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function norm(vector) = sqrt(vector[0]*vector[0]+vector[1]*vector[1]+vector[2]*vector[2]);
function unitVector(vector) = vector / norm ( vector );
function barycenter(vector1, vector2, ratio) = (vector1*ratio + vector2*(1-ratio) );
module slice(
AShaftBottom,
AShaftTop,
BShaftBottom,
BShaftTop,
ABottom,
ATop,
BBottom,
BTop,
AThreadDepth,
AThreadRatio=0.5,
AThreadPosition=0.5,
AThreadAngle=20,
BThreadDepth,
BThreadRatio=0.5,
BThreadPosition=0.5,
BThreadAngle=20,
showVertices=false
)
{
polyPoints=[
AShaftBottom,
AShaftTop,
ATop,
barycenter(ATop,ABottom,AThreadPosition+AThreadRatio/2) + unitVector(ATop-ABottom)*AThreadDepth/2*tan(AThreadAngle),
barycenter(ATop,ABottom,AThreadPosition+AThreadRatio/2) - unitVector(ATop-ABottom)*AThreadDepth/2*tan(AThreadAngle) + unitVector(ATop-AShaftTop)*AThreadDepth,
barycenter(ATop,ABottom,AThreadPosition),
barycenter(ATop,ABottom,AThreadPosition-AThreadRatio/2) + unitVector(ATop-ABottom)*AThreadDepth/2*tan(AThreadAngle) + unitVector(ATop-AShaftTop)*AThreadDepth,
barycenter(ATop,ABottom,AThreadPosition-AThreadRatio/2) - unitVector(ATop-ABottom)*AThreadDepth/2*tan(AThreadAngle),
ABottom,
BTop,
barycenter(BTop,BBottom,BThreadPosition+BThreadRatio/2) + unitVector(BTop-BBottom)*BThreadDepth/2*tan(BThreadAngle),
barycenter(BTop,BBottom,BThreadPosition+BThreadRatio/2) - unitVector(BTop-BBottom)*BThreadDepth/2*tan(BThreadAngle) + unitVector(BTop-BShaftTop)*BThreadDepth,
barycenter(BTop,BBottom,BThreadPosition),
barycenter(BTop,BBottom,BThreadPosition-BThreadRatio/2) + unitVector(BTop-BBottom)*BThreadDepth/2*tan(BThreadAngle) + unitVector(BTop-BShaftTop)*BThreadDepth,
barycenter(BTop,BBottom,BThreadPosition-BThreadRatio/2) - unitVector(BTop-BBottom)*BThreadDepth/2*tan(BThreadAngle),
BBottom,
BShaftBottom,
BShaftTop
];
polyTriangles=[
[ 0,1,5], [1,2,3], [1,3,5], [0,5,7], [0,7,8], //A side of shaft
[1,0,12], [1,10,9], [1,12,10], [0,14,12], [0,15,14], // B side of shaft
[0,8,15], // bottom of shaft
[1,9,2], // top of shaft
[3,2,10], [2,9,10], [4,3,10], [10,11,4], // top of thread
[6,4,11], [11,13,6], // tip of thread
[7,6,13], [13,14,7], [8,7,14], [14,15,8], // bottom of thread
[3,4,5], [5,4,6], [5,6,7], // A side of thread
[11,10,12], [11,12,13], [12,14,13] // B side of thread
];
if (showVertices==true) for (i=[0:15]) translate(polyPoints[i]) color([1,0.5,0.5]) cube(0.25,true);
polyhedron( polyPoints, polyTriangles );
}
module trapezoidThread(
length=45, // axial length of the threaded rod
pitch=10, // axial distance from crest to crest
pitchRadius=10, // radial distance from center to mid-profile
threadHeightToPitch=0.5, // ratio between the height of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
profileRatio=0.5, // ratio between the lengths of the raised part of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
threadAngle=30, // angle between the two faces of the thread
// std value for Acme is 29 or for metric lead screw is 30
RH=true, // true/false the thread winds clockwise looking along shaft, i.e.follows the Right Hand Rule
clearance=0.1, // radial clearance, normalized to thread height
backlash=0.1, // axial clearance, normalized to pitch
stepsPerTurn=24, // number of slices to create per turn,
showVertices=false
)
{
numberTurns=length/pitch-1;
steps=stepsPerTurn*numberTurns;
startLength=0.25; // number of turns for profile to reach full height
function profileRatio(i)= profileRatio*(1-backlash);
function threadAngle(i)= threadAngle;
function threadPosition(i)= ( profileRatio(i) + threadHeightToPitch*(1+clearance)*tan( threadAngle(i) ) )/2;
function threadHeight(i)= pitch*threadHeightToPitch*(1+clearance);
function pitchRadius(i)= pitchRadius;
