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Background Pony #51D0
@Squishment
Close. The engine also turns a magneto, a little tiny generator, that provides current for the spark plug so it can produce its spark and ignite the fuel.

To be a bit more specific. When the piston is near the top of its space inside the cylinder, the fuel goes in and becomes a fuel-air mixture. The spark plug ignites the fuel-air mixture at that moment. The fuel burns, a chemical reaction where the fuel breaks down, oxygen is absorbed, and the mixture of chemicals that makes up the exhaust is produced. It is also at this moment, at this instant, that the potential energy in the fuel is released. The burning fuel transfers its energy to the air and exhaust mixture inside the cylinder, creating a great increase in pressure that pushes equally in all directions. The energized gases push the piston downward with great force and it slides down, away from the spark plug. This is the instant where chemical energy is translated into the motion of mechanical parts, where chemical energy becomes mechanical energy. And the piston is connected to a rod that pushes on the crankshaft, turning the motion of the piston into torque and rotating the crankshaft.

The engine goes through this cycle over and over many times a second while it is running. Fuel is pumped into the cylinder, the inertia of the rotating crankshaft moves the piston up and compresses the air and fuel mixture, the spark ignites it, moving the piston back down. Round and round it goes until it no longer gets fuel or a spark. Putt putt putt putt.

If you look at the percentage of the chemical energy released by burning the fuel that gets turned into mechanical energy as measured at the crankshaft, it's not terribly efficient, but for power-to-weight ratio, nothing beats it. This is why airliners don't have steam engines or electric motors. Four stroke engines are much more efficient than two stroke engines but they're also bigger, heavier, and much more mechanically complex.
Background Pony #68E40

@Background Pony #51D0
Had to watch a video to try wrapping my head around what you've said.
Air goes in through an intake port, piston goes to the top, spark plug ignites and pushes it downwards, the compressed air goes through some kind of tunnel that leads to the exhaust port and fuel comes out and that somehow creates energy that makes the chain rotate right?

To answer your question, yes that was what I was going for.
Background Pony #51D0
@Squishment
They're not horribly complex. Single-cylinder two-stroke engine. Driveshaft has a sprocket on the end with teeth like a gear. Engine runs, sprocket turns, cutting chain has one end wrapped around the sprocket so it moves the chain. There may be controls like a throttle and a safety bar you have to hold down while it's running. There may be some kind of clutch or transmission so that if the chain jams it doesn't destroy the engine. But that's the general gist of it. An electric chainsaw—there are such things, though I don't know how practical they are—is the same with a different powerplant.

I guess this one has a hopper you put magically charged crystals in it, and you turn it on and it makes the chain spin until you turn it off or the crystal runs out of juice, right?