3.3.2 Data Plots

To generate a data plot, we must first generate some data. SolveMech is used to return 20 solution points as the crank is rotated through a full turn, with the crank arm length set to three units.

This generates a list of 20 solutions.

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Since the primary function of the quick return mechanism is to reciprocate the slider, the X position of the slider is plotted as a function of time. Each solution rule returned by SolveMech contains a rule specifying the value of time T so a list of {x, y} pairs for ListPlot can easily be obtained with one replacement operation.

Here is a plot of slider position versus time.

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More complicated functions can also be plotted in this manner.

Here is a plot of connecting rod angle versus time.

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To create a series of plots while varying the value of crank arm, the Table function is used in conjunction with SolveMech to generate a nested list of solutions. Note that at each invocation of SolveMech the value of time T is taken from 0 to 1, which takes the angular coordinate of the crank 2 from 0 to 2 pi. This requires the value of 2 to jump from 2 pi back to 0 in one step at each new invocation of SolveMech, which is a rather large single step for the numerical solution method. To avoid possible numerical difficulties, the initial guesses are reset with SetGuess at each invocation of SolveMech.

This generates a nested list of solutions.

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To generate a series of plots a rather obtuse invocation of ListPlot is used.

This shows a plot of slider position at varying values of crankarm.

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