function minorRadius(i)= pitchRadius(i)-(0.5+clearance)*pitch*threadHeightToPitch;
function ShaftX(i)= 0;
function ShaftY(i)= 0;
function ShaftZ(i)= pitch*numberTurns*i;
function X(i)= ShaftX(i)+minorRadius(i)*cos(i*360*numberTurns);
function Y(i)= ShaftY(i)+minorRadius(i)*sin(i*360*numberTurns);
function Z(i)= ShaftZ(i);
if (RH==true)
for (i=[0:steps-1])
{
slice(
AShaftBottom= [ShaftX(i/steps), ShaftY(i/steps), ShaftZ(i/steps) ],
AShaftTop= [ShaftX((i+stepsPerTurn)/steps), ShaftY((i+stepsPerTurn)/steps), ShaftZ((i+stepsPerTurn)/steps) ],
BShaftBottom= [ShaftX((i+1)/steps), ShaftY((i+1)/steps), ShaftZ((i+1)/steps) ],
BShaftTop= [ShaftX((i+1+stepsPerTurn)/steps), ShaftY((i+1+stepsPerTurn)/steps), ShaftZ((i+1+stepsPerTurn)/steps) ],
ABottom= [X(i/steps), Y(i/steps), Z(i/steps) ],
ATop= [X((i+stepsPerTurn)/steps), Y((i+stepsPerTurn)/steps), Z((i+stepsPerTurn)/steps) ],
BBottom= [X((i+1)/steps), Y((i+1)/steps), Z((i+1)/steps) ],
BTop= [X((i+1+stepsPerTurn)/steps), Y((i+1+stepsPerTurn)/steps), Z((i+1+stepsPerTurn)/steps) ],
AThreadDepth= min(min(i,steps-i)/stepsPerTurn/startLength,1)*threadHeight(i),
AThreadRatio= min(min(i,steps-i)/stepsPerTurn/startLength,1)*profileRatio(i),
AThreadPosition= threadPosition(i),
AThreadAngle= threadAngle(i),
BThreadDepth= min(min(i+1,steps-i-1)/stepsPerTurn/startLength,1)*threadHeight(i+1),
BThreadRatio= min(min(i+1,steps-i-1)/stepsPerTurn/startLength,1)*profileRatio(i+1),
BThreadPosition= threadPosition(i),
BThreadAngle= threadAngle(i+1),
showVertices=showVertices
);
}
if (RH==false)
mirror([0,1,0])
for (i=[0:steps-1])
{
slice(
AShaftBottom= [ShaftX(i/steps), ShaftY(i/steps), ShaftZ(i/steps) ],
AShaftTop= [ShaftX((i+stepsPerTurn)/steps), ShaftY((i+stepsPerTurn)/steps), ShaftZ((i+stepsPerTurn)/steps) ],
BShaftBottom= [ShaftX((i+1)/steps), ShaftY((i+1)/steps), ShaftZ((i+1)/steps) ],
BShaftTop= [ShaftX((i+1+stepsPerTurn)/steps), ShaftY((i+1+stepsPerTurn)/steps), ShaftZ((i+1+stepsPerTurn)/steps) ],
ABottom= [X(i/steps), Y(i/steps), Z(i/steps) ],
ATop= [X((i+stepsPerTurn)/steps), Y((i+stepsPerTurn)/steps), Z((i+stepsPerTurn)/steps) ],
BBottom= [X((i+1)/steps), Y((i+1)/steps), Z((i+1)/steps) ],
BTop= [X((i+1+stepsPerTurn)/steps), Y((i+1+stepsPerTurn)/steps), Z((i+1+stepsPerTurn)/steps) ],
AThreadDepth= min(min(i,steps-i)/stepsPerTurn/startLength,1)*threadHeight(i),
AThreadRatio= min(min(i,steps-i)/stepsPerTurn/startLength,1)*profileRatio(i),
AThreadPosition= threadPosition(i),
AThreadAngle= threadAngle(i),
BThreadDepth= min(min(i+1,steps-i-1)/stepsPerTurn/startLength,1)*threadHeight(i+1),
BThreadRatio= min(min(i+1,steps-i-1)/stepsPerTurn/startLength,1)*profileRatio(i+1),
BThreadPosition= threadPosition(i),
BThreadAngle= threadAngle(i+1),
showVertices=showVertices
);
}
rotate([0,0,180/stepsPerTurn])
cylinder(
h=pitch,
r1=0.999*pitchRadius-(0.5+clearance)*pitch*threadHeightToPitch,
r2=0.999*pitchRadius-(0.5+clearance)*pitch*threadHeightToPitch,$fn=stepsPerTurn);
translate([0,0,length-pitch])
rotate([0,0,180/stepsPerTurn])
cylinder(
h=pitch,
r1=0.999*pitchRadius-(0.5+clearance)*pitch*threadHeightToPitch,
r2=0.999*pitchRadius-(0.5+clearance)*pitch*threadHeightToPitch,$fn=stepsPerTurn);
}
module trapezoidThreadNegativeSpace(
length=45, // axial length of the threaded rod
pitch=10, // axial distance from crest to crest
pitchRadius=10, // radial distance from center to mid-profile
threadHeightToPitch=0.5, // ratio between the height of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
profileRatio=0.5, // ratio between the lengths of the raised part of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
threadAngle=30, // angle between the two faces of the thread
// std value for Acme is 29 or for metric lead screw is 30
