help modelling a curved back rest

[prettygoodnotbad]

I'm trying to model a part which sort of throwing me for a loop.

It's a back rest for a chair which starts from the arm rest and curves around the back. It changes width along the way with the very back being wider then the thickness of the armrests at the front.

This is what I have so far:

 

It was done by first sketching out the U shape then extruding it, then sketching out the profile of the "wave" and intersecting it with my U extrusion. The thing is that this gives me a result that isn't exactly what I want but I'm not sure exactly how to approach or even explain what it is I'm trying to achieve. Basically what bugs me is how the first curve at the bottom as you go up the "wave" where the back gets wider doesn't follow the curve of the "U"

Below is an attempt at a sketch of what I'm trying to do, the pink being what I would like. Essentially so the curve goes around the U in a more natural way, rather then cut out right through with the intersect method. The thing is that I've been racking my brain over this for a few hours and have no clue how I would make this work.

I've also attached an f3d of this file if need be

[davebYYPCU · Accepted solution]

Move the Timeline to before the second extrude,

Modify Sketch 2 to be the cutter, 

Create a 3d sketch, Project to Surface, the ramp in Sketch 2, with Along Vector

Sweep, (cut).

Might help....

[TrippyLighting]

Fo product design including furniture design it would serve you well if you familiarize yourself with the tools in the Patch environment.

[TheCADWhisperer]

Make use of obvious symmetry about the Origin.

Using symmetry about the Origin will pay dividends throughout the design process.