Here is a simple DIY desktop catapult you can make with just a few hours and some easy-to-get materials. In the video I used mortise and tenon joinery but you can get good results with just glue and brad nails.

Step 1: Making the Catapult

Tools

Table or Hand Saw
Drill

Materials

Oak or other hard wood
Rubber Band
Short Twine or small rope
Metal Latch release or gate release
3/16” metal rod
3/8” metal rod or 3/8” oak dowel

Cut List

Base – 5 x 1 3/8 x 8 ½” Oak, mahogany or laminate any wood together
Boom, Catapult Arm – 12 x ¾ x ¾”, you could also go ½” square for a smaller machine
2 Long Post – 5 ¾ x ¾ x ¾”
2 Short Angle 3 x ¾ x ¾”
2 Long Angle 5 ¾ x ¾ x ¾”

Method

Cut the 2 long posts square and glue to the base, use some screws or brad nails to secure. Cut the 2 long angles and 2 short angles at 45 degrees and attach to the long posts on the base. Use brad nails or screws with glue for the best result. You can always add additional support if needed.

For the rubber band, just use a common office version and for the cup either buy a thick piece of lumber or laminate thinner pieces together. Drill out a 1 ½” bowl and screw to the boom/arm.