Thread.py

import cadquery as cq
from cadquery import *
from math import *

def helix(r0,r_eps,p,h,d=0,frac=1e-1):
    
    def func(t):
        
        if t>frac and t<1-frac:
            z = h*t + d
            r = r0+r_eps
        elif t<=frac:
            z = h*t + d*sin(pi/2 *t/frac)
            r = r0 + r_eps*sin(pi/2 *t/frac)
        else:
            z = h*t - d*sin(2*pi - pi/2*(1-t)/frac)
            r = r0 - r_eps*sin(2*pi - pi/2*(1-t)/frac)
            
        x = r*sin(-2*pi/(p/h)*t)
        y = r*cos(2*pi/(p/h)*t)
        
        return x,y,z
    
    return func

def thread(radius, pitch, height, d, radius_eps, aspect= 10):
    
    e1_bottom = (cq.Workplane("XY")
        .parametricCurve(helix(radius,0,pitch,height,-d)).val()
    )
    e1_top = (cq.Workplane("XY")
        .parametricCurve(helix(radius,0,pitch,height,d)).val()
    )
    
    e2_bottom = (cq.Workplane("XY")
        .parametricCurve(helix(radius,radius_eps,pitch,height,-d/aspect)).val()
    )
    e2_top = (cq.Workplane("XY")
        .parametricCurve(helix(radius,radius_eps,pitch,height,d/aspect)).val()
    )
    
    f1 = Face.makeRuledSurface(e1_bottom, e1_top)
    f2 = Face.makeRuledSurface(e2_bottom, e2_top)
    f3 = Face.makeRuledSurface(e1_bottom, e2_bottom)
    f4 = Face.makeRuledSurface(e1_top, e2_top)
    
    sh = Shell.makeShell([f1,f2,f3,f4])
    rv = Solid.makeSolid(sh)
    
    return rv

radius = 4
pitch = 2
height = 4
d = pitch/4
radius_eps = 0.5
eps=1e-3

core = cq.Workplane("XY",origin=(0,0,-d)).circle(4).circle(3).extrude(height+1.75*d)
th1 = thread(radius-eps,pitch,height,d,radius_eps)
th2  =thread(radius-1+eps,pitch,height,d,-radius_eps)

res = core.union(Compound.makeCompound([th1,th2]))

show_object(res)