This is a one-DOF (degree of freedom) six-bar rigid-body mechanism. Traditional engineering kinematics states that the mechanism will have the same motion regardless of the shapes of the rigid links. This makes for interesting motion as the links all move with respect to each other.
Because the links for this mechanism are shaped such that, in one of the mechanism's positions, the links conform to the BYU "Y" logo shape, this is a developable mechanism.
A developable mechanism is a mechanism that, at some point in its motion, conforms to a developable surface. In other words, it is a device that can move and that is shaped to match a curved surface (or combination of curved surfaces) in a certain position. In this case, the developable surface that the mechanism conforms to is a generalized cylinder whose planar image is that of the BYU "Y" logo.
Visit https://www.compliantmechanisms.byu.edu/about-developable-mechanisms to learn more about developable mechanisms
We recommend that you print one test link to make sure that the sizes are correct before you print all the rest of the links.
This Thing can be 3D printed using any rigid filament. We print with PLA and find that works well. Support material is not necessary, but may help ensure the countersink holes come out the right depth. This Thing should not be scaled, as it will mess up the hole sizes.
Assemble the pieces using LEGO connector pieces (the black or grey round cylindrical ones).
Use the pictures or your intuition to figure out the order of the links.
Link Y1 connects to links Y2, Y4, and Y6.
Link Y2 connects to links Y1 and Y3.
Link Y3 connects to links Y2, Y4, and Y5.
Link Y5 connects to links Y3 and Y6.
Link Y6 connects to links Y5 and Y1.