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joiners.scad
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@ -1224,7 +1224,7 @@ module rabbit_clip(type, length, width, snap, thickness, depth, compression=0.1
// Module: hirth()
// Usage:
// hirth(n, ir|id=, or|od=, tooth_angle, [cone_angle=], [chamfer=], [rounding=], [base=], [crop=], [anchor=], [spin=], [orient=]
// hirth(n, ir|id=, or|od=, tooth_angle, [cone_angle=], [chamfer=], [base=], [crop=], [anchor=], [spin=], [orient=]
// Description:
// Create a Hirth face spline. The Hirth face spline is a joint that locks together two cylinders using radially
// positioned triangular teeth on the ends of the cylinders. If the joint is held together (e.g. with a screw) then
@ -1256,29 +1256,22 @@ module rabbit_clip(type, length, width, snap, thickness, depth, compression=0.1
// or/od = outer radius or diameter
// tooth_angle = nominal tooth angle. Default: 60
// cone_angle = raise or lower the angle of the teeth in the radial direction. Default: 0
// chamfer = chamfer teeth by this fraction at tips and half this fraction at valleys. Default: 0
// roudning = round the teeth by this fraction at the tips, and half this fraction at valleys. Default: 0
// chamfer = chamfer teeth by this fraction at tips and half this fraction at valleys. Default: 0.05
// base = add base of this height to the bottom. Default: 1
// crop = crop to a cylindrical shape. Default: false
// anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#subsection-anchor). Default: `CENTER`
// spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#subsection-spin). Default: `0`
// orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#subsection-orient). Default: `UP`
// Example: Basic uncropped hirth spline
// hirth(32,20,50);
// hirth(32,20,50, tooth_angle=60,chamfer=.05);
// Example: Raise cone angle
// hirth(32,20,50,cone_angle=30);
// hirth(32,20,50, tooth_angle=60,cone_angle=30,chamfer=.05);
// Example: Lower cone angle
// hirth(32,20,50,cone_angle=-30);
// Example: Adding a large base
// hirth(20,20,50,base=20);
// Example: Only 8 teeth, with chamfering
// hirth(8,20,50,tooth_angle=60,base=10,chamfer=.1);
// hirth(32,20,50, tooth_angle=60,cone_angle=-30,chamfer=.05);
// Example: Only 8 teeth
// hirth(8,20,50, tooth_angle=60,base=10,chamfer=.05);
// Example: Only 8 teeth, cropped
// hirth(8,20,50,tooth_angle=60,base=10,chamfer=.1, crop=true);
// Example: Only 8 teeth, with rounding
// hirth(8,20,50,tooth_angle=60,base=10,rounding=.1);
// Example: Only 8 teeth, different tooth angle, cropping with $fn to crop cylinder aligned with teeth
// hirth(8,20,50,tooth_angle=90,base=10,rounding=.05,crop=true,$fn=48);
// hirth(8,20,50, tooth_angle=60,base=10,chamfer=.05, crop=true);
// Example: Two identical parts joined together (with 1 unit offset to reveal the joint line). With odd tooth count you can use the CENTER anchor for the child and the teeth line up correctly.
// hirth(27,20,50, tooth_angle=60,base=2,chamfer=.05)
// up(1) attach(CENTER,CENTER)
@ -1288,83 +1281,102 @@ module rabbit_clip(type, length, width, snap, thickness, depth, compression=0.1
// up(1) attach(CENTER,"mate")
// hirth(26,20,50, tooth_angle=60,base=2,cone_angle=-30, chamfer=.05);
module hirth(n, ir, or, id, od, tooth_angle=60, cone_angle=0, chamfer, rounding, base=1, crop=false, orient,anchor,spin)
module hirth(n, ir, or, id, od, tooth_angle=60, cone_angle=0, chamfer=0.05, base=1, crop=false, orient,anchor,spin)
{
ir = get_radius(r=ir,d=id);
or = get_radius(r=or,d=od);
dummy = assert(all_positive([ir]), "ir/id must be a positive value")
assert(all_positive([or]), "or/od must be a positive value")
assert(is_int(n) && n>1, "n must be an integer larger than 1")
assert(ir<or, "inside radius (ir/id) must be smaller than outside radius (or/od)")
assert(all_positive([tooth_angle]) && tooth_angle<360*(n-1)/2/n, str("tooth angle must be between 0 and ",360*(n-1)/2/n," for spline with ",n," teeth."))
assert(num_defined([chamfer,rounding]) <=1, "Cannot define both chamfer and rounding")
assert(is_undef(chamfer) || all_nonnegative([chamfer]) && chamfer<1/2, "chamfer must be a non-negative value smaller than 1/2")
assert(is_undef(rounding) || all_nonnegative([rounding]) && rounding<1/2, "rounding must be a non-negative value smaller than 1/2")
assert(all_nonnegative([chamfer]) && chamfer<1/2, "chamfer must be a non-negative value smaller than 1/2")
assert(all_positive([base]), "base must be a positive value") ;
tooth_height = sin(180/n) / tan(tooth_angle/2); // Normalized tooth height
conic_ht = tan(cone_angle); // Normalized height change corresponding to the cone angle
ridge_angle = atan(tooth_height/2 + conic_ht);
valley_angle = atan(-tooth_height/2 + conic_ht);
angle = 180/n; // Half the angle occupied by each tooth going around the circle
factor = crop ? 3 : 1; // Make it oversized when crop is true
factor = crop ? 2/cos(cone_angle) : 1;
// inner/outer radius to the side face of the end of a tooth profile, adjusted to provide excess for making the shape round at the end
ir_side = ir/factor*cos(180/n);
or_side = or*factor*cos(180/n);
outside_halfseg = or_side*2*tan(90/n); // Side length of 2n-gon
outside_botseg = or_side*2*tan(180/n); // Side length of n-gon
// Decrease in outer radius needed for the triangles to touch each other around the edge
delta = or_side*(1 - 2*outside_halfseg/outside_botseg);
tooth_height = 0.5/tan(tooth_angle/2); // Unscaled tooth height (for tooth with width 1)
h = tooth_height * 2*outside_halfseg; // Scaled tooth height
lean = asin(2*delta/h); // Angle at which triangle needs to tilt for valid joint
profile = is_undef(rounding) || rounding==0 ?
