Compound angle for rotary axis.

[StefanV]

I own vCarve Pro9 and don't mind upgrading to Aspire if that's what it takes to make this possible.

I need to fit a thin laminate (Formica) "A" into a 90 degree corner. Of course, as a top view when everything is mounted this will look like a perfect triangle. But being bend down over a 40 degree curve with a radius of 34mm, I have 2 big challenges:

- The Formica itself, How do I go about creating the outline for the toolpath when the piece gets unfolded, for me to be able to cut it as an 2 dimensional flat on the CNC?

- The cleats I will put against each side of the corner "B & C", mirror image each). Their top surface (in green) starts as a perfect horizontal flat in the back corner, but this angle changes as we move towards the front of the path the Formica will be fit against. It's a compound angle between the curves of that unfolded triangle, and moving toward a perfect straight corner between the sides by the end of the cleat.

In my mind it is easy to cut the top side of these cleats in a template that is fixed in a rotary axis, . I can see how the combination of the 5th axis turning the part at the right time, with the right toolpath on X and Y to move from end to end, makes this a simple straight cut for the Z-axis.

No, I do not have the option to cut this path into the sides, I need to create these cleats. I would need to cut about 50 each left and right per month for a long time to come, so I think it's worthwhile figuring it out, to give me the flexibility of modifications in the future.

If it doesn't work graphically, I see myself making a long excel sheet with angles and sines calculating a thousand points on the path, but there's going to be a lot of trial and error before I get that translated into 5th axis G-code

Any advice is appreciated. Thanks!

Stefan

[eph210]

Unless I misunderstand here, I don't see any compound angles. The formica will be cut flat as a triangle with the 2 longer sides the length of the arc. All the sides of the triangle will be straight lines. VCP can give you the length of the arc, use the measure tool and select span length. The cleats are the section of arc that you have drawn with the ends mitred. That will also be a 2D cut.
Euan

[FixitMike]

The attached picture and file show how to construct the Formica outline as a 2D cut. Also, the cleat outline.
The cleats can be cut as flat (2D) objects. The surfaces where the Formica contacts them will be slightly off from theoretically perfect, but I don't believe anyone will notice the difference. I would suggest overlapping the cleats at the corner, rather than a miter joint. Same as
the wall is drawn. Much simpler.

Corner Triangle.crv

(54.5 KiB) Downloaded 122 times

Corner Triangle.crv

(54.5 KiB) Downloaded 122 times

[eph210]

Thank you for the corrections, Mike. I realized I was in error at work this morning.
I blame it on the lack of coffee.
Euan

[StefanV]

Thanks Mike, this is the way I had start laying it out in 2D (Corel Draw) and if there isn't a function in VCarve or Aspire that can make it more accurate, than that's the way I'll go. I have it manually spot-chekced every 5 degrees for accuracy. I can work with this, see my drawing, same logic as yours.

For the cleat, I must disagree, the Formica doesn't fit at all if I just cut it flat. Note that the bottom edge of the Formica is a straight line between the 2 corners, not a circle. If it were a circle, a flat cleat would work. But in my case, the view from the top is a 45 degree angle on the wall. So I made my spreadsheet;

Providing the long straight side of the cleat is along the Y-axis and aligned in the center of the rotary axis, flat to the table to start;

Column C is my 40 degree cleat, transferred to radians in column D
Column E, the sine, is the projection of the cleat on the Y-axis
Column F is the same number in proportion to the total radius of 434mm. Shows that the cleat is 278.97mm long.
Column H is the cosine of the angle, the projection of the cleat on the X-axis.
Column I is what that represents in mm for my 434mm radius. This would be a full slice of a circle, I only want the end part (cleat) of 101.54mm wide, so that's what I calculate in column O

This would be it if the cleat could be cut flat with a 90 degree side all its length. But, I know the angle at it's widest (line 5) is 90 degrees to the cleat, flat part, straight cut on Z. And I know the angle at the end (line 45) is 45 degrees to the cleat. So we need to turn the rotary to 45 degrees to have a straight Z-cut again at the end. Only problem, as you turn the cleat on the rotary axis, the cleat becomes more narrow from a top (Z) point of view. This is direct relative to the cosine of the angle from 0 to 45 degrees, so

Column K are the rotary steps to go from 0 to 45 degrees, based on 12,000 microsteps per circle (200 step motor, 6/1 belt reduction, 10x microstep)
Having my cleat Y-axis movement based on 40 equal steps, I divide my 45 degree travel in 40 equal steps also in column L
Going trough radians in column M, this gives me a cosine in column N that represents the % portion of the total width of the cleat, standing at the angle in column L in the rotary axis.
So,... applying that % to the actual with of the cleat (X-axis) in Column P, I should have the perfect X-Y-A path to cut.

The Z- movement of the point to cut is just above 2", so with a longer spiral cutter I should be able to cover that without moving the Z-axis up or down. I could calculate the Z-position if I wanted to,...

This should give me the exact cleat-shape going from 90 degrees on top to 45 degrees at the end.

Never knew learning sine and cosine in school would have such as practical application one day. Yet, I would have liked to dump a graphic file into aspire and get a 1,000 line gcode without worries, rather than writing it myself.

Am I crazy?

[StefanV]

Can't attach Excel files Here's a pdf version.

Stefan

[StefanV]

Here are the same 5 degree steps laid out on the rotary axis on a 3/4 thick cleat, note that the 8th position is at 45 degrees but has no length (it's just a line down the center)

To the x-axis movement we need to add 1/2 diameter of the cutting bit.

[FixitMike]

I'm sure this could be modeled in Aspire with a 2 rail sweep. Or toolpathed in VCarve Pro with Paul Rowntree's FlutePlus gadget.

Another possibility: 3D print the cleats as a single piece.

[FixitMike]

Here's a crude example of a varying slope made with multiple fluting toolpaths. I used a 3/8" end mill, paths that were spaced .125 apart, and .02 change of depth for the adjacent ones. Putting the paths closer together with less slope change between adjacent ones would make it smoother.
If I used paths that were .010 apart, with a ball nosed cutter, and varying starting depths I believe I could get very close to what you want.
But a two rail sweep in Aspire would be much easier.

Another program you that I suspect would be better to do the job for you is Paul Rowntree's CSV. You can find it here: http://paulrowntree.weebly.com/gadgets.html

And another idea: model this in SketchUp and import the 3D for the cleat. (I've never done this, I just suspect it would be easier than multiple fluting toolpaths.

You don't really need a 5th axis to cut the cleat. The Vectric 3D programs use multiple close passes with a ball nose bit to cut sloped surfaces. The thing that a 5th axis would give you is the ability to do undercuts. But you don't need that capability for this project.

Let us know how this works out. If you manage to program the cleat I would certainly like to see how you do it.

[FixitMike]

Well, I did it with Aspire. Here's a picture of the result. I'm not posting the file itself as no else can open it because it was done with a trial copy of Aspire.
The cleat does not have the necessary corner miter. It would be easier to cut it on a table saw.

[StefanV]

Well, I did it with Aspire. Here's a picture of the result. I'm not posting the file itself as no else can open it because it was done with a trial copy of Aspire.
The cleat does not have the necessary corner miter. It would be easier to cut it on a table saw.

Formica cleat.PNG

Mike, I upgraded to Aspire, educated myself on the 2 rail sweep and I'm trying to copy your result. I understand the 2 rails (They are running in to the length of the cleat right?) and the contour you use. I do need a flat contour on top, but that's not a problem.

How did you get the cleat to take on the curved shape?

thanks,

Stefan

[StefanV]

ok, found it, thanks