19. Internal Combustion Engines

• Internal combustion engines contain a wide variety of kinematics and dynamics problems.

• Some of the criteria for differentiating engines includes,

Fuel Air Mixing

Otto cycle: air/fuel mixed before compression, equal fuel-air ratio. A highly volatile fuel is required.

Diesel: air/fuel mixed after compression, excess air. Compression is the main source of ignition.

Cylinder Exhaust

two stroke: within one cycle of the piston a compression and exhaust occur. Basically the mixture is ignited, the gas expands, and near the end of compression the cylinder is opened to vent the gas, at the same time new fuel-air is injected. The valves are then closed, the cylinder advances, and ignition occurs again. These engines are simpler, but less efficient.

four stroke: In this engine the piston cycles twice. One cycle is to intake fuel-air mixture and combust it. The second cycle is to vent the cylinder. The four strokes are expansion, exhaust, intake, compression.

Cylinder Arrangement

single cylinder: only one cylinder

in-line: all of the cylinders are side by side in a line.

V block- there are two rows of cylinders that form a V-shape

opposed-piston: there are two rows of cylinders that are 180° away from each other

radial: cylinders are arranged at regular intervals about a single cam shaft

Connecting Rods

Single crank per pair of cylinders

fork and blade design

articulated rod

separate crank throws for each piston

19.1 Power

• We can estimate the power generated in the combustion cycle using the gas pressure and change in volume.

• Basically in an engine the volume of gas is constant, except during ignition, where the volume of gas is almost instantly increased. This results in a corresponding increase in pressure, that drives the displacement of the piston.

• For a typical engine the cylinder pressure curves will look something like those below from Shigley and Uicker for a 401 cubic inch V6 truck engine.


• We can also estimate actual horsepower and torque of the motor by braking the engine, and calculating powers over a range of speeds. [Shigley and Uicker]


• In an engine typical component massed are, [Shigley and Uicker]


• We can typically relate engine power to displacement volume, with some variance considered for engine type,


• The ideal pressure volume diagram for an engine is shown below. It does not have the rounding seen on the practical graph before (the rounding is the result of slow valve openings, and the finite time for combustion).


• We can find the work done by the engine by looking at the change in pressure and volume on the expansion stroke.

19.2 Kinematics and Dynamics

• Basically the engine has rotating parts that generally behave as multiple crank slider mechanisms. The force is applied on the slider, and the crank is rotated as a result.

• This analysis begins with a model of the mechanism. We can use this to do a static and kinematic analysis of the mechanism. We can find the driving force on the piston as a pressure of the gas es it expands, and the area of the piston.


• Next, to do the dynamic analysis of the engine we need dynamic parameters for each of the components. In practice we would also need to consider the bearings, pins, etc.


• The results of this analysis will be a time variant function for each cylinder. These can then be combined for all of the cylinders in the engine to get an overall dynamic function for the engine. The total mass of the engine will tend to act as an inertial dampener for the reciprocating forces in the engine.

19.3 References

19.1 Shigley, J.E., Uicker, J.J., “Theory of Machines and Mechanisms, Second Edition, McGraw-Hill, 1995.