My sister asked me if I would be interested in repairing the back of a barstool.  The stool is metal but has (had) a piece of wood molding on the back.  Somehow the wood was broken off on one of the stools.  Unfortunately she didn't keep the broken pieces so I could assess whether it could be fixed so I was stuck with making a new one.  Fortunately, she had a second chair with an intact rail on it that I could look at for inspiration.  She would have been perfectly fine if I had cut a 2x4 into a matching arc, stained it and attached the chair but that would be too easy.  Instead I decided to see if I could mimic the shape of the old rail. 
 

I probably could have come up with a simpler profile that I could cutout with my band saw and profile on my router table but that is no fun.   Instead I decided to see if I could do this with my CNC machine.  You know...the hard way.  

The software I have for design and creating tool paths for my CNC is Vectric VCarve Pro.  It is good for creating 2D designs but not great for 3D design.  I explored ways to create a similar shape with just 2D paths and profile bits but decided that would be too easy too.  

While Vcarve has no 3D design tools, you have to upgrade to their Aspire product for that, it can import 3D objects to carve with 3D toolpaths so I all really need is to create a STL file that can be imported.  I turned to OnShape for this and with its parametric design paradigm, it turned out to be fairly simple. 

The first step was sketching an arc that matched the back of the chair.  I determined the (approximate) radius of the arc by measuring the width (cord of the arc) and the height of the arc from the cord.  Onshape makes this easy and it calculates the resulting radii. 

I printed a full scale drawing to see if it fit the arc of the chair back.  It was close but it was easy to adjust height dimension in Onshape until I got it to match.  Note that the second arc is the center line of the bottom of the chair where the screw holes are.  I measured the distance between the different holes and using constraints figure out where they will go when I later mill them on the CNC.  These were added later to Vcarve for drilling on the CNC with 2D tool paths and not part of the 3D design. 

The next step was to sketch out the profile in Onshape.  It did not need to be an exact match but I used the measurements noted to get close enough. 

Note that I only need the curved molding at the top.  The rectangular area at the bottom of the sketch will be cut with simple 2D tool paths and not exported as a STL. The last step was to sweep the profile along the arc and you have a 3D shape.   Only the gray rounded top will be exported as a STL file and imported into Vcarve.

The STL file is imported into Vcarve

Because of the shape has undercut areas, this 3D shape must be milled from both sides.  The bottom has a flat area so this is the area that is milled first.  If I milled the top first the curved surface would make holding it while doing the bottom difficult.  You can see the various tool paths created for the bottom in the lower right hand corner of the above screen shot.    The first toolpath is for aligning the workpiece to make sure that I can fit the entire profile within the workpiece.  You will see in later steps why this is important.  The 2 leveling paths are for insuring that the bottom is perfectly flat.  I had to do this because the drive belt on my planer broke when I tried to send my blank through it.  The rough profile removes excess wood with a 1/2" end mill to avoid stressing the 1/4" end mill used for the 3D carving.  The alignment holes are the holes used to join the profile and the simpler base together with dowels and also provide alignment holes that match the dowels on the spoil board so that it is perfectly oriented when I flip it over.  The holes also match where the threaded inserts will be added in the base to screw the piece to the chair back.  Simulation so far:

Next step is 3D roughing. This removes the bulk of material so that the later 3D finishing pass is removing as little material as possible with the ball nose end mill.

And 3D finishing pass:

The piece is then flipped over and mounted to the spoilboard with double sided tape using the alignment holes to position it. 
3D Roughing

3D Finishing.

Next was creating the tool paths for the base.  These were drawn using the shape of the bottom of the 3D model to define the path vectors.

The alignment holes were also created here using the dimensions laid out in Onshape and following a curve down the middle of the shape.  The same holes were used to drill the alignment holes for dowels in the spoil board.  This would have been easier if Vcarve used a parametric paradigm like Onshape does.  It took some tweaking to get them space out properly.

I used the same leveling tool path that was used on the top molding to ensure it was level and the rest was simply a matter of creating a profile toolpath.

Note that I cut half of the profile from each side and the alignment holes are also cut into both sides.  The opposite side toolpaths are identical, though the holes are not symmetrically spaced so they are flipped on the other side.  Vcarve does the flipping for you for two sided projects by mirroring to the other side when you copy them there.  

BTW, I actually started this project almost a year ago.   The first prototype milled from a 2x4 actually milled up great but didn't quite match the arc as well as I wanted so I had to go back to Onshape to modify it.  When I recreated the tool paths with the new STL shape I had some issues with my second prototype toolpaths.  I got disgusted and set it aside for about 9 months and just started working on it again a couple of weeks ago.  

Next up will be prepping the wood and showing some of the milling steps.