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Polar Coordinates CNC?
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Ken Jenkins
Interesting idea ... but why? It seems to me the particulars
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of the math involved would not make arriving at the end use coordinates any easier. Do you have a particular application in mind? I'm just curious why Polar over Cartesian would be any better and if so why it hasn't been done? Ken Message: 9 |
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The application would be the same as any other - i.e. router/plasma
application (4'x8' as practical size for discussion purposes). I would think that Linear moves in polar space would be roughly the same and no more complicated than arc/circular moves in cartesian space - would they? I think that a polar machine could be a more cost effective approach given that you eliminate many of the most expensive components of the system (the long axis). Parallelism is eliminated as a requirement which generally requires you to do "special" things to tie the parallel sides of a large gantry style machine together either via encoders or long belts if using multiple drives. You lose a certain amount of rigidity with a gantry machine that either must be made up by stiffer slides or beefier components on the gantry itself. All of these result in a large heavy gantry which of course requires a larger motor(s) to drive. It looks to me like a lot of these issues can be avoided on a polar based machine as there is a single pivot point and therefore single drive point. A very large machine would have to either have an extremely heafty arm or would have to be supported on the outer end of the boom. So significantly larger sizes likely are not practical. I think the biggest problem with a polar machine is one of accuracy... i.e. the accuracy will "expand" as you go out from the central pole. That's ok as long as you can get sufficient accuracy in towards the pole/pivot point. This factor would also likely dictate the largest practical size. As a test application I was thinking of a 4x8 application using 2 quadrants. 4' x 1.414 (2*sqrt (2) ) makes a boom of 6' able to cover the entire area of a 4'x8' sheet. Why hasn't this been done before? I don't know - I expect that the cartesian basis of g-codes themselves have preselected this to a degree. A Polar router has some similarities to a hexapod in my mind in that it requires ongoing trig conversion for each axis/movement. But it's obviously been handled for hexapods which I think are significantly more complicated than the polar option. So it seems doable... Lee Wenger Denver, CO |
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Fred Smith
--- In CAD_CAM_EDM_DRO@y..., "wenger2k" <wenger2k@y...> wrote:
The application would be the same as any other - i.e. router/plasmaapproach given that you eliminate many of the most expensive components ofthe system (the long axis Why hasn't this been done before? I don't know - I expect that theIt's been done many times. It is referred to as a rotary axis. If a rotary axis is oriented parallel to a spindle (Z), it is identified as a C axis. The complete range of movement can be defined as X-Z-C coordinate triples. Since G-code by definition is the tool movement, the entire coordinate system is covered by this. Several of the G- code intrepreters can output rotary axis code. The problem with this method of control is that the linear movements by definiiton are approximated by tiny arc movements. Since most movement is linear, the programs become quite large. 10 years ago it was a no-brainer as the controllers could not process large programs. Today it may be economically feasable to produce rotary code (polar to you) that can be processed, and the result could be a machine with a linear and a rotary axis. One draw back is that as the radius increases in size, the machine accuracy decreases. This is not the case with dual linear machines. a 3 place decimal degree is much more accurate at a 2 inch radius than it is at a 20 inch. You may need to spend more than you would think to get a reasonable angular resolution at the longest radius. A 2000 line encoder, a 4 foot diameter would be 150.8 circumference. yields .0754 inch per encoder line. This would not be too practical. However, IF, (very big if) you could get a decent circular rack at 4 foot diameter, you could get excellent resolution from a stepper motor. Also might get some decent resolution from a pully or gearbox setup for a center drive. It's almost intriguing enough to start throwing a prototype together. ;-) Best Regards, Fred Smith - IMService |
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Ken,
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Here is one reason; it's called necessity :-) I wanted to make some decorative wooden gears that appeared to be too big to do on the Sherline. But, by mounting the blank on the rotary, I only had to access from the center of the rotary to the outermost point on the circumference yet could still cut anywhere on the full disk. There may be better ways, but I just drew it up in the normal X-Y fashion and wrote up a small VB app to convert the Y's to C's. The only tricky part was that a new feed rate has to be entered for each block, due to the way that my controller (CNCPro) handles rotary feeds. So, to answer your question, it basically doubled my capacity for this rather unique job. Hope this helps, Al Lenz --- In CAD_CAM_EDM_DRO@y..., Ken Jenkins <kjenkins@b...> wrote:
Interesting idea ... but why? It seems to me the particulars |
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Alan Marconett KM6VV
Hi Al,
