One rotating crankshaft angle θ drives the piston, the valves and the spark — 720° = one full cycle.
A four-stroke engine turns fuel into rotation in a fixed four-step sequence. The key idea: a single crankshaft angle θ drives everything at once — the piston position (through the connecting rod), which valve is open, and when the spark fires. Because the cam turns at half crank speed, the sequence repeats every 720° = two crankshaft revolutions, one full cycle.
The crankshaft rotates; the connecting rod converts that rotation into the piston's up-and-down motion using honest crank-slider geometry (not a fake sine). Each 180° is one stroke: Intake (intake valve open, piston down, charge drawn in) → Compression (both valves shut, piston up, charge squeezed; spark fires at the top) → Power (burnt gas expands and forces the piston down — the only stroke that does work) → Exhaust (exhaust valve open, piston up, spent gas pushed out). Valves lift ONLY on their own stroke; the spark flashes once per cycle at the end of compression.
J.B. Heywood, Internal Combustion Engine Fundamentals (1988); R. Stone, Introduction to Internal Combustion Engines. Square 86×86 mm gasoline geometry; P–V is the Otto air-standard idealisation (explicitly a teaching model).