As an 18th century reenactor portraying a carpenter with a colonial militia I needed a small saw to make things like tent pegs and chair legs. Not finding anything suitable in antique shops I decided to build one based on paintings and drawings of that era.
Even simple tools of the era were hand made and often had pleasing curved shapes. Straight wood is good for making straight things, but straight things are boring. To make strong curved wooden shapes requires curved wood. So I went to my firewood pile and found a curved piece of seasoned oak. I bought a Jorgensen saw blade from Grizzly and planned out the saw to fit the blade.
I hot glued the log to a piece of thin plywood to give me a flat side to start work from. With my band saw I cut a thick plank from the log, thick enough to make both end pieces of the saw. With a hand plane I finished the plank on both sides.
I drew the profile of one end piece on the plank to match the curve of the wood grain. Then I cut the profile and split the plank to make a matched pair of end pieces. They cleaned up nicely with the hand plane.
Some slots and grooved pins hold the blade to the ends.
Larger saws usually have two thin curved crossbars that brace against each other. But for a saw this small a single crossbar will do. The tenon is tapered so it fits in the mortise with a little play and the ends can pivot as the blade is tightened.
A loop of string is twisted with a small stick to provide tension for the blade.