# Peaucellier–Lipkin Linkage in C++ ImGui

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Similar to my previous article, where I depicted the **Hoecken linkage**, the following one converts rotational motion to a straight line (it is not an approximation as it was discussed previously).

This ingenious innovation is applicable to many machines and solutions (engines, turbines, pumps, etc).

In order to be consistent I decided to organize the following article using the same setup presented previously.

I will demonstrate a mathematical model and display the results of the simulations. Please consider one of my previous articles where I gave the introduction and provide information on how to compile and run programs.

The source code you find on my** ****GitHub**.

# Peaucellier–Lipkin Linkage

We can model the linkage as follows,

The kinematics equation of the above linkage can be expressed as follows,

where,

Finally,

The result of the motion can be depicted in the below figures. The string line on the right side displays the position of point C (and of arms DC and BC). The left side of the figure shows the rotational motion of point A around O.

The motion of the discussed linkage was simulated using the C++ ImGui.

Thank you for reading.