I believe Dr. Scholl designed the original sandal carefully, based on a study of the natural barefoot gait.
Later versions, especially in women's styles, diverged somewhat from this ideal.
This shows the finished sandals (a bit dirty; I've been wearing them in the yard).
Total cost: about $25 ($5 for the wood, $20 for a commercial sole). Using an old car tire for the sole might work - I tried, but had trouble cutting the steel belting.
Step 1: The original sandals
Step 2: Preparation
Step 3: Rough cut out
Step 4: Gluing riser
Step 5: Router Jig
Originally, I had intended to make a pantograph , using an electric drill with a rotary rasp, that would allow free movement in three dimensions. But it seemed simpler to adapt a drill press, and make a jig to move the workpiece sideways. This allows movement in two dimensions. The 3D shape is built up in slices, like an analog TV picture. The blank and pattern are screwed to the jig from underneath. This leaves a couple of screw holes in the sandal, but they are covered by the rubber sole.
The drill press is actually an adapter to take an electric drill. It's not very good quality, and I had no qualms about drilling holes in it. I mounted a horizontal bar on the press traveller, and mounted a vertical probe in it, parallel to the drill bit.. When the drill lever is lowered, the probe moves in concert with the drill bit. The thing is not very rigid; you have to stop lowering when you see the probe touch the pattern, not when you feel resistance. The probe certainly won't act as a stop.
For horizontal movement, the wood blank and pattern (old sandal) are mounted on a wooden jig. The horizontal spacing of the blank and pattern matches the spacing of the drill bit and probe. There is a wooden rail clamped to the table to which the press is secured, and spacers fitted to hold the jig level. Thus it is possible to slide the jig horizontally in a straight line by holding it against the rail. The drill bit will trace a line across the blank, while the probe tracks the same path across the pattern.
To carve a parallel track, the rail is unclamped and moved towards the drill. The position of the probe is checked to make sure it traces the same line. The drill press allows the drill to be swung from side to side when a nut is loosened; with this setup, the probe rotates with the drill and moves horizontally. Given the geometry of the clamps and table, it is easier to swing the left end of the rail to move the drill across the workpiece (in reality, move the workpiece across the drill), and to swing the drill to move the probe across the pattern.
The drill is set up with a hemispherical router bit about 1cm diameter. When this is used as a router, sliding the workpiece while keeping the drill depth the same, it will carve a semi-cylindrical slot.
In practice, since the press is not particularly well-made and the jig has only limited constraints on uncontrolled movement, it is easier and safer to use the press as a press - drill a hole, raise the drill, slide the work sideways, then drill another hole
The video shows the steps of lining up the probe and router bit so that they track properly.
Step 6: First cuts with the router
This shows the initial removal of material using the router bit as a drill. There is a vacuum hose set up behind the drill; there is quite a lot of material to remove and it has to end up somewhere.
Another approach would be to use a drill, not a router bit, and make a series of drill holes using the probe to control the depth. That would leave a rectangular blank covered with a grid of small holes. Then use some other method to remove excess wood, such as a hammer and chisel or grinder, stopping when the pilot holes are no longer visible.
SAFETY: Wear eye protection (got my reading glasses); wear ear protection (I did with the grinder,; it's noisy); tie back hair (didn't do that); have a kill switch (yes, but not positioned to be usable); keep hands away from tool (oops!); wear a dust mask and/or control dust (forgot the mask, did have a vacuum); keep workplace tidy (you're kidding, right?)
Step 7: Halfway routed
WARNING - this operation is potentially unsafe. I cut my finger on the router when it caught on the work and pulled the entire jig - work, patter, and my hand - to the left. It can also cut into the work where it is supposed to be higher. The risk can be minimised by 1) making more, smaller cuts 2) moving the work against the direction of blade rotation, not with it. That way if the blade catches it will push the work out away from the blade rather than pulling it in. The problem is that, having made the first slot, you are working on only one side of the blade so there is an unbalanced force. Re-engineering the jig and rail so that the work is mechanically held against the rail would help, as would turning the whole thing into a milling machine by adding a screw drive.
Step 9: Final cut around outline
Step 10: Sanding the upper surface
There is a vacuum set up to one side of the work, with a large funnel to try and catch the dust. It was only partly successful. This sander makes a lot of very fine dust that gets on everything. It would be better to do this outdoors, or in some kind of booth where the dust can be better controlled.
Step 11: Planing the sole
Step 12: Fitting the sole
Step 13: Fitting the strap
That's it, the sandals are finished. I put a bit of sealant stain on the edges; I think if the wood gets wet it contributes to cracking. I should probably sand the top surfaces again and treat it with wood oil; the green colour is grass stain - I was wearing them in long grass.
Step 14: Cross-sections
You can see the original image by clicking the thumbnail, then clicking the [i] icon (top left), then clicking "original image".
These traces were made using the tool shown in the photo. I'm not sure what it's called. This step is not required to make the sandals using the method described earlier, but might be one approach to generating a data file for a milling machine.