I have included an instructional video and a step-by-step photo instructable. If you have any questions or any of these instructions are unclear to you please let me know and I will try to clearify.
I think this instructable meets the requirements of the Epilog challenge and the Launch it! contest so I am entering it in those.
Step 1: Gather Materials
-A 2x4 in any type of wood, prefer few defects of course (at least 27" long)
-1/2" Sch 40 PVC pipe (at least 22" long)
-Red oak 1x2 (53" or more, other hardwoods are OK)
-A 1/2" x 5.5" x 48" poplar board
-3/8" poplar dowels (recommend three 48" dowels)
-5/16" dowel (at least 10")
-Larger dowel, 3/4" to 1" diameter (at least 6" long)
-hot glue stick
-String (I used 9/16" venetian blind chord, it is mixed polymers)
-Two 1/4-20 bolts, 3" long, with nuts.
-Wood screws (at least 6, ones that are 2"-3" long would be great)
-Spray on clear coat
-Brown spray paint
-1.5" wide hinge
-1.5" wide by 1/4" thick oak or poplar board (10")
All of that is available at a hardware store, mine was from Lowes mostly.
Step 2: Look at the Plans:
I don't think any more instruction is needed for this step unless the plans are unclear to you (they look fine to me but let me know if there is an issue).
Step 3: Cut the Parts
Step 4: The Arrow Box
Sand the bottom edge of the front magazine spacer ("L" shaped one) so it is rounded concave. Then line up the magazine walls and spacers and glue them together (see pictures for position if it is not obvious to you). Clamp these together or stack weights on them while the glue dries. Once it is dry, sand it so all the layers line up smoothly without rough or uneven edges.
Then mark the lines shown in picture 6 on the arrow trough. There is one line going crossways on the board 12" back from the front (the end without the 1/4" hole is the front), and a line down the center from the front all the way back to the 12" line. Carve grooves along those lines with a dremmel sanding wheel. The front-to-back line is the trough the arrows ride in, and the side to side line is a notch that catches the bow string.
Glue the arrow trough on to the bottom of the magazine walls.
Cut or sand a 5/16 or 3/8" dowel in half lengthwise, so it is flat on one side. Cut about 10" of it and glue that 10" piece to the bottom of the arrow trough. Position it so it starts at the front edge of the arrow trough, is running lengthwise centered side to side.
Step 5: The Lever
Step 6: The Stock
Step 7: The Bow
Once you have done that squirt some hot glue into both ends of the pipe, this will be a filler. Heat the 3" long sections on both ends of the pipe (one at a time) and press them as shown in picture 6. The end of the pipe should be completely closed after this pressing. Be sure that when you press it the pipe is rotated so that the part that was wider from being pressed between the 2x4s is the part that becomes flat.
Heat the center 1.5" wide section of the pipe and bend the bow limbs (each half of the pipe) slightly back and upward.
Then cut / sand the now flattened limb tips into a roughly parabolic shape and smooth out the edges with sand paper. File a notch into the limb tips for the string to catch on (called knocks). Drill holes and screw the bow into the notch in the stock.
For the string, just tie a loop in each end and make it so it looks just on the long side of the right length. Tie knots in the string to shorten it one at a time. Keep putting it on the bow to check if it's tight.
**To heat the pipe I am using a propane heater but you can use a torch, a heat gun, an electric or gas stovetop, camp fire, bbq, etc. Try to move the pipe around a lot in the heat to keep from scorching it. It will become soft and flexible.
Step 8: The Ammo
Then drill a hole in the other end of each one (drill press is much nicer for this than a hand drill). The exact size of the hole will depend on your arrow points. The arrow point is suppose to glue in to this hole. I used a 13/64" bit for mine. After you have the holes drilled epoxy in the arrow points. You may want to sand the area where dowel and point meet after gluing depending on how well the sizes match up.
Step 9: Finish
Set the magazine on the stock, slip the lever over that and line up the holes, and put the bolts through (you don't need to put on the nuts right now). Then string the bow and push the lever forward until it catches in the notch in the arrow trough. Pull the lever back. You will immediately notice that it does NOT fire. Don't worry I haven't mislead you. Let the lever forward and push the string out of the notch with your thumbs. Now all you need to do to finish the mechanism is to sand the front edges of the notch (the one the string catches in) to smooth and round it off. Keep doing the test with the lever until you get it sanded smooth enough to where it does fire. Now it's done!
At this point I chose to stain and clearcoat the wood parts and paint the bow brown. Obviously you can decorate yours however you want. After you have done whatever surface treatments you are going to do, it is a good idea to put vegitable oil on the center of the bow string to help it slide easier and not wear through as fast.