While looking at the Stirling engine design, I wondered why you needed a cooling piston. Room temperature air should be cool enough. That and if you have a pressure release valve you can release the pressure in the cylinder. So this is my test subject. When heat is applied to the base, the air in the cylinders expands. As one cylinder reaches the top of it's cycle, the hot air and pressure is released. causing the other cylinder to have greater pressure and for it to rise. One concern with this is if the air only has one out, eventually you'll run out of air in the cylinders to cause a difference in pressure. So I added 2 small holes on the inverse side of the release holes, so hopefully the cycle will raise the piston enough to reach here, and as the air is escaping the larger hole hopefully it will be drawn into the smaller.

A perpetual motion machine with magnets that I just thought up. Ok, there are two grooves in the bottom to hold two magnets. One you have north facing up, and the other south facing up. You put a third magnet in the cylinder, and seal it with the cap. Once you know you have the polarities right glue it on there. so the cylinder should rotate, north should meet north moving the magnet to the opposite end of the cylinder, causing it to drop down the other way. South meets south and back the other way it goes. So I hope. Designed to fit this magnet. http://www.kjmagnetics.com/proddetail.asp?prod=ZD6