13.2.2 Bifurcation

Another common modeling problem is bifurcation, a condition where more than one solution to the system of constraint equations exists, representing multiple possible assembled configurations. When the previously defined crank-with-link model is modified so that it can converge, it is able to converge to either of two solutions depending on the values of the initial guesses.

Here is one possible configuration of the crank-with-link model with a reasonable value of len.

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And here is the other possible configuration of the crank-with-link model.

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Once a model is apparently functioning properly, the value of a graphic image of the model cannot be overemphasized. A rudimentary graphic image can immediately show errors that may have gone unnoticed, such as the fact that a model has converged on the wrong side of a bifurcation, or simply that the model has been defined incorrectly. Errors that are difficult to detect from the numbers alone are often easily seen in the graphic.

Here is a simple graphic of the crank-with-link model at both positions.

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