diff --git a/geometry.scad b/geometry.scad index 6a69e11..b18456f 100644 --- a/geometry.scad +++ b/geometry.scad @@ -472,6 +472,73 @@ function line_from_points(points, fast=false, eps=EPSILON) = // Section: 2D Triangles + +// Function: law_of_cosines() +// Usage: +// C = law_of_cosines(a, b, c); +// c = law_of_cosines(a, b, C); +// Description: +// Applies the Law of Cosines for an arbitrary triangle. +// Given three side lengths, returns the angle in degrees for the corner opposite of the third side. +// Given two side lengths, and the angle between them, returns the length of the third side. +// Figure(2D): +// stroke([[-50,0], [10,60], [50,0]], closed=true); +// color("black") { +// translate([ 33,35]) text(text="a", size=8, halign="center", valign="center"); +// translate([ 0,-6]) text(text="b", size=8, halign="center", valign="center"); +// translate([-22,35]) text(text="c", size=8, halign="center", valign="center"); +// } +// color("blue") { +// translate([-37, 6]) text(text="A", size=8, halign="center", valign="center"); +// translate([ 9,51]) text(text="B", size=8, halign="center", valign="center"); +// translate([ 38, 6]) text(text="C", size=8, halign="center", valign="center"); +// } +// Arguments: +// a = The length of the first side. +// b = The length of the second side. +// c = The length of the third side. +// C = The angle in degrees of the corner opposite of the third side. +function law_of_cosines(a, b, c, C) = + // Triangle Law of Cosines: + // c^2 = a^2 + b^2 - 2*a*b*cos(C) + assert(num_defined([c,C]) == 1, "Must give exactly one of c= or C=.") + is_undef(c) ? sqrt(a*a + b*b - 2*a*b*cos(C)) : + acos(constrain((a*a + b*b - c*c) / (2*a*b), -1, 1)); + + +// Function: law_of_sines() +// Usage: +// B = law_of_sines(a, A, b); +// b = law_of_sines(a, A, B); +// Description: +// Applies the Law of Sines for an arbitrary triangle. +// Given two triangle side lengths and the angle between them, returns the angle of the corner opposite of the second side. +// Given a side length, the opposing angle, and a second angle, returns the length of the side opposite of the second angle. +// Figure(2D): +// stroke([[-50,0], [10,60], [50,0]], closed=true); +// color("black") { +// translate([ 33,35]) text(text="a", size=8, halign="center", valign="center"); +// translate([ 0,-6]) text(text="b", size=8, halign="center", valign="center"); +// translate([-22,35]) text(text="c", size=8, halign="center", valign="center"); +// } +// color("blue") { +// translate([-37, 6]) text(text="A", size=8, halign="center", valign="center"); +// translate([ 9,51]) text(text="B", size=8, halign="center", valign="center"); +// translate([ 38, 6]) text(text="C", size=8, halign="center", valign="center"); +// } +// Arguments: +// a = The length of the first side. +// A = The angle in degrees of the corner opposite of the first side. +// b = The length of the second side. +// B = The angle in degrees of the corner opposite of the second side. +function law_of_sines(a, A, b, B) = + // Triangle Law of Sines: + // a/sin(A) = b/sin(B) = c/sin(C) + assert(num_defined([b,B]) == 1, "Must give exactly one of b= or B=.") + let( r = a/sin(A) ) + is_undef(b) ? r*sin(B) : asin(constrain(b/r, -1, 1)); + + // Function: tri_calc() // Usage: // tri_calc(ang,ang2,adj,opp,hyp); @@ -750,8 +817,8 @@ function adj_opp_to_ang(adj,opp) = function triangle_area(a,b,c) = assert( is_path([a,b,c]), "Invalid points or incompatible dimensions." ) len(a)==3 - ? 