Telescoping Tubes Overlap

Technical
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Hey everyone,

Our robot currently has a telescoping arm with one tube extending out and one tube stationary. I want to reduce the length of the arm while retracted. My plan is to reduce the length of the stationary tube, however, this decreases the amount of overlap between the two tubes when the arm is fully extended. Is there some equation or general rule of thumb for how much overlap I should have for my arm to ensure minimal slop (currently I have about 9 inches of overlap between the two tubes when fully extended)?

Also, is my approach to reducing the retracted arm length optimal, and if not what would be better?

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I’ll preface this with we aren’t the best team in the world, or the most proficient in design. But we have it working and it isn’t too bad.

I dont think there is any rule of thumb, at least I havent heard of one. I would just design and test, and if there is too much slop, add overlap. Although in some cases it’s the bearing block design and tolerances that cause the majority of the slop, so don’t overlook that.

Our extension this year has a single stage, and we have machined HDPE as the bearing blocks (climber in a box style). At max extension theres ~3" of overlap, and I haven’t observed any issues with ours yet, it is kinda small scale though. Because it’s attached to another system, the extension is only required to be 19" and it has a pretty light claw end effector so the forces are relativley low.
A larger telescoping pair will probably require more overlap than ours, and obviously the more overlap there is, the less slop you will get. Wired Boars (7407) appear to have 8" of overlap between their stationary and first stages (although it’s not a telescoping arm it’s an elevarm).

I believe your approach is correct, you will have to reduce the stationary (I assume outer) tubes length, but also the inner tube too, as the length from the back of the outer tube to the front of the inner tube doesnt change by shrinking the outer tube alone. As you have stated, this will reduce your overlap for the same amount of extension. AFAIK, the overlap required for any given telescoping pair of tubes is whatever it has to be to meet your design goals. If you aren’t happy with the slop in the system, add more overlap.

I could also be very wrong here and there very well may be an actual equation for the optimal overlap. But that’s for someone more knowledgable to correct me on, and I hope they do because if it’s out there I’d love to learn about it.

Sorry this got very long, TLDR:

I dont think there is a set formula or rule of thumb, I would just design it and test it until you have no, or at least a manageable level of, slop.
We have 3" of overlap on a smallish telescopic pair of tubes, 7407 appears to have 8" of overlap on their elevarm.
You have the right approach, you just need to also remove material from the extending inner tube as the length from tip to tail doesnt change just by cutting down the stationary outer tube (unless your design is different from what I’m thinking).

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The rule of thumb from FRC antiquity was 30% of its total length. Even back then some teams “cheated” it down to 20%.

These days, teams are often far more aggressive with their overlap. Improvements in FRC manufacturing and bearing sourcing have led to more aggressive arm design.

That being said, this is also a year in which many arms and elevators are being taxed in ways they haven’t in a very long time. Extensions are not mostly vertical this year. These lateral and multi-axis loads being placed on extensions this year are going to push these designs much harder than vertical elevators or even many climbing mechanisms have been pushed.

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Your post is very accurate - most overlaps are eyeballed.

In terms of slop, I think a good rule of thumb is to have between one quarter and one fifth of each stage’s length be reserved for overlap. For instance, if your first stage tube is 20" long, you should have 4 or 5 inches of overlap. This is just a ballpark estimate, though.

Mathematically, the slop at the end of the stage is the product of the slop in the bearing assembly and the quotient of the extended length and overlap length. For instance, if a single-stage arm extends 20" from the fixed part and has an overlap of 4" with 0.01" of slop on the bearing, it will have 0.04" of slop at the tip of the stage.

Across multiple stages, the slop will grow also with the harmonic number H_N of the travel.

A key decider of your overlap can also be the load on the bearing assembly. I wasn’t able to track it down on short notice, but there was a paper published to CD roughly ten years ago studying impulse accelerations of robot impacts with bumpers, demonstrating impact accelerations on the order of 10 g.

If you imagine driving around at full speed with your end-effector fully extended vertically (at full speed), we can model how much load the impact will cause on your bearing assembly. With an extension length l, overlap length o, end-effector mass m, and robot acceleration a, the force on the bearing acting as a fulcrom will be as follows:

F = (\frac{l}{o} + 1) m a

Using l=40", o=8", m=10 lb, and a=10 g, we get a force of up to 600 lb on the bearing. Naturally, this is a worst-case scenario: the peak impulse force with the arm in its worst location on a robot accelerating at top speed. However, you can use this to get a good estimate of the forces on your bearing (and decide an overlap from there).