Using blender, in File->user prefernces->Add-ons->Add Mesh->Add Mesh: Extra Objects
While Drawing Add->Mesh->Math Fuction->XYZ Math Surface
pinion
x=a*cos(6.28*(v)-c)
y=a*sin(6.28*(v)-c)
z=h*u
u=0-1 step 1
v=0-1 step 12
a=sqrt(2.25+(0.25*h*h*u*u)) -- 1.5 is inner radius of small hyperboloid
b=0
c=atan((0.5*h*u)/1.5) -- atan(2) for large and complementary 90-atan(2) is atan(0.5)
f=0
g=0
h=10 -- double height

crown
x=a*cos(6.28*(v)-c)
y=a*sin(6.28*(v)-c)
z=h*u
u=0-1 step 1
v=0-1 step 12
a=sqrt(9+(4*h*h*u*u)) -- 3 is inner radius of large hyperboloid
b=0
c=atan((2*h*u)/3) -- atan(2) angle for hyperboloid
f=0
g=0
h=5