0.5*norm(cross(c-a,c-b)) - : 0.5*cross(c-a,c-b); + ? 0.5*norm(cross(c-a,c-b)) + : 0.5*cross(c-a,c-b); @@ -816,7 +883,7 @@ function plane3pt_indexed(points, i1, i2, i3) = function plane_from_normal(normal, pt=[0,0,0]) = assert( is_matrix([normal,pt],2,3) && !approx(norm(normal),0), "Inputs `normal` and `pt` should 3d vectors/points and `normal` cannot be zero." ) - concat(normal, normal*pt)/norm(normal); + concat(normal, normal*pt) / norm(normal); // Function: plane_from_points() diff --git a/involute_gears.scad b/involute_gears.scad index a424eac..ababec9 100644 --- a/involute_gears.scad +++ b/involute_gears.scad @@ -130,12 +130,12 @@ function base_radius(pitch=5, teeth=11, PA=28) = // Usage: // x = bevel_pitch_angle(teeth, mate_teeth, [drive_angle]); // Description: -// Returns the correct pitch angle (bevelang) for a bevel gear with a given number of tooth, that is +// Returns the correct pitch angle for a bevel gear with a given number of tooth, that is // matched to another bevel gear with a (possibly different) number of teeth. // Arguments: // teeth = Number of teeth that this gear has. // mate_teeth = Number of teeth that the matching gear has. -// drive_angle = Angle between the drive shafts of each gear. Usually 90º. +// drive_angle = Angle between the drive shafts of each gear. Default: 90º. function bevel_pitch_angle(teeth, mate_teeth, drive_angle=90) = atan(sin(drive_angle)/((mate_teeth/teeth)+cos(drive_angle))); @@ -160,15 +160,18 @@ function _gear_q7(f,r,b,r2,t,s) = _gear_q6(b,s,t,(1-f)*max(b,r)+f*r2); // // Arguments: // pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. // teeth = Total number of teeth along the rack -// PA = Controls how straight or bulged the tooth sides are. In degrees. +// PA = Pressure Angle. Controls how straight or bulged the tooth sides are. In degrees. // clearance = Gap between top of a tooth on one gear and bottom of valley on a meshing gear (in millimeters) // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle // interior = If true, create a mask for difference()ing from something else. -// valleys = If true, add the valley bottoms on either side of the tooth. +// valleys = If true, add the valley bottoms on either side of the tooth. Default: true +// center = If true, centers the pitch circle of the tooth profile at the origin. Default: false. // Example(2D): // gear_tooth_profile(pitch=5, teeth=20, PA=20); // Example(2D): -// gear_tooth_profile(pitch=5, teeth=20, PA=20, valleys=true); +// gear_tooth_profile(pitch=5, teeth=20, PA=20, valleys=false); +// Example(2D): As a function +// stroke(gear_tooth_profile(pitch=5, teeth=20, PA=20, valleys=false)); function gear_tooth_profile( pitch = 3, teeth = 11, @@ -176,7 +179,8 @@ function gear_tooth_profile( clearance = undef, backlash = 0.0, interior = false, - valleys = true + valleys = true, + center = false ) = let( p = pitch_radius(pitch, teeth), c = outer_radius(pitch, teeth, clearance, interior), @@ -186,23 +190,22 @@ function gear_tooth_profile( k = -_gear_iang(b, p) - t/2/p/PI*180, //angle to where involute meets base circle on each side of tooth kk = r, , , , , , , , ); +// bevel_gear(pitch, teeth, face_width, pitch_angle, , , , , , , , , ); // Description: -// Creates a (potentially spiral) bevel gear. -// The module `bevel_gear()` gives an bevel gear, with reasonable -// defaults for all the parameters. Normally, you should just choose -// the first 4 parameters, and let the rest be default values. The -// module `bevel_gear()` gives a gear in the XY plane, centered on the origin, -// with one tooth centered on the positive Y axis. The various functions -// below it take the same parameters, and return various measurements -// for the gear. The most important is `pitch_radius()`, which tells -// how far apart to space gears that are meshing, and `outer_radius()`, -// which gives the size of the region filled by the gear. A gear has -// a "pitch circle", which is an invisible circle that cuts through -// the middle of each tooth (though not the exact center). In order -// for two gears to mesh, their pitch circles should just touch. So -// the distance between their centers should be `pitch_radius()` for -// one, plus `pitch_radius()` for the other, which gives the radii of -// their pitch circles. -// In order for two gears to mesh, they must have the same `pitch` -// and `PA` parameters. `pitch` gives the number -// of millimeters of arc around the pitch circle covered by one tooth -// and one space between teeth. The `PA` controls how flat or -// bulged the sides of the teeth are. Common values include 14.5 -// degrees and 20 degrees, and occasionally 25. Though I've seen 28 -// recommended for plastic gears. Larger numbers bulge out more, giving -// stronger teeth, so 28 degrees is the default here. -// The ratio of `teeth` for two meshing gears gives how many -// times one will make a full revolution when the the other makes one -// full revolution. If the two numbers are coprime (i.e. are not -// both divisible by the same number greater than 1), then every tooth -// on one gear will meet every tooth on the other, for more even wear. -// So coprime numbers of teeth are good. +// Creates a (potentially spiral) bevel gear. The module `bevel_gear()` gives a bevel gear, with +// reasonable defaults for all the parameters. Normally, you should just choose the first 4 +// parameters, and let the rest be default values. The module `bevel_gear()` gives a gear in the XY +// plane, centered on the origin, with one tooth centered on the positive Y axis. The various +// functions below it take the same parameters, and return various measurements for the gear. The +// most important is `pitch_radius()`, which tells how far apart to space gears that are meshing, +// and `outer_radius()`, which gives the size of the region filled by the gear. A gear has a "pitch +// circle", which is an invisible circle that cuts through the middle of each tooth (though not the +// exact center). In order for two gears to mesh, their pitch circles should just touch. So the +// distance between their centers should be `pitch_radius()` for one, plus `pitch_radius()` for the +// other, which gives the radii of their pitch circles. In order for two gears to mesh, they must +// have the same `pitch` and `PA` parameters. `pitch` gives the number of millimeters of arc around +// the pitch circle covered by one tooth and one space between teeth. The `PA` controls