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This IS an interesting subject! Last week I was trying to develop a tool path to cut some detail on the periphery of block of aluminum. While I had digitized the surface I wanted (of a Stuart steam engine cylinder), and COULD cut that as a final, what I wanted to do was develop a tool path to "rough" it out first. Most of the surface is cylindrical, with flat surfaces on one side tangent, and ending in a flat on one end of the otherwise pear shape. Onto the surface would be cuts to make flanges at either end of the cylinder, and projections at several points for exhaust pipe, and drain cocks. Only way I know to create this contour is by projecting the required radius at various points along the periphery (like working sheet metal). I'm assuming a 4-axis CAD/CAM program will have a better way to do this, but I haven't been able to afford this for a "hobby" project. SO, I'm looking for better ways to design things like this! I wouldn't call this a Rho-Theta type application, just a simple cylindrical projection. Perhaps you'd like to describe a little more of your project and approach. Alan KM6VV alenz2002 wrote:
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Ray Henry
Lee
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I think that the essence of your analysis of the mechanical stuff is true for a Puma robot type of thing but I can't see how that truth affects whether it is programmed in polar or Cartesian coordinates. The EMC could rather easily be configured to run such a device, it has Puma kinematics in the source files, but current programming is with respect to Cartesian space. When we command a coordinated move like g1 f10 x1 y2 z3 what the interpreter does is compute a vector and uses the f10 as the feedrate along that vector so in effect it is a polar move. I can't for the life of me see how specifying three angles and a distance would be more efficient or would somehow alter the fundamental thinking about milling or turning. Ray ? ?From: "wenger2k" <wenger2k@...> |
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Fred Smith
--- In CAD_CAM_EDM_DRO@y..., Ray Henry <rehenry@u...> wrote:
along that vector so in effect it is a polar move. I can't for thelife of me see how specifying three angles and a distance would be moremilling or turning.It's the machine that is simpler. Think of a turntable (like a lazy susan) with the part mounted in place on the turntable. The rotation is C axis Now place a single horizontal linear axis parallel to the face of the turntable (X) above the work piece, and mount a Vertical Z axis onto the X. (R is not a valid CNC linear axis so I will refer to it as X.) The machine is simplified to a single linear X and a bearing for C. Instead of at least 4 precision linear guide components for a linear gantry style machine, you reduce it to 2 (shortest possible) plus the bearing (Actually only 1 if you use a dove tail arrangement like a Bishop-Wisecarver rail). The Z axis is the same mechanism in this case. The intriguing part is how to accurately position the work piece because there are no straight edges to indicate, away from the central X axis. I'm thinking of mounting a vise. How to indicate it in, is a much different thought process if only one horizontal axis is linear. I guess you could indicate one face, set zero degrees, rotate 180 degrees and tram for centrality, or rotate 90 degrees and use an edge finder to set the X distance and angle to a part edge. I would guess that you would want to have an axis transform for the vise to avoid going nuts trying to mount it square to the X axis. Logically it's the same as setting X & Y, but it's still a mind twister. Fred Smith - IMService |
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Ray Henry
Hi Fred.
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Well, yea. I can see the device but it seems to me that by the time you build C with center bearings, drive, and some sort of support for cutting forces around the outside of the suggested 4' diameter you'd have more work into it than a conventional mill and all to save two slides, a ball screw, and their supports. I did recently see a mega lathe with a C axis on the flat like this. The turntable (spindle) had to be 10 - 12 feet across. There was an X gantry that looked more like a press brake spanning the whole wheel. Z with a tool holder hung from one side of the gantry. The shop guy said they found it in a farmers field and that it had been surplus from the Rock Island Arsenal. It took several guys a few months to clean up and get going. He thought it could hold 0.0005 on an 8' diameter wheel but he's still looking for a micrometer that size.<g> Ray ? ?From: "Fred Smith" <imserv@...> |
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IMService
Date: Mon, 4 Nov 2002 06:30:22 -0600 Well, yea. I can see the device but it seems to me that by the time youA turntable with skate wheels around the OD sitting on a 1/4 thick, flat rolled sheet would probably be flat enough for most CNC router work. They usually are happy with a 6 inch Z travel. Remember the X is fixed and technically it only has to go to the center. 2 feet of precision guide ways to support an axis that in all other designs requires 4 feet plus another 4 feet of support on each side. This is a major reduction in complexity with very little loss of resolution, repeatability, or massiveness. I did recently see a mega lathe with a C axis on the flat like this. TheMy interest was actually sparked in making a small bench top machine. I'm thinking 12x12 inches rectangle (on the turntable), maybe less. 6 inch Z height. Rack and pinion on the X and Z w/B-W skate wheel guides, and a large spur gear and pinion w/ motor mounted vertically, underneath the turntable. disk overhang protects the moving parts from dust and swarf. Angle Iron/channel frame. Might be a kick-butt kind of kit or entry level machine with a router motor installed. Best Regards, Fred Smith- IMService Listserve Special discounts and offers are at: |
