Re: [OpenSCAD] how to make the groove more width?
I'm not sure what you're trying to do (can't see the original message on my
phone) but it may be that minkowski would help? I'm thinking something like
difference your original from a bounding cube to get a female mould. Then
minkowski the female mould to expand it, and difference that from the
original.
Frank
On 19/01/2017 04:30, "Parkinbot" rudolf@parkinbot.com wrote:
I guess you want the groove to keep its shape independently of the twist
angle. This is not so easy to do, because need a /proper/ helix object for
difference. There is some threading code out there (e.g. Thingiverse) to do
this.
With some limitation it can also be created by linear_extrude(), but it
needs an ellipse that exactly compensates the angle introduced by the twist.
The following code introduces an operator doing this and rewrites your code
partly for proper application
$fn= 30;
h = 60;
OR = 12;
r = .5;
g = OR;
tw = 720; // use negative value for CCW
N=4;
slot();
module slot(groove = true){
difference()
{
cylinder(h,r=OR,center=true);
if(groove){
for(w=[0:N-1])
linear_extrude(height=h+.1, center=true, convexity=2, twist=tw)
rotate([0, 0, w*360/N])
translate([g, 0, 0])
groove_shape(h, tw, OR, r) circle(r=r);
}
}
}
module groove_shape(h=1, twist=0, R, r) // operator module
{
U = R2PI;
x = U/360*twist;
a = atan(x/h);
f = a==0?1:tan(a)/sin(a);
scale([1, f])
children();
}
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From my understanding, Parkinbot's post is the solution to your question.
It's also a good demo or making a spring, I believe.
$ Runsun Pan, PhD $ libs: doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), synwrite ( 2 ); $ tips: Collection of tips on github
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As I wrote the approach is limited. For to do springs, it needs more.
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2017-01-19 11:30 GMT-02:00 Parkinbot rudolf@parkinbot.com:
As I wrote the approach is limited. For to do springs, it needs more.
Would you elaborate on that? I don't see any way to get a circular
transversal section from a linear_extrude.
Ronaldo wrote
Would you elaborate on that?
As long as nobody provides a definition for "side tracking a thread" I'll
try.
An ellipse is just an approximation of the proper shape. It can be used to
carve grooves as in the example, but ... you name it. It lacks a radial
transformation and thus gets worse with growing twist/height ratio.
But if you take a perfect spring object and calculate a 2D shape from it,
using projection(cut=true), you will obviously get a shape so that
linear_extrude() does what you want. Of course in a practical sense there
are restrictions.
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Ronaldo, this is your linear_extrude circle with radial transformation. As I
said it gets worse with the ratio growing. The transformation is non-affine,
so you can't express it with multmatrix.
R=12;
h=100;
r = 2;
twist = 720;
linear_extrude(height = h, twist = twist, slices = 200)
polygon(groove_circle(R, r, twist, h));
function groove_circle(R=30, r=7, twist, h) =
let(a = atan(2RPI/360twist/h),
f = a==0?1:tan(a)/sin(a)) // factor
[for(i=[0:10:359])
let(v=[rsin(i)+R, frcos(i)])
let(n2 = sqrt(v[0]*v[0]+v[1]*v[1])) // radial transformation
(R+v[0])*v/n2];
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Thanks, Rudolf. You saved me the trouble of checking your helical
projections.
I have tried some changes in your code and observed that the helix section
is poor when the number of points in the circle is drastically reduced to 3
or 4 points, that means when the section is a triangle or square instead of
a circle. Then I realized that I should finely resample the polygon
(triangle or square) to get a better helical projection. And that is enough
to correct the helix section shape. That is the code I have used:
function groove_triangle(R=30, r=7, twist, h) =
let(// a = atan(2RPI/360twist/h),
// f = a==0?1:tan(a)/sin(a)) // factor
f = h==0? 1: norm([2RPI/360twist,h])/h) // factor
/* [for(i=[0:120:359])
let(v=[rsin(i+90)+R, frcos(i+90)])
let(n2 = sqrt(v[0]v[0]+v[1]v[1])) // radial transformation
(R+v[0])v/n2];/
let(v = [for(i=[0:120:359]) [rsin(i+90)+R, frcos(i+90)]])
[ for(i=[0:2], j=[0:9])
let( w = v[i]*(10-j)/10+v[(i+1)%3]*j/10 )
let(n2 = norm(w)) // radial transformation
(R+w[0])*w/n2];
Thank you to point me out that linear_extrude twist could be properly used
to sweep any shape along a helical path.
BTW, I have changed your computation of the f factor to a simpler
expression without trigs.
2017-01-19 23:55 GMT-02:00 Parkinbot rudolf@parkinbot.com:
Ronaldo, this is your linear_extrude circle with radial transformation. As
I
said it gets worse with the ratio growing. The transformation is
non-affine,
so you can't express it with multmatrix.
R=12;
h=100;
r = 2;
twist = 720;
linear_extrude(height = h, twist = twist, slices = 200)
polygon(groove_circle(R, r, twist, h));
function groove_circle(R=30, r=7, twist, h) =
let(a = atan(2RPI/360twist/h),
f = a==0?1:tan(a)/sin(a)) // factor
[for(i=[0:10:359])
let(v=[rsin(i)+R, frcos(i)])
let(n2 = sqrt(v[0]*v[0]+v[1]*v[1])) // radial transformation
(R+v[0])*v/n2];
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Ronaldo,
thanks for going through my code, your optimizations and hints. Yes, it is
no surprise that a non-affine projection can/will transform lines into
curves. In the given case the x-dimension has to go through a circular
projection to get the job done. So the solution needs a skilled hammerer and
special nails - and is obviously beyond the scope of native OpenSCAD.
Which "helical projections" do you mean? The gears are already in radial
form and my springs and coils lib doesn't use this weired approach. Of
course, a proper sweep() (or hull() discretisation) over an orthogonally
oriented extrusion shape is the best approach.
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I have called "helical projection" what you call circular projection.
But your skilled hammer, as any other tool, has its own limitation. It
doesn't reproduce a sweep for lower h values. Neither even two giants,
Newton and Einstein, created tools for all scales.
2017-01-20 15:42 GMT-02:00 Parkinbot rudolf@parkinbot.com:
Ronaldo,
thanks for going through my code, your optimizations and hints. Yes, it is
no surprise that a non-affine projection can/will transform lines into
curves. In the given case the x-dimension has to go through a circular
projection to get the job done. So the solution needs a skilled hammerer
and
special nails - and is obviously beyond the scope of native OpenSCAD.
Which "helical projections" do you mean? The gears are already in radial
form and my springs and coils lib doesn't use this weired approach. Of
course, a proper sweep() (or hull() discretisation) over an orthogonally
oriented extrusion shape is the best approach.
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Parkinbot wrote
... As I said it gets worse with the ratio growing.
What ratio did you infer to ? Can't figure it out from your code.
$ Runsun Pan, PhD $ libs: doctest , faces ( git ), offline doc ( git ), runscad.py ( 2 , git ), synwrite ( 2 ); $ tips: Collection of tips on github
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