One freedom, whatever the size
A Miura sheet of 4×4 panels, folded. There are 24 creases, so 24 unknown fold angles; 9 interior vertices, so 27 closure equations. Subtracting gives -3, and the mechanism has one freedom — the rank of the constraint Jacobian is 23, leaving 4 constraints that repeat what the others have already said. Every panel here is a rigid body and every crease a hinge; the sheet is not bending anywhere and no material is being stretched. The check that says so is on the page: each vertex is computed independently from every panel that meets it, and the 25 readings agree to 7.3e-14 of a panel's length. positioned by solving, not by drawing.
Many of one thingdraggable: fold angle of one crease (rad)wide
Where it is used
- Many loops, one freedom Many of one thing
- Each one moves, and together they do not Many of one thing
- The freedom that survives repetition Many of one thing
- Every vertex is a spherical linkage Many of one thing
- It moves to first order and not at all Many of one thing
- Where the branches meet Many of one thing
- Six things a network is not Drawn wrongly
- What a pattern has to satisfy Many of one thing
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