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During my civil engineering studies, I've come across the notion of a "Polplan", a method for determining the possible infinitesimally flexible configuration of a statically indeterminate truss or more general for any multi-beam structure.

An example of the Polplan

In the figure provided you see most of the parts that make up a Polplan: There are "main poles" (Hauptpole), which denote the center of a infinitesimal rotation of the corresponding rigid body. You can also see the "secondary poles" (Nebenpole), which denote the locations where any two rigid bodies exibit the same infinitesimal displacement. In orange you can see the infinitesimal displaced figure.

There are certain rules (which can be found on the German Wikipedia here), which allow to deduce the "Polplan" for any statically underdeterminant structure.

Is there an english term for this procedure?


EDIT: Not the original question, only the context:

My goal with this question is to find out whether there is a nice mathematical framework with which one can deduce the polplan without solving the constraint satisfaction problem given by the rules. The english term would allow me to find english ressources on it.

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  • $\begingroup$ So which do you want? the English equivalent to "polplan"? The existence of a nice mathematical framework? or can it be solved without solving for the constraints? Perhaps you may need to consider : Free Body Diagram. $\endgroup$
    – Solar Mike
    Commented Aug 6, 2023 at 9:51
  • $\begingroup$ I edited the question to make it more clear. Both would be nice, but I can work with only the english term. $\endgroup$
    – Noiv
    Commented Aug 6, 2023 at 10:09
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    $\begingroup$ the Wikipedia calls it pole plan in the translation $\endgroup$
    – jsotola
    Commented Aug 7, 2023 at 0:14

2 Answers 2

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It's a drawing board technique called a velocity diagram, and you have solved a puzzle which is why some vehicle dynamics texts refer to instantaneous centres of rotation as poles.

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I found this link that explains the rules of polplan clearly, and you can use the translate option of chrome to translate it into english.

https://www.ingenieurkurse.de/baustatik-1/kurs-baustatik/statische-bestimmheit-polplan.html

Hope this helps you as it did for me.

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  • $\begingroup$ Welcome to Engineering! So as to avoid link-rot, please expand your answer to include the relevant information from the link provided, at least the most essential points. Feel free to quote directly from the source. $\endgroup$
    – Wasabi
    Commented Oct 29, 2023 at 14:09

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