piston rod via the crosshead at one end and to the driver bolster at the other). The motion of the drive rod is linear at one end (the piston end) and circular at the other (where it is pinned to the drive wheel). Note the drive rod in the referenced image below (this image is of a model pump engine, but the motion is similar to a locomotive). There is also a nice explanation and animation of this on How Stuff Works.

-dave

[Andrew Blair]

Heres a quick drawing. The dimensions and proportions are way off, but it illustrates the idea well. Al, I did think about the friction between robots and the fact that you would still be locked in somewhat if you changed direction while pushing, but we normally have so much pushing force that I doubt it would be a problem. But even if we did get stuck, you could just back away slightly before switching direction.


The other nice thing here, that I can't really illustrate without a full drawing, is that you aren't turning the wheel in place like a traditional crab, you are instead turning it in an arc, so the force required to swing the module should be far less, especially with a high traction wheel.

[RyanN]

Originally Posted by KenWittlief

Since you only care about the end positions, all you need is a piston and a lever. The piston does not need to go to its stops, put mechanical stops on the lever that can be adjusted to set the alignment for each wheel.

if fact, it could be spring loaded in one direction, so the robot will default to one direction if your pnuematics fail (or simplify your pnuematics so they are only driven in one direction.

I agree, a simple lever and pneumatic piston is all you would need, a mechanical stop will certainly work. Remember, simplicity is your friend. More complicated things tend to break more, and are harder to fix. All you need to have is a piston on a hinge and a lever attached to the wheel base.