Making a catapult with your kids, for your kids to use and play with isn't as hard as you think. The key is to simplify and work on a smaller scale..
Find a medium-sized, heavy block of wood. A wooden box would be perfect, just make sure it is heavy enough that it won't tip when weight is added to its top. This will be the base for your catapult.
Nail or screw two length of 1-by-4 wood, to two opposite sides of the box or block. Make making sure they are equal in length and longer than the base.
Drill a hole at the top end of each 1-by-4 that is big enough for your dowel to fit through and rotate smoothly.
Cut your dowel to 1/2 inch beyond both sides of the uprights and insert into the holes.
Glue small blocks on the ends of the dowel to prevent it from slipping out of the uprights.
Drill a small hole through the middle of the dowel, centered lengthwise, through which you will insert a smaller dowel to serve as the launching arm.
Slide in the smaller dowel. The dowel should be long enough so one end touches the base with at least half extending above the large dowel. Glue the smaller dowel.
Fasten the bottom of a small plastic cup to the upper end of the small dowel with hot glue.
Secure a hook screw to the original larger dowel -- just in front of where the small dowel goes through, then another directly opposite at the front base of the foundational box.
Take a rubber band and loop it around each hook to add tension.
Launch your catapult. Place a small object in your cup and pull the arm back, away from the hook on the base of the box, so it pulls tight. Then let go.
Empty plastic yogurt containers make effective catapult cups. The more rubber bands you add, the greater your tension and the power of your catapult.
Do not launch items directly at anyone's face. Use caution with power tools.