I'm not sure if anyone is interested in using exponential math with Vectric products, but here is an example.
Vectric Math

 Vectric Apprentice
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Vectric Math
Mike Queen
Microsystems World CNC (WinCNC)
https://www.youtube.com/user/cncMike304
Microsystems World CNC (WinCNC)
https://www.youtube.com/user/cncMike304

 Vectric Wizard
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Re: Vectric Math
Hi Mike
You are right, being able to do math inside A/VCP is a big plus.
In the video you are designing a butterfly shape to cut into a cylinder with a rotary axis. Is the original butterfly shape the cross section of a beam that is going to be inserted into the CNC'ed cutout, so the beam is perpendicular to the cylinder axis? If so, does stretching of the butterfly along X (to match the arc length) preserve the correct dimensions along Y after wrapping? Perhaps I don't understand the geometry correctly, but I don't think that using the rotary axis (in a wrapped job with the stretched butterfly) would give the desired result; cutting the original butterfly using an XYZ mill would. I appreciate the problem of cutter length ... I am just wondering about getting the desired cutting shape for a beam that is to meet the cylinder at 90 degrees..
Or perhaps I don't understand the geometry right ...
Cheers!
You are right, being able to do math inside A/VCP is a big plus.
In the video you are designing a butterfly shape to cut into a cylinder with a rotary axis. Is the original butterfly shape the cross section of a beam that is going to be inserted into the CNC'ed cutout, so the beam is perpendicular to the cylinder axis? If so, does stretching of the butterfly along X (to match the arc length) preserve the correct dimensions along Y after wrapping? Perhaps I don't understand the geometry correctly, but I don't think that using the rotary axis (in a wrapped job with the stretched butterfly) would give the desired result; cutting the original butterfly using an XYZ mill would. I appreciate the problem of cutter length ... I am just wondering about getting the desired cutting shape for a beam that is to meet the cylinder at 90 degrees..
Or perhaps I don't understand the geometry right ...
Cheers!
Paul Rowntree
WarpDriver, StandingWave, Topo and gadgets available at PaulRowntree.weebly.com
WarpDriver, StandingWave, Topo and gadgets available at PaulRowntree.weebly.com

 Vectric Apprentice
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Re: Vectric Math
Hi Paul,
This would have worked better if my customer had XYZ and a rotary axis, but all he had was a Y axis and multiple rotary axes that were locked together with a single pneumatic Z with several routers that was either up or down.
First I'll tell you that the cutout that I did here was not the real shape. That had more sharp angles and I did have to slightly alter the original drawing to correct for the thickness of the pipe. Once that was done it worked fine. I was trying to create a notch on each side of the pipe so that their part could slip completely through it.
I did this video to show the math and how it could be used for "outside the box" projects, but I assure you that my customer is using it to create his parts. I didn't have to alter the height dimension because I wasn't stretching that around anything.
This would have worked better if my customer had XYZ and a rotary axis, but all he had was a Y axis and multiple rotary axes that were locked together with a single pneumatic Z with several routers that was either up or down.
First I'll tell you that the cutout that I did here was not the real shape. That had more sharp angles and I did have to slightly alter the original drawing to correct for the thickness of the pipe. Once that was done it worked fine. I was trying to create a notch on each side of the pipe so that their part could slip completely through it.
I did this video to show the math and how it could be used for "outside the box" projects, but I assure you that my customer is using it to create his parts. I didn't have to alter the height dimension because I wasn't stretching that around anything.
Mike Queen
Microsystems World CNC (WinCNC)
https://www.youtube.com/user/cncMike304
Microsystems World CNC (WinCNC)
https://www.youtube.com/user/cncMike304
 TReischl
 Vectric Wizard
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Re: Vectric Math
This is the classic problem of cutting rotary with the tool on centerline.
The rotary software I wrote years ago worked by projecting the shape onto the inner diameter then reprojecting those points back to the OD as a ray from the center of the tube. In our case it worked well because almost all the work being done was tubes inserted into other tubes and then welded. So that V gap was a great place to put weld.
I even did a function for doing rectangular tubing on the rotary.
If ya think about it, whatever passes into the tube must clear the ID, that results in the points needing to be reprojected onto to OD.
Right now I am starting to investigate what it takes to add another axis to a Gecko G540 and a smoothstepper so I can cut off axis and avoid all this crazy reprojecting stuff!
Great video though showing the issues and how to overcome them!
The rotary software I wrote years ago worked by projecting the shape onto the inner diameter then reprojecting those points back to the OD as a ray from the center of the tube. In our case it worked well because almost all the work being done was tubes inserted into other tubes and then welded. So that V gap was a great place to put weld.
I even did a function for doing rectangular tubing on the rotary.
If ya think about it, whatever passes into the tube must clear the ID, that results in the points needing to be reprojected onto to OD.
Right now I am starting to investigate what it takes to add another axis to a Gecko G540 and a smoothstepper so I can cut off axis and avoid all this crazy reprojecting stuff!
Great video though showing the issues and how to overcome them!
"If you see a good fight, get in it." Dr. Vernon Jones

