I'm still reading and thinking about your control concept, also
because we made some reasoning previosly that this control concept
would be useful for a cutter table with a cutting wheel as a cheaper
replacement for laser shape-cutting. It never left the stage of being
a nice idea, but I see you are thinking about developing the same.

For anybody interested, both cutting machines work in a similar way as
a pizza-cutter wheel does work. You work in 2.5D space with the wheel
turning in the proper direction. I think the Z axis could be used in
either on/off mode (piston) or in true 3 axis mode where it would go
up and down to preset heights. I'm not sure if any of the more
complicated commands are useful for this mode of operation.

On Tue, Jan 27, 2009 at 9:00 PM, Eric H. Johnson
<ejohn...@camalytics.com> wrote:
> Hi all,
>
> I am looking at doing a retrofit on an XY table with a tangential ultrasonic
> knife. There are several issues to address, and my current thoughts on how
> to address them are presented below. Any better ideas, easier ways of doing
> it, something already implemented which I have missed, or means of making it
> more generic are appreciated.
>
> The table has conventional X and Y axes, Z is performed pneumatically with
> just an up and down position. The A or rotational axis should orient the
> knife tangent to the direction of motion defined by X and Y.
>
> My thought is to use a custom kinematics module to handle the rotational
> axis. There are a couple of issues:
>
> 1> It needs to look back far enough in time while the system is in motion to
> get a position enough different from the current position to calculate a
> valid slope. Update rates of 1ms or faster for the servo task may result in
> only an encoder tic or two difference, which likely would be too inaccurate
> to calculate a valid tangent. For my application an error of even +/- a
> couple degrees is tolerable, but certainly the closer the better.
>
> 2> Handling rotation when going through Pi (180 degrees) in the positive
> direction or -Pi (-180 degrees) in the negative direction. Doing a raw
> arctan2 gives a result in the range of -Pi to Pi, which would result in a
> full de-rotation when passing through those points. The axis has no
> mechanical restriction as to the number of times it can rotate, so the
> preferred method would be to add or subtract the difference in the angle
> from the previous angle. IOW it would allow a spiral to be done without the
> head ever de-rotating.
>
> 3> If the vector angle defined between two vectors exceeds a specified
> angle, the head needs to lift, rotate to the new angle, and then drop as
> there is only so far the head can turn within the material being cut.
> Currently I don't see a way to do this automatically within the kinematics
> and am considering using a preprocessor to insert the commands for these
> head lifts. I could use M3 / M5 to both start and stop the ultrasonics and
> perform the head lift.
>
> 4> The time to lift the head could be done with a dwell, but there are
> sensors to indicate when the head has reached the up and down positions.
> Based on air pressure and a couple of other things, there is some variation
> in the time it takes to move from the down position to the up position and
> vise-versa. Implementing some means of delaying the next motion until the
> head state condition is satisfied would be preferable.
>
> I suppose I could implement a pseudo Z axis which returns the values of 1.0
> when in the up position, -1.0 when in the down position and 0.0 for any
> other state of the two sensors. I suspect faking out the following error on
> this axis may still present a problem however.
>
> Anyway, any input is appreciated.
>
> Regards,
> Eric
>
>
>
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