let(
chamfer=default(chamfer,0),
vchamf = chamfer*(ridge_angle-valley_angle),
pts = [
[-angle*(1-chamfer/2), valley_angle+vchamf/2],
[-angle*chamfer, ridge_angle-vchamf]
]
)
concat(pts, reverse(xflip(pts)))
: let( f=echo(dround=rounding),
vround=rounding*(ridge_angle-valley_angle),
profpts = [
[ -angle, valley_angle+vround/2],
[ -angle*(1-rounding/2), valley_angle+vround/2],
[ -angle*rounding, ridge_angle-vround],
[ 0, ridge_angle-vround]
],
// Using computed values for the joints lead to round-off error issues
joints = [(profpts[1]-profpts[0]).x, (profpts[3]-profpts[2]).x],
segs = max(16,segs(or*rounding)),
rpts = round_corners(profpts, joint=joints,closed=false,$fn=segs)
)
concat(rpts, reverse(xflip(select(rpts,1,-2))));
// project spherical coordinate point onto cylinder of radius r
cyl_proj = function (r,theta_phi)
[for(pt=theta_phi)
let(xyz = spherical_to_xyz(1,pt[0], 90-pt[1]))
r * xyz / norm(point2d(xyz))];
[0,-1/2+chamfer/4,(-1/2+chamfer/2)*tooth_height],
[0,-chamfer/2,(1/2-chamfer)*tooth_height]
];
profile = concat(profpts, reverse(yflip(profpts)));
bottom = min([tan(valley_angle)*ir,tan(valley_angle)*or])-base;
safebottom = min([tan(valley_angle)*ir/factor,tan(valley_angle)*or*factor])-base-(crop?1:0);
trans_prof = function(R,data)
let(halfseg = R*2*tan(90/n))
yrot(cone_angle,right(R, 2*halfseg*cos(cone_angle)*yrot(lean-cone_angle,data)));
topinner = [for(ang=lerpn(0,360,n,endpoint=false))
each zrot(ang,cyl_proj(ir/factor,profile))];
topouter = [for(ang=lerpn(0,360,n,endpoint=false))
each zrot(ang,cyl_proj(factor*or,profile))];
// used to get top ridge line range
topspan = [
trans_prof(ir_side, [0,1/2,tooth_height/2]),
trans_prof(or_side, [0,1/2,tooth_height/2])
];
// For uncropped case we scale to match user's desired radius exactly
real_or = topspan[1].x;
real_ir = topspan[0].x;
scale = crop ? 1 : or/real_or;
echo(scaled_ir=real_ir*scale);
// used to get true bottom at true target radius; has the endpoints of the bottom valley without chamfer/rounding
botspan = zrot(-180/n, [
trans_prof(ir_side, [0,1/2,-tooth_height/2]),
trans_prof(or_side, [0,1/2,-tooth_height/2])
]);
// Bottom guaranteed to be lower than anything in the polyhedron so it doesn't self-intersect
safebottom = min(column(botspan,2))-base/scale-(crop?1:0);
// Actual bottom interpolated at the specified ir/or
bottom = crop ? let(bottab = submatrix(botspan, [0,1], [0,2]))
min(lookup(ir,bottab), lookup(or,bottab))-base/scale
: safebottom;
// Vertical correction for cone angle so that center of the joint is at the origin
zshift = crop ? sin(cone_angle)*or : sin(cone_angle)*real_or;
topouter = [for(ang=lerpn(0,360,n,endpoint=false)) each zrot(ang,trans_prof(or_side, profile))];
topinner = [for(ang=lerpn(0,360,n,endpoint=false)) each zrot(ang,trans_prof(ir_side, profile))];
botinner = [for(val=topinner) [val.x,val.y,safebottom]];
botouter = [for(val=topouter) [val.x,val.y,safebottom]];
vert = [topouter, topinner, botinner, botouter];
anchors = [
named_anchor("teeth_bot", [0,0,bottom], DOWN),
named_anchor("teeth_bot", [0,0,(bottom+zshift)*scale+base], DOWN),
named_anchor("mate", [0,0,0], UP, spin=n%2==0 ? 180/n : 0)
];
attachable(anchor=anchor,spin=spin,orient=orient, r=or, h=-2*bottom,anchors=anchors){
attachable(anchor=anchor,spin=spin,orient=orient, r=or, h=-2*(bottom+zshift)*scale,anchors=anchors){
scale(scale)
up(zshift){
zrot_copies(n=n)
stroke(trans_prof(or_side,profile),color="red", closed=false,width=.01);
intersection(){
vnf_polyhedron(vnf_vertex_array(vert, reverse=true, col_wrap=true, row_wrap=true),convexity=min(10,n));
vnf_polyhedron(vnf_vertex_array(vert, reverse=true, col_wrap=true, row_wrap=true),convexity=20);
if (crop)
zmove(bottom)tube(or=or,ir=ir,height=4*or,anchor=BOT);
}
}
children();
}
}
}