After a little research and reading of the forums i decided that i liked the 12 ft top beam as a way to improve the overall accuracy of the machine without resorting to a tensioning system. Having said that I’ve been unable to find any info on what changes to make to the placement/ length of the bungee cords and amount to lengthen the chain (i ordered some more chain which just arrived today)
Here is a screen shot of a simple drawing of the frame showing the length of the chain of a standard frame from the motor to the farthest corner in red and in yellow the is the length of chain on a12 ft top beam that is 24 inches above the top of the cutting area.
Obviously the ring radius isn’t accounted for but it will have negligible impacton the difference between the 2 chain lengths. Considering we’re working with chains i think rounding to the nearest inch is good enough and that difference is about 15 inches. So my plan at the moment is to add that much chain to each side. Is there a reason this wont work?
Regarding the stretchy cord i plan to move the outer attachment point inboard 6 inches and the pulleys in the middle out about 6 inches to makeup for the length in the top beam. Again are the considerations here that I’m unaware of? Anything else i need to be aware of?
play around with the spreadsheet before you decide how much you want to raise the top beam
it really is as simple as you think it is, but you may also want to look at the weight based tension option instead of the stretchy cord.
at 12’, you need about 12.5’ of chain because you need to be able to measure between the motors, so the chain needs to be able to go over both motors (this is actually slightly longer than you need for the angle you are showing)
Ok so add a minimum of 18 inches of chain to each side. As far as height goes my basement ceiling is the limiting factor and although i could conceivably go maybe 2 inches higher i risk scraping motors on the joists when i move it if I did that, and although I haven’t looked at the spreadsheet (or looked for it for that matter) i get the impression that with a 12 ft top beam you don’t want to go lower or you’ll have issues with cutting in the upper middle area.
This is correct, your diagram looked like you were making the top beam
significantly higher than stock
If you look at the spreadsheet and compare stock to 12’ top beam, you will see
the tension on the chains change significantly (going up both in the bottom
corner and at the top center, faster in the bottom corners), raising the beam
higher will lower the chain tension (lowering it faster in the top center than
the bottom corner)
by playing around with the top beam length and the top beam height, you can look
to find the best position (or at least see what the numbers are so if the
resulting machine has problems, you can adjust it and try again)
When considering the height of the motors above the work piece, consider the stiffness of the kinematics equations. Raising the beam reduces this stiffness; it makes the calibration easier and more accurate. At the top-center of the work piece, very small changes in chain length result in large sled movement. This makes the system more sensitive to measurement inaccuracies, and difficult to calibrate. Within the range we are discussing (top-beam distance to top of work sheet), I think increasing this height will directly translate to easier and more accurate calibrations. Of course, there are diminishing returns in addition to physical size constraints.
For the tensioning system for the slack chain, I bought a roll of 1/8 shock cord. I stretched it all the way from one side of the beam to the other, then back. The cords from the two sides cross each other twice. Once on the way out, and once on the way back to connect to the chain. I feel this is a very good solution. I haven’t tried the 3/16 shock cord.
The bigger factor is the chain angles.
As the chain angle gets closer to horizontal (the top center of the workpiece),
less of the tension on the chain translates into vertical force to oppose
gravity (and the more the two motors have to pull against each other to have the
horizontal forces cancel while the vertical forces match the weight of the sled)
making the top beam longer hurts a bit here
you go from a triangle that’s 60" horzontally and 18" vertically (a ratio of
3.33 and angle of 17 degrees from horizontal) to 72" horizontally and 18"
vertically (a ratio of 4 and angle of 14 degrees from horizontal)
raise the top beam 6" (24 from the top of the workpiece) and the ratio is 3.37
or 15 degrees.
As the chain angle gets closer to vertical (the near bottom corner of the
workpiece) the more of the tension on the chain translates into vertical force
to oppose gravity (and the less tension is left to either move the sled
horizontally or to oppose the tension from the other motor). Since the other
chain is at a much shallower angle, the tension on this other chain has to be
MUCH less to have everything balance.
making the top beam longer helps a huge amount here.
you go from a triangle that’s 12" horizontally and 64" vertically (a ratio of
5.22, angle of 79 degrees from horizontal) to one that’s 24" horizontally and
64" vertically (a ratio of 2.6, and angle of 69 degrees from horizontal)
raise the top beam 6" and the ratio is 2.91 and the angle 71 degrees
Which spreadsheet is this?
I’m currently in the middle of designing my frame and need to figure out my top beam dimensions and placement based off a working area of 2400 x 1200mm and a bed size of 2700 x 1500mm