Delta Platform for Milling?

I'm not that familiar with the limitations of the Delta platform, but what are people's thoughts on using a Delta design for CNC milling?

The standard CNC milling design is a large bed with a gantry in the X and the toolhead moving in Y/Z. This design is good for a couple of reasons but the design is popular mostly because it's very rigid. This is important in milling because of the stresses on the milling bits. But because the milling tool only moves in the vertical, and milling is inherently a subtractive process, you can't easily make the same holes and voids as with 3D printing. However with a Delta platform you could orientate the milling bit more freely and create more complex outputs from the stock.

The drawbacks I see are (1) the software needs to do more work to avoid collisions and (2) I know nothing about the rigidity of a Delta design, so this might be a total pipe dream. How much force can you reasonably apply on the toolhead? I'm guessing there's fairly decent leverage that might be bad news.

I'm thinking something like a Dremel with a flex-shaft to keep the weight down on the toolhead. But that's the easy bit (ha ha). Has anybody tried this already?

There are commercial mills buit this way using what look like hydraulic rams for arms.
It's interesting because they can orient the milling head.
The issue is going to be getting enough rigidity, my guess is for the same rigidity as a conventional mill you'd be looking at significantly more weight.

Delta mill

Edited 1 time(s). Last edit at 08/25/2012 01:09PM by Polygonhell.

That milling video shows a complex control logic for 6 separate axis.

the Rostock/Delta that 3D'ers are messing with right now, could only do the 2D paths plus z plunge kind of work.
That tilting head would require six towers all driven separate, and a lot of pioneering/trailblazing.

I would guess that chatter is the next issue/challenge.
The cutting edges create impact and vector forces with each swipe.
high frequency thumping that will rattle the delta mercilessly.
You might be able to get away with having a very heavy head and taking very small feed and speeds.
It might work, but be an unsatisfying mechanism.

I think the milling machine that is you'tubed shows the heft needed to combat the forces.
I'd guess there's 300 lbs of moving metal, and probably very little joint slop.

but, I think a Rostock like mechanism would work for small 1/8 to 1/4 inch mills. add like 10 lbs in dead weight on the head.

Spindle motors are the bomb! dremels and routers don't have the bearing system to combat the RPM and forces and are low quality.

I like the idea of trying. why not. I would think that ball screws would be great to drive the towers, with lots of power advantage and enough speeds to move the blocks. The rostock belt idea might contribute to chatter.


Dave

My engineer's feeling says, you have to extend the design to at least four motors to get the head position reasonable sturdy. And the height shouldn't be _that_ high, so the axes don't bend less.

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I think the calibration would be the hardest part. Homing with a 6-actuator head is non-trivial. In fact with any more than three actuators, it's non-trivial.

Annirak Wrote:
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> I think the calibration would be the hardest part.
> Homing with a 6-actuator head is non-trivial. In
> fact with any more than three actuators, it's
> non-trivial.


In fact calibration of 6-dof robot is quite easy. Just take some measurements and solve machine dimensions as optimalization problem - you dont even need to understand the problem, just use snandard solvers for bunch of points.

ledvinap Wrote:
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> In fact calibration of 6-dof robot is quite easy.
> Just take some measurements and solve machine
> dimensions as optimalization problem - you dont
> even need to understand the problem, just use
> snandard solvers for bunch of points.

The point is not initial calibration, it's that you have a multiply constrained system. Which means that it must all work together all the time. With the rostock, there is a 1:1 mapping: at every point in the build area's 3-space, you can move any arm actuator to any point in its travel and it will correspond to a single point in the 3-space without binding the machine. There is an elegance to that simplicity, which is not present in a delta bot with four or more actuators. In fact, with a rostock-style 4-arm bot, you cannot move any one arm at a time: you must always move at least two to prevent binding. This means that the bot must not slip between power-on cycles or the bot must have perfect knowledge of the exact position of its arms at any time.

Clearly this is much more complex. Part of the beauty of the rostock platform is that the arms can start in any arbitrary position at power-on and home to the top for initial calibration, then home to three points on the bottom for secondary calibration. With 4+ arm bot, that is not an option, since homing to the top could, in some circumstances, bind.

