Here's one I built earlier! Much earlier, something like 25 years ago.
In the haze of time I am not 100% sure what motivated me to build this up. I guess I had a fondness for Bantams as I was riding around on a plunger D1 at the time plus I had a few parts lying around and someone I knew had a rigid D1 frame for sale. Apparently back in the day it was fairly popular to transplant a Villiers engine into a Bantam - I only found this out after building the bike.
The 6E Villiers motor had been used in a scrambler and was a known runner. To fit it in to the Bantam frame the original lugs were cut off the frame and three horseshoe shaped clamps were brazed on in appropriate places - two for the front mount and one for the rear. These were then joined across with pipe. Engine plates were cut from ally plate and made to give the engine a slightly forward facing cant to look nice and racy. The frame lugs were narrower than the engine mount spacing, this meant that it was fairly easy to get chain line right with spacers either side of the lugs. The frame was gusseted around the headstock to cope with the extra power!
The rear wheel came from a later Bantam, forks and front wheel were an autojumble find from a Bantam race bike (Honda originally I believe). Cast off alloy guards were used and brackets made up. The exhaust was from a BSA A65 and thankfully it fitted and gave a nice mid-level line. All in it only cost a little more than £100 to buy the parts needed for the project.
Rather amazingly the bike was a lot more than the sum of its parts. It would hold 70mph (I was lighter then!) and was a lot of fun. It lived outside my flat in London for a while and was taken around Brands Hatch when the Festival of 1000 Bikes was held there. Eventually I sold it on to a mate when I realised I had too many bikes (in particular Bantams - there were three at the time). He kept it for a while and then sold it on to another friend. It's been off the road a while now but is still in decent nick and ready to go.