An engine puts the auto in automobile; without one, you merely have a carriage and have successfully shifted yourself backwards by 120 years. A century-plus of engine development has brought forth a vast array of solutions to the internal combustion problem. Virtually every person who has set their mind to building a car has experimented with the number, orientation, and even shape of the cylinders.
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In a rotary engine, the output (more accurately eccentric) shaft is not 'geared.' There is, however, one pair of gears per rotor: the smaller one with external teeth is fixed, the larger one with internal teeth is attached to the inside of the rotor. These gears merely keep the rotor and eccentric shaft motion in phase and do not transmit torque.
You are wrong about the Chrysler Turbine engine. While 130 horses is not earth-shattering in a post-war car, 465 lbs. ft. is EXCELLENT. Performance was good. The reason Chrysler killed the Turbine-as-a-car engine project was super-high production costs, that would have made it impossible to sell at a reasonable price, and, it was discovered in later versions, very high exhaust emissions that seemingly couldn't be cleaned up, which would have made cars so equipped illegal for street use.
That Honda engine was not a 4 cylinder emulating an 8.
It was only two of those pistons emulating their proven V-4 design.
Basically removing the cylinder walls between each pair of V-4 pistons increased displacement allowing a lower friction reduction in bore radius that also ran cooler.