spiral formula?

snipped-for-privacy@gmail.com wrote:


Rich,
Thanks for posting the picture :-) Keep on making chips!
Fred
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Google for Archimedan spiral and you should find some links that will help with the design.
The basic formula is something like:
r = b * theta^a
where r = the radius, theta = the angle in the X-Y plane b = a scaling factor a = coefficient that determines the degree of the spiral
Work out the values of "r" for different angles (theta in radians, I think) and from that calculate the X-Y coordinates for various points. Play with "a" and "b", to get the right number of spirals and distances between.
We did this at work for a small, flat-sheet, lab-scale membrane housing a while back. We wanted a spiral groove in the face plate to direct fluid flow in a spiral out from the center inlet to the outlet at the periphery of the circular membrane. If it would help, I can email you the Excel spreadsheet I used to calculate the coordinates that made up the curve. I used a mechanical 3-D program (Alibre) to generate the dimensioned part with the spiral groove, importing the coordinates from Excel to define the path of the spiral. From there a DWG file was exported and sent off to the machinist, who had no problem making the part. That's probably a lot more work and expense than is justified for you, but it can be done pretty easily given the right software and hardware tools.
That said, someone here will probably describe a simple method using a Dremel tool and protractor <g>.
Mike
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There is an infinite universe of spirals out there. The simplest being a constantly expanding radius vs rotational angle. Then you get into exponential functions, hyperbolic functions, etc. etc. The CNC program has to be capable of plotting the selected function. Bugs
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Google for Archimedan spiral and you should find some links that will help with the design.
The basic formula is something like:
r = b * theta^a
where r = the radius, theta = the angle in the X-Y plane b = a scaling factor a = coefficient that determines the degree of the spiral
Work out the values of "r" for different angles (theta in radians, I think) and from that calculate the X-Y coordinates for various points. Play with "a" and "b", to get the right number of spirals and distances between.
We did this at work for a small, flat-sheet, lab-scale membrane housing a while back. We wanted a spiral groove in the face plate to direct fluid flow in a spiral out from the center inlet to the outlet at the periphery of the circular membrane. If it would help, I can email you the Excel spreadsheet I used to calculate the coordinates that made up the curve. I used a mechanical 3-D program (Alibre) to generate the dimensioned part with the spiral groove, importing the coordinates from Excel to define the path of the spiral. From there a DWG file was exported and sent off to the machinist, who had no problem making the part. That's probably a lot more work and expense than is justified for you, but it can be done pretty easily given the right software and hardware tools.
That said, someone here will probably describe a simple method using a Dremel tool and protractor <g>.
Mike
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Send me your email address and I will send you a copy of lisp code that will work with autocad or intelicad to generate the spiral. Also I have a program I wrote [qbasic] that will convert HPGL [not HPGL/2] to gcode. [versions available for emco f1, hurco, Bport BOSS] Not hard to rewrite for most any controller as it only does straight lines.
GmcD
On 18 Jun 2005 12:07:50 -0700, snipped-for-privacy@gmail.com wrote:

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wrote:

I think you're describing an Archimedian spiral. To calculate the points along the toolpath:
If the center of the spiral is at (h,k),
r = (0.5 + 0.25) * angle / (2 * pi)
x = h + r * cos(angle)
y = k + r * sin(angle)
If it starts out at angle=0, then the spiral will start off in the positive x-direction and proceed in a counter-clockwise pattern. You can fudge its behavior by playing with the starting value for angle, the polar expressions, and by adding an offset to angle.
HTH -- Morris
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