how flat or +// bulged the sides of the teeth are. Common values include 14.5 degrees and 20 degrees, and +// occasionally 25. Though I've seen 28 recommended for plastic gears. Larger numbers bulge out +// more, giving stronger teeth, so 28 degrees is the default here. The ratio of `teeth` for two +// meshing gears gives how many times one will make a full revolution when the the other makes one +// full revolution. If the two numbers are coprime (i.e. are not both divisible by the same number +// greater than 1), then every tooth on one gear will meet every tooth on the other, for more even +// wear. So coprime numbers of teeth are good. // Arguments: // pitch = The circular pitch, or distance between teeth around the pitch circle, in mm. // teeth = Total number of teeth around the entire perimeter @@ -467,139 +462,127 @@ module gear( // PA = Controls how straight or bulged the tooth sides are. In degrees. // clearance = Clearance gap at the bottom of the inter-tooth valleys. // backlash = Gap between two meshing teeth, in the direction along the circumference of the pitch circle -// bevelang = Angle of beveled gear face. -// spiral_rad = Radius of spiral arc for teeth. If 0, then gear will not be spiral. Default: 0 -// spiral_ang = The base angle for spiral teeth. Default: 0 -// slices = Number of vertical layers to divide gear into. Useful for refining gears with `spiral`. -// scale = Scale of top of gear compared to bottom. Useful for making crown gears. +// pitch_angle = Angle of beveled gear face. +// cutter_radius = Radius of spiral arc for teeth. If 0, then gear will not be spiral. Default: 0 +// spiral_angle = The base angle for spiral teeth. Default: 0 +// slices = Number of vertical layers to divide gear into. Useful for refining gears with `spiral`. Default: 1 // interior = If true, create a mask for difference()ing from something else. // anchor = Translate so anchor point is at origin (0,0,0). See [anchor](attachments.scad#anchor). Default: `CENTER` // spin = Rotate this many degrees around the Z axis after anchor. See [spin](attachments.scad#spin). Default: `0` // orient = Vector to rotate top towards, after spin. See [orient](attachments.scad#orient). Default: `UP` +// Extra Anchors: +// "pitchbase" = At the natural height of the pitch radius of the beveled gear. +// "flattop" = At the top of the flat top of the bevel gear. // Example: Beveled Gear -// bevel_gear(pitch=5, teeth=36, face_width=10, shaft_diam=5, spiral_rad=-20, spiral_ang=35, bevelang=45, slices=12, $fa=1, $fs=1); +// bevel_gear(pitch=5, teeth=36, face_width=10, shaft_diam=5, pitch_angle=45, spiral_angle=0); +// Example: Spiral Beveled Gear and Pinion +// t1 = 14; +// t2 = 32; +// a1 = atan(t1/t2); +// a2 = atan(t2/t1); +// down(pitch_radius(5, t1)) +// zrot(180/t2) bevel_gear(pitch=5, teeth=t2, face_width=10, shaft_diam=6, pitch_angle=a2, left_handed=true, slices=8, orient=UP); +// back(pitch_radius(5, t2)) +// bevel_gear(pitch=5, teeth=t1, face_width=10, shaft_diam=6, pitch_angle=a1, slices=8, orient=FWD); module bevel_gear( - pitch = 3, - teeth = 11, - face_width = 6, - bevelang = 45, - shaft_diam = 3, - hide = 0, - PA = 20, - clearance = undef, - backlash = 0.0, - spiral_rad = 0, - spiral_ang = 0, - slices = 2, - interior = false, - anchor = CENTER, - spin = 0, - orient = UP + pitch = 3, + teeth = 11, + face_width = 6, + pitch_angle = 45, + shaft_diam = 3, + hide = 0, + PA = 20, + clearance = undef, + backlash = 0.0, + cutter_radius = 30, + spiral_angle = 35, + left_handed = false, + slices = 1, + interior = false, + anchor = "pitchbase", + spin = 0, + orient = UP ) { - thickness = face_width * cos(bevelang); - slices = spiral_rad==0? 