First of all there is a competition that take place every year in the province of Quebec for students of the Cegep (a level between high school and university specific to the province of Quebec) called "Science on tourne". Last year we had to make a machine to calculate time. I mean that the machine had to make 2 electric contacts with a predetermined time between those 2 contacts. The one who was closer to the time we had to do was the winner. To do so we were only allowed using mechanical energy such as springs, gravity, gas and similar power sources. This year they have a completely new goal (as every year). We must build an independent cart that will go through a half circular pattern as fast as possible and then take a tennis ball and swing it up in a box about 2 meter away. I started a brainstorm on my side to find any possible way to achieve this. I divided the problem in 2 parts. The first one is to get the cart up to the other side so I need a propulsion system and a steering system. I have to tell you that we are only allowed to take 1 action on the cart to start it up at the beginning and then it must be independent. Here the idea I had about the way to move it up.
Propulsion
1- Use a air tank, a regulator and a pneumatic motor. The problem with this one is that the wheel will turn too fast and they will just slip from the surface.
2- Use an heavy object attached with a steel wire to one of the shafts attached to the wheels. It's at the moment the best propulsion methods that I found but it will be probably kinda slow... Maybe a heavier mass would make it faster but it will also give more inertia to the cart itself so I'll have to make some test to see if it's a good idea.
Direction
As I have a circular pattern to follow I tough to use 2 wheels of different size to keep it turning. I would use bigger wheels on the outside to get it turning the right way. I'll calculate the size with the travel they will have to do (travel of the outsides wheel/travel of the inside wheel)
Now I come to the last and hardest part. I must find a way to tap, slap or catch and throw a tennis ball 2 meter away. I tough about using a mass attaching at a pole that would swing down like on a ballista. The pole would hit the ball or hit something that would throw out the ball.
Here is a link to a adobe document that show how the cart has to travel and how are placed the boxes at the end of the trip (dimensions are in centimetre) http://sot.bdeb.qc.ca/pdf/airedejeu.pdf
I may translate specific rules to get it more specific to you but what I would like would be some feedback such as other way I may had forgot to achieve the things I described. I hope I was clear enough Feel free to make any suggestion even if they seem strange to you.