Interactive Dynamics
Kinematic Analysis of the Crank, Connecting Rod, and Piston in an Internal Combustion Engine
Two-Stroke Spark
Ignition Engine

Figure 1.
The figure at the left shows a cut-away view of a two-stroke, single-cylinder spark ignition engine. You can see the spark plug at the top, the piston below the spark plug, the connecting rod connected to the piston, and the crank connected to the bottom of the connecting rod. The large anvil-shaped thing on the crank is a counterweight to balance the crank.

Interesting Engine Facts

  • In a Formula 1 engine, the maximum piston acceleration is over 8000g, which puts a load of over 3 tons on each connecting rod.
  • Maximum piston speed is about 47.2 m/s. The piston in a 1996 Ford Zetec-R accelerates to that in 1/1000 second.

The Ferrari F50
Figure 2.
Front view of the F50.
Figure 3.
Rear quarter-panel view of the F50.
Figure 4.
The engine in the F50.
The engine in this car, is a little different than the one shown above in Figure 1. This Ferrari has a 12-cylinder, 286.7 cubic-inch, 513 horsepower engine! The car weighs 2700 lbs, has a top speed of 202 mph, and can do 0-60 mph in 3.7 seconds!


Internal combustion (IC) engines are at the heart of many of the devices we use every day (e.g., automobiles, motorcycles, lawn mowers, recreational vehicles, etc.). Early internal combustion engines were based on steam engines and the first IC engine to come into general use was built by Lenoir in 1860. The engines in use today (see Figure 5), though highly optimized in many ways, operate on the same general principles that Lenoir's engine did more than 130 years ago.

Figure 5. Cut-away view of a Chrysler 2.2 liter four-cylinder engine (longitudinal section).

Today's activity is the first part of a two-part activity in which you will play the role of an automotive engineer. In this activity, you will perform a complete kinematic analysis of part of the innards of a piston engine. In second part of this activity (starting in a week or so), you will do a thorough kinetic analysis of the very same system. Your eventual goal is to:

  1. find acceleration curves for the important parts of the crank, connecting rod, and piston within the engine;

  2. find the forces at critical locations within this same system;

  3. understand why engines are designed the way they are.

Kinematic Analysis

You will begin by doing a kinematic analysis of the slider-crank (i.e., crank, connecting rod, and piston) mechanism shown in Figures 6 and 7.

Figure 6. Schematic of the slider-crank mechanism to be analyzed.

Figure 7. Another schematic of the slider-crank mechanism showing the mass centers of the crank and the connecting rod.

The slider-crank mechanism shown is driven by the combustion process that occurs above the piston at C. This combustion process generates a time-dependent force P(t) which drives the piston down. The motion of the piston drives the crankshaft at A around by way of the connecting rod BC. In addition, there is a "resistance" torque generated at the crank due to frictional and load resistance applied to the crankshaft. See the QuickTime movie shown in Figure 8 for a nice demonstration of the way this all works.

Figure 8. QuickTime movie of a slider-crank mechanism similar to ours.

We will assume the physical parameters of each of the components are as given in Table 1.

Table 1: The physical parameters of each of the components
of the slider-crank mechanism.
Dimension Length
Distance r from A to B 36 mm
Distance L from B to C 125 mm
Distance a from B to D 40 mm

Now, assuming that the crankshaft angle is q, that the angular velocity of the crankshaft is w, and that the angular acceleration of the crankshaft is a, determine as a function of these parameters and the given geometry:

  1. The acceleration of point D, the mass center of the connecting rod.

  2. The angular acceleration of the connecting rod.

  3. The acceleration of the piston.

Steady-State Analysis

Now assume that the angular velocity of the crank is a constant 3000 rpm. Plot the above three accelerations as a function of the crank angle q.

Limit Case Analysis

After completing the above kinematic analysis, your next task is to find those positions that are "limiting positions" of your slider-crank mechanism. That is, what are the crank angles that give the highest linear and angular accelerations of each of the components (really just the connecting rod and the piston). Why do you suppose you would want and/or need to find these locations?

Activity Pre-Report

We would like a simple pre-report consisting of the derivations of the accelerations, the above asked for plots, and the results of your Limit Case Analysis. In addition, don't even bother to turn your work in if you don't use proper vector notation.

Due Date of the Pre-Report: April 8 at the beginning of class.

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Prepared by Gary L. Gray and Francesco Costanzo.
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© Copyright 1998-1999 by Gary L. Gray and Francesco Costanzo. All rights reserved.