Hexapod designs?

[chuckknigh]

What level of detail do you need, from the hardware side of the project?

The basic geometry is simple...it's a standard octahedron, with some variable length struts. We have 2 possible configurations. (imagine triangles) One has 2 variable length legs per triangle, and a fixed base...this is a traditional hexabot. The other has a fixed leg length, and a variable base length...this is the rotobot.

With a traditional hexabot, "home" is fairly simple to define, as a return of all legs to some standardized length...the home switch could be within each leg assembly. I don't know if that's how they do it in industry, but it makes sense to me...

With a rotobot, it becomes a little more complicated...each leg has to return to a predefined position, probably equidistant, at 60 degrees apart. Same disclaimer as above.

Do you need any other information? I'd think anything machine specific, like the exact leg length, would be a variable...something to set up in a configuration file.

Seriously, think about it, and let us know the specifics of what you need... I've included a picture of a traditionally designed hexapod.

-- Chuck Knight

[chuckknigh]

Something just occured to me. This is going to be hard to explain...forgive my ramblings.

Most of us have no real use for 5 or 6 DOF machines. The majority of our work is done in either 2 1/2 or 3D space.

So, it might be possible to simplify the design of the hexapod to a tetrapod.

Thinking about it, it's a fairly simple matter to take something like a tetrahedron and distort it within 3D...it wouldn't give control over such things as yaw, but how many of us would use that?

It might be a simpler initial project, and would require only 3 stepper controllers (instead of 6), if I have it figured right...the only thing I can't figure out is how to hold the cutter rigidly at the vertex of the tetrahedron. Maybe something like making each arm a parallelogram linkage, so that the end of the strut is always aligned as vertical? I know that'd work for something with a fixed strut length.

Am I missing something? I WELCOME input...

Let's see..basic regular Platonic solids are tetrahedron (4 sides), hexahedron (6 sides, cube), octahedron (8 sides), dodecahedron (12 sides), and icosahedron (15 sides). The hexahedron is not inherently stable...the 2 lowest order units, that are inherently stable, are the tetrahedron and the octahedron.

I might have to play with some models, to see what kind of movements I can get out of these things. If a tetrahedron based model would work, that'd be a MUCH simpler homebuilt project...not to mention a heck of a lot cheaper!

I'm virtually positive a "hexaglide" tetrahedron would work just fine...not sure if a tetrahedron with a fixed base (traditional design, like the picture above) could be done with ease in a home shop, though...and that's my goal.

-- Chuck Knight

[bb99]

I I’ve been thinking of something like the rotobot but that isn’t a requirement. I’ll begin to play with the math and let you know what I come up with.

--bb99

[chuckknigh]

OK, this is the geometry I'm playing with, now. I'm tentatively calling it a tetrabot, after its base solid, the tetrahedron.

Compare it to the hexabot, above -- same triangular base, and the "tip" should be able to move by varying the lengths of the struts. The hard part will be keeping the router bit "vertical" but I think I've already solved that problem by using a parallelogram linkage.

I'll build a model, soon, and test out what is, at the moment, purely theoretical. It works in my mind's eye, though... ;-)

Hmmm...now that I've mentioned it publically, I wonder if I could still get a patent on it? Wouldn't mind being the patent holder for something simple, like this...

-- Chuck Knight

[bb99]

Ahhh, and the software is working flawlessly in my mine!

OK, now down to the nuts and bolts... I’ve got a few questions for you.

1. I believe there are 6 edges in your drawing. Will all 6 be able to elongate/shrink in length?
2. If so, then how are the legs mounted to the base?
3. How is the table mounted to the legs?
4. Could you put a horizon line in your drawings and use some color scheme to differentiate between moving and non-moving parts?
5. The original design you shared had the rotation about the z-axis as being an integral, however with this design, I’m not seeing it. Can you explain?

--bb99

[jimbo]

...

[bb99]

Thanks for the links! Lot's of stuff to go through.

--bb99

[chuckknigh]

Ahhh, and the software is working flawlessly in my mine!

:-) Exactly.

Before I build anything, I've found that it's always a good idea to create a dynamic model in my mind. Once I *understand* how it's supposed to work, and how the parts all interact, I can draw it, and then build it. It's just the way I design things...

On a related note, I'm guessing you have a basic framework for the software, already...it might not be formalized, but it's something you're working out in your mind.

OK, now down to the nuts and bolts... I’ve got a few questions for you. 1. I believe there are 6 edges in your drawing. Will all 6 be able to elongate/shrink in length?

There are 3 ways to do it...

First, keep the base triangle a fixed size. Make the upright legs of variable length, like one the hexabot platform a few messages back.

Second, keep the upright legs a fixed length, and vary the geometry of the base.

Third, make everything variable.

I think, for the purposes of my thought experiment, I'll focus on the first two. And, the problem of keeping the router orientation fixed is easier to solve on the variable base/fixed uprights version of the design.

I'm calling it the router end -- it is just the articulated "tip" of the machine. Conceivably, you could also mount a workpiece on it...and move it under a fixed spindle.

