Here's one for you. I took a Scout Leader training course that they called "Bushcraft". Basically you do everything in the Scout handbook that has to do with camping. So we are not asking the kids to do anything we have not done ourselves. Huge fun! But I digress.
One of our enablers, er facilitators, built this bowsaw whilst we were stopped for lunch on the trail. The string was in his pocket, the blade was inside his belt, the sticks he cut with his knife and whittled the joints. Took him maybe 15 minutes to make the frame. And it works, but I suspect that your first few efforts would fail until you understood the joints and geometry better. I'm sure a good galoot like you can figure it out...
galootcentral.com/components/cpgalbums/userpics/10074/100_5533.JPG