Some trigonometry complications for a simple model
I've run into a peculiar aspect of my code and I don't know if it's my
ignorance of the software or an undocumented (or documented) feature.
Code comments relative to this problem are located at
// bolt thread opening @ 255 degrees (also 15 degrees)
and
// nut recess cut-out @ 255 degrees (also 15 degrees)
This model is a simple ring with three holes spaced around the
circumference. One hole is at 45 degrees absolute and the other two are 120
degrees spaced relative. The problem arose when using the appropriate
absolute values in the code. The placement of the 3.5 mm holes appeared to
be no trouble. The second and third figures should be 15 (135 - 120) and 255
(135 + 120), based on the 135 figure for the recess placed at 45 degrees.
The inner diameter of the ring gets three $fn = 6 cylinders to provide for
nut recesses. The holes, nuts and bolts will provide centering capability of
the ring when mounted to the intended cylinder. The 45 degree nut recess
placement was simple (in my opinion) by using the pythagorean theorem. If
that's incorrect, please advise.
The second and third recesses provide the trouble. Using trigonometry, I was
able to place the solids used in the difference function in what appeared to
be the correct locations under the surface of the inner diameter. Closer
examination and use of the # feature showed the placement to be incorrect.
By increasing the "abitmore" figure for the nut recess depth/thickness in
the ring, I was able to observe the cut at the outer diameter of the ring
begin to chop away asymmetrically from the cylinder place radially at the
same location. The increase of the "abitmore" figure created small triangles
on either side of the circle, increasing in size as the number was adjusted.
By so doing, I discovered that I had to change the rotation angle of the
solid that creates the nut recess by one degree from the figures noted
above. This is not a serious problem, generally speaking, as one degree from
120 isn't going to affect the practical use of the device, but I'd like to
understand and/or avoid this problem should I build a similar model in the
future.
Top image - before +/- 1 change, bottom image - after change.
http://forum.openscad.org/file/n18287/asym_cut_15.png
http://forum.openscad.org/file/n18287/sym_cut_14.png
The synopsis is that my bolt cut-outs are one degree different rotation from
desired. They match the nut solid cut-out rotation angle, also one degree
incorrect, while the trigonometry figures to place the nut solid cut-outs
match the desired figures.
I could have perhaps adjusted the trig figures and left the nut solid
rotations and bolt cut-out rotations with the desired figures, but I expect
that would still place one segment of figures disparate from the others.
What have I done wrong, or what is wrong with OpenSCAD that this works only
when there is a difference of one in the figures?
Please note that I'm not a coding wizard by any means. It's quite a
challenge to keep my models at least moderately parametric, but then again,
I like some challenge in my life! My fillets aren't as parametric as they
could be, I suppose, but that's trivial code in general and not worth the
neurons at this point.
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After forgetting to add the file to my post, I edited it and added the file.
A message appeared to inform me that the changes are not going to be sent to
the mailing list and to reply to the message to correct that. I'm now adding
the same file to this message to ensure it makes it to the list.
line_mount_3nuts.scad
http://forum.openscad.org/file/n18288/line_mount_3nuts.scad
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Please also note that the increases to the "abitmore" figure were done in
each individual location in the code for trouble shooting purposes only. I
don't want the nut-recesses to extend to the outer diameter. The un-modified
code is correct for depth placement.
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Without digging thru your code, may I suggest an approach like this
$fn = 30;
module ring(){
difference(){
cylinder(5,d=30);
translate([0,0,-.1])cylinder(6,d=25);}}
module bolt_hole(deg){
rotate([0,0,deg])
translate([0,-12,2.5])rotate([90,0,0]){cylinder(5,d=1.5);
cylinder(1,d=2.5,$fn=6);}}
difference(){
ring();
bolt_hole(45);
bolt_hole(45+120);
bolt_hole(45-120);}
Larry
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Your suggestion is a good bit simpler than my implementation. I'm likely to
swap out my adjusted code for yours with appropriate values to fit my model.
Perhaps someone with a penchant for self-torture can figure out why I have
to have one degree value change for my code in order to accomplish what I
did.
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On 08/31/2016 03:22 PM, fred_dot_u wrote:
one degree value change for my code
The (automatically set) number of facets around the ring ID isn't a
multiple of three, so the 120° spacing for the nut traps doesn't align
with the facets: one or both sides of each trap will "dig into" a facet.
Setting $fn=8*3 tidies things up a bit.
Then you'll see the difference between a true cylinder and OpenSCAD's
inscribed polygon representation: the ID facets are closer to the center
than the true cylinder's ID, so the points of the nuts don't quite break
through the facets. Turns out the precisely calculated trig position
isn't quite what you want; you must either embiggen the ring ID or move
the nut traps closer to the center to make the answer come out right.
Because you only care about radial position of the nut trap bases
(toward the OD), make the "nuts" twice as tall (toward the ID) as they
are now, so they punch through whatever stands in their way. That takes
care of facet misalignment, inscribed polygon ID, and all that.
When making cutouts, nothing exceeds like excess, at least when there's
nothing you care about standing in the way.
Works for me, anyhow...
--
Ed
softsolder.com
Feel free to adapt my code. That's what it's for.
Since I centered the holes in height (Z axis), if you change both cylinders
in the ring by adding center=true, it will drop the ring so you can see how
the bolt holes interact with the ring.
For more information on inscribed vs circumscribed cylinders see
https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/undersized_circular_objects
When I print objects with holes, I need to fudge them a bit larger than just
making them circumscribed if I actually want a bolt to pass thru.
Larry
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