Your delayed "Geneva" gear makes an excellent object for a simple numeric simulation. Of course, you can still determine the gear's motion analytically but in a computer simulation you may throw in irregularities, changing torque, friction, etc. Good stuff - will have a look at it at the IAM Seminar.
Plus the reciprocating external combustion engine (not the internal combustion one) will make another excellent subject. Especially playing with the dimension of the links and rods that transmit the piston's motion into that of the valve letting in hot gas/vapour and releasing the exhaust would be quite exciting! We can be able to see how lower temperatures of the exhaust result in higher engine power! Didn't think about this as a subject of an exercise - thank you for this.