 Vectric Wizard
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Re: Vectric Math
Hi Mike. Glad to see that it worked and the part is in production. I can see the ID/OD problem, but that is not what I am imagining here. Perhaps I am not seeing this right ..
The first attachment's shape has varying 'height' cutout, like the crosssection of a weird beam that is to stick into the part I am working. The horizontal 'stick' protrusion is at exactly 1/2 the distance from the Y=0 of the beam (flat bottom of vector, at 0 degrees) and the tip of the triangle (90 degrees in this example). When wrapped (second image), the 'stick' will still be exactly 1/2 of the way from 0 to 90 degrees, measured along the arc (ie at a rotary angle of 45 degrees). From the perspective of the incoming beam shape, the stick protrusion is no longer 1/2 of the way from the centre line and the end of the cutout.... it is closer to 70% of the way to the edge. I think this will always be an issue if the Y dimension changes as the wrap angle moves from centre to its maximum... to capture the beam's crosssection a trig distortion, not a stretch along X would seem to be required.
The first attachment's shape has varying 'height' cutout, like the crosssection of a weird beam that is to stick into the part I am working. The horizontal 'stick' protrusion is at exactly 1/2 the distance from the Y=0 of the beam (flat bottom of vector, at 0 degrees) and the tip of the triangle (90 degrees in this example). When wrapped (second image), the 'stick' will still be exactly 1/2 of the way from 0 to 90 degrees, measured along the arc (ie at a rotary angle of 45 degrees). From the perspective of the incoming beam shape, the stick protrusion is no longer 1/2 of the way from the centre line and the end of the cutout.... it is closer to 70% of the way to the edge. I think this will always be an issue if the Y dimension changes as the wrap angle moves from centre to its maximum... to capture the beam's crosssection a trig distortion, not a stretch along X would seem to be required.
Last edited by PaulRowntree on Sun Aug 09, 2015 4:11 pm, edited 1 time in total.
Paul Rowntree
WarpDriver, StandingWave, Topo and gadgets available at PaulRowntree.weebly.com
WarpDriver, StandingWave, Topo and gadgets available at PaulRowntree.weebly.com

 Vectric Wizard
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Re: Vectric Math
When the video got to using trig to measure the angle of the radial lines, you could skip the trig and simply use the dimension tool to reveal the angle. Click on each end point.

 Vectric Apprentice
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Re: Vectric Math
Yes. I only did the trig to prove the length was correct. Good point. I forgot to mention that.4DThinker wrote:When the video got to using trig to measure the angle of the radial lines, you could skip the trig and simply use the dimension tool to reveal the angle. Click on each end point.
Mike Queen
Microsystems World CNC (WinCNC)
https://www.youtube.com/user/cncMike304
Microsystems World CNC (WinCNC)
https://www.youtube.com/user/cncMike304