Model parabolic helix

[detandj]

I would like to model a helix curve that follows a paraboloid (shape of a reflector).

I tried to make a helix, but only arrive at making a linearly varying helix (following a cone).

 

[dgallup]

Assuming you used the helical sweep function, when you sketch the profile of the trajectory, draw a parabola instead of a straight line.

 

[cadcamguy]

you can create a curve by equation with

x=t
y=0
z=t^2

basic reflector shape


then use that curve to create a revolved surface

create another curve by equation ... a flat spiral

r=.25+t*.75
theta=360*t*7
z=0

project that curve to the surface

you can use the projected curve for a sweep or vss

you can offset the revved surface to allow for your section

 

[jeff4136]

Guess this is a little late to help the OP
(took a bit of review and head scratching)
but, fwiw, to add to ...

A non-rational degree 2 bezier describes a precise
parabolic curve. A Sketcher Conic Arc entity with
rho = 0.5 is that curve.

(It might be worthwhile to review the definition
of 'rho'. It is the ratio of distances ...
chord to a parallel line tangent to the curve
divided by chord to tangent vector intersection.)

System tolerance b-spline approximations of
parabolic curves with monotone rate (maximum
curvature at one end) can be created using
the equations
x = t, y = t^2 or x = t, y = t^(1/2)

The equations
r = t^(1/2), theta = 360 * turns * t, z = t
will create a helical curve tracing the form
of a parabolic revolute.

The attached (WF2) might help connect the dots.

-Jeff Howard (wf2)
Sure it's true. I saw it on the internet.