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Hi All,
Now as a real mind twist, try to imagine the "bridge" over the top of the rotating table as a semicircle. The only linear motion is the Z axis, mounted on that rainbow over the rotating table. I had some concept sketches done a few months ago, but ran into the problem of cutting a straight line with no kerf angle. Basically this is designed for contouring work with the center of the volume at the center of rotation, but has some limitations relative to lead angle of the tool vs. wall angle on the part. It would also require a long Z axis travel. My next version included a linear axis under the main rotary table, allowing straight line machining and vertical axis holes to be drilled anywhere on the table. So 2 rotary and 2 linear axis to handle 5 axis contouring. How can a control software accomodate this machine? Allan |
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Raymond Heckert
Fred, I have to agree with the other Ray H. A Polar
machine/software making a move from X(1) to X(2) must calculate every position along the path, whereas a Recti-linear machine merely has to say' "Am I at X(2) yet?... no, well, then add another pulse at the X-axis." Now, it's true, that in a Rect. machine/software, interpolating a circular move, the program must calculate every point on the path, but so must a Polar machine/software. Polar machines must, of necessity be more complex. I trained o a FANUC 120-iL Robot Welder at the Lincoln Electric School in Cleveland, OH, a couple of years ago, and that was one complex machine. Six axes, and four different reference frames (points of view). Fortunately, the programming was done via a Pendant, so it was relatively easy... But the machine was complex. It was really fearsome, to watch that robot welding, just thinking about all the calculations it had to be making every few microseconds. RayHex ---------- From: Fred Smith <imserv@...>wrote: can't for thealong that vector so in effect it is a polar move. I distance would be morelife of me see how specifying three angles and a thinking aboutefficient or would somehow alter the fundamental mounted inmilling or turning.It's the machine that is simpler. place on the turntable. The rotation is C axisface of the turntable (X) above the work piece, and mount a VerticalZ axis onto the X. (R is not a valid CNC linear axis so I will referto it as X.) bearing for C. Instead of at least 4 precision linear guide componentsfor a linear gantry style machine, you reduce it to 2 (shortestpossible) plus the bearing (Actually only 1 if you use a dove tailarrangement like a Bishop-Wisecarver rail). The Z axis is the samemechanism in this case. |
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Ray Henry
Okay. I'll pose the design to a few folk that I know and see what they
say about the EMC running it. It will not be programmed with polar coordinates at this point. Ray Subject: Re: Re: Re: Polar Coordinates CNC?<s> My interest was actually sparked in making a small bench top machine. ? |
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Yes but moving from x(0)y(0) to x(1)y(1) requires the same sort of calc.
However you cut it though, the inherent differences in accuracy at differing radii in polar machine, is the death knell for practicality. At 08:23 PM 11/4/02 -0600, you wrote: Fred, I have to agree with the other Ray H. A Polaraol://5863:126/rec.crafts.metalworking or go thru Google.com to reach it if you have trouble. sister site to the CCED group, as many of the same members are there, for OT subjects, that are not allowed on the CCED list. DON'T POST IF YOU CAN NOT ACCEPT THIS.....NO EXCEPTIONS........ billRegards, Hoyt McKagen To prevent virus propogation, don't put this addy in your book Belfab CNC - US Best MC - Camping/Caving - Two-Wheel-Tech List - Never trust a fat man |
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Ray Henry
Hi Hoyt
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I can see the "inherent differences in accuracy" issue but let me pose a question based on the assumption that we build Fred's 12" square prototype. In order to do this we would need a 17 inch platter. My math may be all squirreled up so correct this. The distance out to a corner of the 12 inch square should be be about 8.5 inches. That works out to about 53.41 inches around the circumference at that size. (zero diameter tool for outside cutting) Assume that we want 0.0005 for the smallest move at a corner of the square. There should be about 106814 of those arcs. If we select a quadrature encoder or used a stepper motor with gearing/belting sufficient to get that resolution, do you think that the greater accuracy as we approach the center would still cause problems? Ray From: bjammin@... |
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At 10:35 AM 11/5/02 -0600, you wrote:
If we select a quadrature encoder or used a stepper motor withOf course not. But don't you then use up more CPU time calculating? IE, either you compute all the arcs regardless of size or you compute fewer arcs depending on the smaller radii on some parts, which latter involves an additional function. But anyway, the error on polar machine is always going to be greater at extremes of the machine, whereas with Cartesian machine it isn't Much the same applies to hexapods. The error is between two and five times the actuator error, compared to the one times actuator error of Cartesian machine. Regards, Hoyt McKagen To prevent virus propogation, don't put this addy in your book Belfab CNC - US Best MC - Camping/Caving - Two-Wheel-Tech List - Never trust a fat man |
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