This is why I called it non-trivial.

Actually the 6 arm bot isn't over constrained, unless you artificially constrain the platform to be horizontal, and not to rotate.
It has 6 DOF XYZ and some degree of roll pitch yaw.

I still think the issue for milling is going to be lateral stiffness.

Polygonhell Wrote:
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> Actually the 6 arm bot isn't over constrained,
> unless you artificially constrain the platform to
> be horizontal, and not to rotate.
> It has 6 DOF XYZ and some degree of roll pitch
> yaw.

Maybe overconstrained is the wrong word. I'm not trying to say that both don't have the same number of degrees of freedom--they do. That's not the problem, it's that the coordinate space is not surjective. That is: not every point in the 6-D control space maps onto a point in the 6-D physical space.

For an example of what I mean by that, try this thought experiment: With a 6-DOF extending-arm delta bot, such as the one that you linked above, fully extend all the odd-numbered arms and fully retract all the even-numbered arms. The machine will bind. In fact, that machine appears to use three pairs of arms, which means that the maximum delta between adjacent arms is roughly the separation between the mounting points (they're slightly trapezoidal, so there's a little more play than this, but it's a good first-order approximation).

The rostock pattern is surjective. That is: for every point in the 3-D control space, there is a point in 3-D physical space. In that respect, the rostock-style design is far easier to control.

Quote

Maybe overconstrained is the wrong word. I'm not trying to say that both don't have the same number of degrees of freedom--they do. That's not the problem, it's that the coordinate space is not surjective. That is: not every point in the 6-D control space maps onto a point in the 6-D physical space.

This is true, but it should not be big problem. You only need to know some approximation of current position (just knowing that current configuration is in working space is enough with some robot configurations) and then you can at least plan homing movements.
For some configurations there may be entire control space without singularity/surjective (arms so short that maximum delta can't be exceeded in your example).

With vertical parallel arms this is event simpler - you can home all actuators in parallel (orientation and position in physical space changes only in Z) and stop actuators that hit limit. You end up with homed robot in topmost position.

BTW: 3-dof case with long enough control rails is not surjective - two cariages can get so far from each other then links are too short.

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ledvinap
This is true, but it should not be big problem. You only need to know some approximation of current position (just knowing that current configuration is in working space is enough with some robot configurations) and then you can at least plan homing movements.

I don't know the math required to work out a homing algorithm that will work for all starting points within the coordinate space without some kind of feedback on the force. Maybe use skipped steps to find binding cases?

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ledvinap
For some configurations there may be entire control space without singularity/surjective (arms so short that maximum delta can't be exceeded in your example).

Granted, but I don't think 6-DOF delta bots are one of these cases. The even/odd extension/retraction case will always be problematic.

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ledvinap
With vertical parallel arms this is event simpler - you can home all actuators in parallel (orientation and position in physical space changes only in Z) and stop actuators that hit limit. You end up with homed robot in topmost position.

I'm not convinced of this. If you have a very off-centred platform and you home by moving all axes up at the same time, everything will be fine until the first carriage hits an endstop. Then, the speed of each carriage must follow a cosine speed curve to prevent binding. Again, maybe skipped step detection is the way to do this.

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ledvinap
BTW: 3-dof case with long enough control rails is not surjective - two cariages can get so far from each other then links are too short.

Certainly, there are ways to make a 3-dof bot non-surjective. Actually all of them are: you can't reach 0 on all rails simultaneously--that would go through your work floor.

Both the Rostok and Stewart platform geometries are well-behaved geometries. There are many robots with 3-rail Rostok geometries. The ABB FlexPicker works that way, with three powered axes, and is not overconstrained. (The Adept Quattro has four powered axes, but the head orientation is fixed, so I think it is overconstrained.) It's a good mechanism for very fast positioning in a big workspace. Makes sense for a 3D printer.

Stewart plaforms are quite strong. The linear actuators see linear loads only; no bending moments are imposed on them. So they don't have to be super-stiff, just powerful. They're used mostly for motion bases for flight simulators, often with thousands of pounds of load. Hydraulic cylinders, pneumatic cylinders, and ball screws have been used to power them.

Seems like overkill for something that just lays down ABS, though.