Your challenge is to build a physical incarnation of three fundamental components of digital logic: an AND gate, an OR gate, and a NOT gate. Bring them to class and be prepared to explain how to interpret inputs, outputs, true, false, and the operation of the mechanism. There are many different ways to proceed, and they are all good. Be as creative as you like or just build your own implementation of something you see below. If you have a specific idea you want to run by me, I would be happy to help.
One of my personal favorite designs uses mechanical linkages and includes a list of many other sources of inspiration, which I have also incorporated here. Another impressive set of linkage gates can be found, with videos and a simulated adder, on Xiaoji's design blog. I also found an excellent academic paper on linkage gates, and another one by the same authors on microflexural gates.
Another project uses Legos, and gets as far as an adder, a flip flop, and clocked logic, and then does it all over again with rotational rather than push-pull interpretations of bits. Another set of Lego gates comes from CMU. Here's a Lego XOR gate. This universal gate can be easily reconfigured to represent AND, NAND, OR, NOR, XOR, or XNOR.
Nanotechnology is one of the main application areas of mechanical logic, and there is an article that presents two ideas in that vein.
If you have the ability and the resources, you might play with 3D printing. Here's a 3D-printed AND gate.
This one doesn't come with a lot of explanation, but it seems to be a sliding paper-and-wire NAND gate.
Some very esoteric possibilities are out there, from the eye computer to the use of live crabs.
Of course, by analogy with the flow of electricity, there's the flow of water. Or you could follow the same analogy by learning about how gates are normally built from transistors, and find some way to build a mechanical transistor.
And, last but not least, there are pulleys and weights. Or, if you prefer, pulleys with springs. One of the best-known physical interpretations of digital logic comes from a Scientific America article from April Fool's Day 1988, describing the pulley logic of the fictional Apraphulian culture.
Remember, these were written for a variety of different audiences. If some of them seem too hard or too easy for you, think about who the author was targetting and get out of it what you can. In particular, one of the most important lessons I ever learned was not to be afraid of material that seemed too technical—it usually turns out to have a simple lesson hidden behind what seemed hard, and, particularly when you have help (me!), you can dig out that simple lesson and use it.
Most of all, have fun! Your job isn't to impress me or understand every resource I've thrown at you, it's to get an intimate understanding of logic gates.