RH=true, // true/false the thread winds clockwise looking along shaft, i.e.follows the Right Hand Rule
countersunk=0, // depth of 45 degree chamfered entries, normalized to pitch
clearance=0.1, // radial clearance, normalized to thread height
backlash=0.1, // axial clearance, normalized to pitch
stepsPerTurn=24 // number of slices to create per turn
)
{
translate([0,0,-countersunk*pitch])
cylinder(
h=2*countersunk*pitch,
r2=pitchRadius+clearance*pitch+0.25*pitch,
r1=pitchRadius+clearance*pitch+0.25*pitch+2*countersunk*pitch,
$fn=24
);
translate([0,0,countersunk*pitch])
translate([0,0,-pitch])
trapezoidThread(
length=length+2*pitch, // axial length of the threaded rod
pitch=pitch, // axial distance from crest to crest
pitchRadius=pitchRadius+clearance*pitch, // radial distance from center to mid-profile
threadHeightToPitch=threadHeightToPitch, // ratio between the height of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
profileRatio=profileRatio, // ratio between the lengths of the raised part of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
threadAngle=threadAngle, // angle between the two faces of the thread
// std value for Acme is 29 or for metric lead screw is 30
RH=RH, // true/false the thread winds clockwise looking along shaft
// i.e.follows Right Hand Rule
clearance=-clearance, // radial clearance, normalized to thread height
backlash=-backlash, // axial clearance, normalized to pitch
stepsPerTurn=stepsPerTurn // number of slices to create per turn
);
translate([0,0,length-countersunk*pitch])
cylinder(
h=2*countersunk*pitch,
r1=pitchRadius+clearance*pitch+0.25*pitch,
r2=pitchRadius+clearance*pitch+0.25*pitch+2*countersunk*pitch,$fn=24,
$fn=24
);
}
module trapezoidNut(
length=45, // axial length of the threaded rod
radius=25, // outer radius of the nut
pitch=10, // axial distance from crest to crest
pitchRadius=10, // radial distance from center to mid-profile
threadHeightToPitch=0.5, // ratio between the height of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
profileRatio=0.5, // ratio between the lengths of the raised part of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
threadAngle=30, // angle between the two faces of the thread
// std value for Acme is 29 or for metric lead screw is 30
RH=true, // true/false the thread winds clockwise looking along shaft, i.e.follows the Right Hand Rule
countersunk=0, // depth of 45 degree chamfered entries, normalized to pitch
clearance=0.1, // radial clearance, normalized to thread height
backlash=0.1, // axial clearance, normalized to pitch
stepsPerTurn=24 // number of slices to create per turn
)
{
difference()
{
cylinder(
h=length,
r1=radius,
r2=radius,
$fn=6
);
trapezoidThreadNegativeSpace(
length=length, // axial length of the threaded rod
pitch=pitch, // axial distance from crest to crest
pitchRadius=pitchRadius, // radial distance from center to mid-profile
threadHeightToPitch=threadHeightToPitch, // ratio between the height of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
profileRatio=profileRatio, // ratio between the lengths of the raised part of the profile and the pitch
// std value for Acme or metric lead screw is 0.5
threadAngle=threadAngle, // angle between the two faces of the thread
// std value for Acme is 29 or for metric lead screw is 30
RH=true, // true/false the thread winds clockwise looking along shaft
// i.e.follows Right Hand Rule
countersunk=countersunk, // depth of 45 degree countersunk entries, normalized to pitch
clearance=clearance, // radial clearance, normalized to thread height
backlash=backlash, // axial clearance, normalized to pitch
stepsPerTurn=stepsPerTurn // number of slices to create per turn
);
}
}