1 : slices; - spiral_rad = spiral_rad==0? 10000 : spiral_rad; - p1 = pitch_radius(pitch, teeth); - r1 = root_radius(pitch, teeth, clearance, interior); - c1 = outer_radius(pitch, teeth, clearance, interior); - dx = thickness * tan(bevelang); - dy = (p1-r1) * sin(bevelang); - scl = (p1-dx)/p1; - p2 = pitch_radius(pitch*scl, teeth); - r2 = root_radius(pitch*scl, teeth, clearance, interior); - c2 = outer_radius(pitch*scl, teeth, clearance, interior); - slice_u = 1/slices; - Rm = (p1+p2)/2; - H = spiral_rad * cos(spiral_ang); - V = Rm - abs(spiral_rad) * sin(spiral_ang); - spiral_cp = [H,V,0]; - S = norm(spiral_cp); - theta_r = acos((S*S+spiral_rad*spiral_rad-p1*p1)/(2*S*spiral_rad)) - acos((S*S+spiral_rad*spiral_rad-p2*p2)/(2*S*spiral_rad)); - theta_ro = acos((S*S+spiral_rad*spiral_rad-p1*p1)/(2*S*spiral_rad)) - acos((S*S+spiral_rad*spiral_rad-Rm*Rm)/(2*S*spiral_rad)); - theta_ri = theta_r - theta_ro; - extent_u = 2*(p2-r2)*tan(bevelang) / thickness; - slice_us = concat( - [for (u = [0:slice_u:1+extent_u]) u] + slices = cutter_radius==0? 1 : slices; + pr = pitch_radius(pitch, teeth); + rr = root_radius(pitch, teeth, clearance, interior); + pitchoff = (pr-rr) * cos(pitch_angle); + ocone_rad = opp_ang_to_hyp(pr, pitch_angle); + icone_rad = ocone_rad - face_width; + cutter_radius = cutter_radius==0? 1000 : cutter_radius; + midpr = (icone_rad + ocone_rad) / 2; + radcp = [0, midpr] + polar_to_xy(cutter_radius, 180+spiral_angle); + angC1 = law_of_cosines(a=cutter_radius, b=norm(radcp), c=ocone_rad); + angC2 = law_of_cosines(a=cutter_radius, b=norm(radcp), c=icone_rad); + radcpang = vang(radcp); + sang = radcpang - (180-angC1); + eang = radcpang - (180-angC2); + slice_us = [for (i=[0:1:slices]) i/slices]; + apts = [for (u=slice_us) radcp + polar_to_xy(cutter_radius, lerp(sang,eang,u))]; + polars = [for (p=apts) [vang(p)-90, norm(p)]]; + profile = gear_tooth_profile( + pitch = pitch, + teeth = teeth, + PA = PA, + clearance = clearance, + backlash = backlash, + interior = interior, + valleys = false, + center = true ); - lsus = len(slice_us); - vertices = concat( - [ - for (u=slice_us, tooth=[0:1:teeth-1]) let( - p = lerp(p1,p2,u), - r = lerp(r1,r2,u), - theta = lerp(-theta_ro, theta_ri, u), - profile = gear_tooth_profile( - pitch = pitch*(p/p1), - teeth = teeth, - PA = PA, - clearance = clearance, - backlash = backlash, - interior = interior, - valleys = false - ), - pp = rot(theta, cp=spiral_cp, p=[0,Rm,0]), - ang = atan2(pp.y,pp.x)-90, - pts = apply_list( - path3d(profile), [ - move([0,-p,0]), - rot([0,ang,0]), - rot([bevelang,0,0]), - move(pp), - rot(tooth*360/teeth), - move([0,0,thickness*u]) - ] - ) - ) each pts - ], [ - [0,0,-dy], [0,0,thickness] + verts1 = [ + for (polar=polars) [ + let( + u = polar.y / ocone_rad, + m = up((1-u) * pr / tan(pitch_angle)) * + up(2*pitchoff) * + zrot(polar.x/sin(pitch_angle)) * + back(u * pr) * + xrot(pitch_angle) * + scale(u) + ) + for (tooth=[0:1:teeth-1]) + each apply(xflip() * zrot(360*tooth/teeth) * m, path3d(profile)) ] - ); - lcnt = (len(vertices)-2)/lsus/teeth; - function _gv(layer,tooth,i) = ((layer*teeth)+(tooth%teeth))*lcnt+(i%lcnt); - function _lv(layer,i) = layer*teeth*lcnt+(i%(teeth*lcnt)); - faces = concat( - [ - for (sl=[0:1:lsus-2], i=[0:1:lcnt*teeth-1]) each [ - [_lv(sl,i), _lv(sl+1,i), _lv(sl,i+1)], - [_lv(sl+1,i), _lv(sl+1,i+1), _lv(sl,i+1)] - ] - ], [ - for (tooth=[0:1:teeth-1], i=[0:1:lcnt/2-1]) each [ - [_gv(0,tooth,i), _gv(0,tooth,i+1), _gv(0,tooth,lcnt-1-(i+1))], - [_gv(0,tooth,i), _gv(0,tooth,lcnt-1-(i+1)), _gv(0,tooth,lcnt-1-i)], - [_gv(lsus-1,tooth,i), _gv(lsus-1,tooth,lcnt-1-(i+1)), _gv(lsus-1,tooth,i+1)], - [_gv(lsus-1,tooth,i), _gv(lsus-1,tooth,lcnt-1-i), _gv(lsus-1,tooth,lcnt-1-(i+1))], - ] - ], [ - for (tooth=[0:1:teeth-1]) each [ - [len(vertices)-2, _gv(0,tooth,0), _gv(0,tooth,lcnt-1)], - [len(vertices)-2, _gv(0,tooth,lcnt-1), _gv(0,tooth+1,0)], - [len(vertices)-1, _gv(lsus-1,tooth,lcnt-1), _gv(lsus-1,tooth,0)], - [len(vertices)-1, _gv(lsus-1,tooth+1,0), _gv(lsus-1,tooth,lcnt-1)], - ] + ]; + thickness = abs(verts1[0][0].z - select(verts1,-1)[0].z); + vertices = [for (x=verts1) down(thickness/2, p=reverse(x))]; + sides_vnf = vnf_vertex_array(vertices, caps=false, col_wrap=true, reverse=true); + top_verts = select(vertices,-1); + bot_verts = select(vertices,0); + gear_pts = len(top_verts); + face_pts = gear_pts / teeth; + top_faces =[ + for (i=[0:1:teeth-1], j=[0:1:(face_pts/2)-1]) each [ + [i*face_pts+j, (i+1)*face_pts-j-1, (i+1)*face_pts-j-2], + [i*face_pts+j, (i+1)*face_pts-j-2, i*face_pts+j+1] + ], + for (i=[0:1:teeth-1]) each [ + [gear_pts, (i+1)*face_pts-1, i*face_pts], + [gear_pts, ((i+1)%teeth)*face_pts, (i+1)*face_pts-1] ] - ); - attachable(anchor,spin,orient, r1=p1, r2=p2, l=thickness) { - union() { - difference() { - down(thickness/2) { - polyhedron(points=vertices, faces=faces, convexity=floor(teeth/2)); - } - if (shaft_diam > 0) { - cylinder(h=2*thickness+1, r=shaft_diam/2, center=true, $fn=max(12,segs(shaft_diam/2))); - } - if (bevelang != 0) { - h = (c1-r1)/tan(45); - down(thickness/2+dy) { - difference() { - cube([2*c1/cos(45),2*c1/cos(45),2*h], center=true); - cylinder(h=h, r1=r1-0.5, r2=c1-0.5, center=false, $fn=teeth*4); - } - } - up(thickness/2-0.01) { - cylinder(h=(c2-r2)/tan(45)*5, r1=r2-0.5, r2=lerp(r2-0.5,c2-0.5,5), center=false, $fn=teeth*4); - } - } + ]; + vnf1 = vnf_merge([ + [ + [each top_verts, [0,0,top_verts[0].z]], + top_faces + ], + [ + [each bot_verts, [0,0,bot_verts[0].z]], + [for (x=top_faces) reverse(x)] + ], + sides_vnf + ]); + vnf = left_handed? vnf1 : xflip(p=vnf1); + anchors = [ + anchorpt("pitchbase", [0,0,pitchoff-thickness/2]), + anchorpt("flattop", [0,0,thickness/2]) + ]; + attachable(anchor,spin,orient, vnf=vnf, extent=true, anchors=anchors) { + difference() { + vnf_polyhedron(vnf, convexity=teeth); + if (shaft_diam > 0) { + cylinder(h=2*thickness+1, r=shaft_diam/2, center=true, $fn=max(12,segs(shaft_diam/2))); } } children(); diff --git a/version.scad b/version.scad index 23b052c..a3c5e94 100644 --- a/version.scad +++ b/version.scad @@ -8,7 +8,7 @@ ////////////////////////////////////////////////////////////////////// -BOSL_VERSION = [2,0,447]; +BOSL_VERSION = [2,0,448]; // Section: BOSL Library Version Functions