1-Rail sweep, with a sine wave rail

I want to create a surface that uses a profile of a picture frame molding. But the rail is not a straight line (or even a simple curve). The rail has a shape like a sine wave. What the result will be is a picture frame molding that has a typical cross section of a molding one would use for a picture frame. But, the difference is that there is a ‘ripple’ pattern along the length of the molding.

My problem is that the cross section profile rotates forward and backward along the path of the rail to keep it perpendicular to the rail at each point. However, what I want instead is for the profile to stay perfectly vertical. That is, it should shift up and down as it follows the rail rather than rotating to stay perpendicular to it. If the profile is drawn on the Y-Z plane and the rail is drawn on the X-Z plane, then the profile at each point in the X direction should always be perpendicular to the X axis (staying parallel to the Y-Z plane).
I don’t see any way to do this in Rhino. Any suggestions I might try?

Try ExtrudeCrvAlongCrv

Perfect! That was just what I was looking for. Thanks.

The Sweep commands swing the profile curves as the rails change direction. The initial orientation between the Profile and the Rail(s) are maintained.

The Extrude commands keep the profile curves in a fixed orientation without regard for what the rail does.

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Only true with Sweep1 if the Refit rail option is selected. Otherwise the resulting surface will be simpler but only an approximation to the orientation of the section to rail being maintained.

All generalizations are false, including this one.