Have you seen the "hexaglide" design? It's an ingenious approach that uses fixed length struts, and a variable geometry "base" of sorts.

http://www.isw-uni-stuttgart.de/pers...e_primod1.html

I think it looks promising, even if it looks like a bit of a kludge. Very home-buildable, and a reasonable model for a 3-axis machine. I think the *6* drive screws are "in the way" in this particular implementation...3 screws won't be, though. And, it could be further modified by mounting the screws horizontally, such that the base of the tetrahedron would move in and out, rather than up and down.

It shows one of countless variations on the construction, though...and a particularly simple one, at that. The picture below is of this type of unit...they call it Modell, and it's based on the hexaglide designs.

2. If so, then how are the legs mounted to the base? 3. How is the table mounted to the legs?

These are some of those details that have to be ironed out, in physical models.

My initial thoughts are twofold, depending on which design works better.

In design 1, the base would be fixed, and the upright legs would be of variable length. They would be fixed to the base with a ball joint, or possibly a u-joint...same difference, in practical terms.

In design 2, the base would be variable, and the uprights would be of fixed length. They, too, would be connected to the framework with ball joints.

In both models, I see the machine "suspended" over a fixed workpiece, and holding a router.

4. Could you put a horizon line in your drawings and use some color scheme to differentiate between moving and non-moving parts?

Once I start doing my own drawings, I'd be delighted to do that. The diagrams, above, are just "clip art" off the web. I think the irregular tetrahedra were from the Math Forum.

5. The original design you shared had the rotation about the z-axis as being an integral, however with this design, I’m not seeing it. Can you explain?

Sure, I posted a rambling message last night, about a different idea I'd had...a simplification of the hexapod concept. By basing a machine on a tetrahedron, rather than an octahedron, we could create a 3 DOF machine with a space frame construction (which means averaged errors, rather than cumulative errors like on a traditional machine)...and do it with only 3 motors, 3 controllers, and 3 actuators...half the complexity, and half the cost of a hexabot. A hexapod is a 5 or 6 DOF machine (depending on whether it's a fixed base or a rotobot) and its capabilities would likely never be used by the home hobbiest.

It's just a different, but related idea that occurred to me, and now I'm trying to figure out the dynamics. A home-buildable, simplified, "tetrabot." At least, that's what I'm calling it, for the time being.

-- Chuck Knight

[chuckknigh]

This is something closer to what I have envisioned...but this one uses 2 tetrahedra to allow the other degrees of freedom. Just imagine it, but with only 3 legs hanging down, and the router head held rigidly vertical.

In fact, this might be a good design on which to base it, as it could add other degrees of freedom by adding another tetrahedral module on top.

BTW, this is a commercial unit designed by Turin, and marketed by Motorola.

-- Chuck Knight

[foamcutter]

Chuck,
Just a thought. Do you think that the "tetrabot" will be as rigid as a hexapod? Also how about using the tetrabot with a verticle rotating work surface for doing 3d? I have been also looking at the different designs and believe the fixed leg length with variable base would be easier and more rigid for the home builder like myself. I'm also thinking it might require less powerful motors to run it. Also wouldn't any backlash in the control threads running the variable base have less effect on the spindle than if the threads were directly in the legs to vary leg length?
You lose me on the parrallel mechanism to keep the spindle straight. Can you please clarify.

I have downloaded the EMC Manuel and am reading thru it. It does appear to have a part about 6 axis control.

I am a little slow to pick some of this up sometimes, but then all of a sudden it will dawn on me so please hang in there with my questions.
Ron

[chuckknigh]

There are only a few basic platonic solids...the tetrahedron, with 4 faces; the hexahedron (cube) with 6 faces; the octahedron with 8 faces; the dodecahedron with 12 faces; and the icosahedron with 15 faces.

The tetrahedron and the octahedron are the two lowest order forms, which exhibit inherent stability.

Now, in English, that means that all their faces are triangulated...triangles make things stiff. A cube is a platonic solid...but none of the sides are triangulated, so it's not inherently stable.

The tetrabot would be at least as rigid as the hexabot, and possibly more rigid, if built to the same tolerances. The higher the number of "edges," the less severe the angle between the faces...less severe angles can result in play in the system.

This is an issue with geodesic domes, which when they get bigger and more complicated (more edges) allows them to sometimes "dimple" inwards. There's just not enough difference between adjacent faces, to keep them apart. The tetrahedron hs the most severe angle between the faces (dihedral angle) and is the strongest and most rigid of the potential structures.

As for the parallelogram linkage, it's a standard engineering solution. Ever seen a "Luxo" lamp? It uses 2 parallelograms to make sure the lamp "head" remains in the same position, regardless of how the arm is moved. Same idea...I want to keep the router in the same position (vertical) regardless of how the arm is moved.

I'll draw up some pictures, etc, and post them, when I get some time.

-- Chuck Knight

[turmite]

Guys I am going to state my ignorance righ here right now, but for the life of me I can't see a real world need for something like the hexapod when it looks to me like anything you can machine with a pod cal already be machined with a 5 axis router that has plenty of software already available. Can someone please explain to me in layman's terms what the "real" advantage of a pod is over an good 5 or 6 axis std machine. Now on the other hand if this quest is because " I want to do it" I fully understand and wholeheartedly cheer you on. I just need a little help understanding the why!

Mike