Reciprocal Kinetic Structures

Hello, I want to study about reciprocal kinetic structures in my article. I am trying to write the algorithm of the system used in another study before. The basic logic is that the elements in the reciprocal system can go up and down by sliding over each other. It describes the motion system of the first visual module. The most important part is that the lengths of the elements do not change as they slide. The second image describes the combination of several modules. I brought the algorithm to a point, but I couldn’t do the ascending and descending part. I would be very happy if you could help. (19.2 KB)

In your file the arcs endpoints located in the hexagon corners are moving along the hexagon edges but in your picture the endpoints are fixed and doesnt move at all.
The structure in the second picture is only possible if the the arc endpoints stay at the hexagon corners otherwise they will be not connected.

Also the arcs are not sliding they rotate around the hexagon corners.
I am not sure how to get the correct length but i guess if you rotate two neibhour hexagon edges around 30° (its the longest distance in a heaxagon from one edge to the other) and create circles with the hex radius around the rotatet hex edges endpoints you get the correct arc length.

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Here is a possible solution for the first picture but it shouldn’t be to hard to get the second picture. (15.7 KB)

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Thank you for your interest and work. You are absolutely right in what you say. I overlooked that the corners must be fixed and that the motion is rotational motion. Your algorithm looks great on hexagonal modules but it doesn’t work on other polygons.I will work on it and try to improve it.


What I’m trying to do is a module that is the fourth image in this gif and rises as it moves. I would be very happy if you could help with this.


Edit: I made it someway. I am sure there is another way to better organize. (25.5 KB)