Gearing — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
Which crease to push
Deciding one fold angle settles every other one on a quadrilateral mesh, which is what makes a self-folding sheet buildable with a single actuator. It leaves a question that sounds like an afterthought: which crease. Driving each of a mesh's twenty-four in turn gives twenty-four different answers to how far an error in it travels — and on the sheet that repeats one vertex, it gives several answers to what shape the sheet takes.
Two drivers and one freedom
Two actuators on a sheet with one degree of freedom are two commands for one number, and if they disagree by a hundredth of a radian the sheet cannot satisfy both. Where it settles is decided by the gearing between the two creases: a strongly geared pair absorbs the disagreement and leaves a quarter of it standing, while a weakly geared pair keeps ninety per cent. The loosest coupling is the expensive one, which is the opposite of what coupling usually means.
A gearing reflects stiffness squared
Two actuators on a sheet with one freedom disagree, and the sheet settles where their stored energy is least. With unequal stiffnesses the answer depends on them only through k₂g² ⁄ k₁ — the second actuator, seen from the first crease, is a spring of stiffness k₂g², the gearing entering squared as a gear train reflects any stiffness. That settles which actuator to make compliant. On a rigid mesh's loosest pair a second actuator ten times stiffer than the first stores fifty times the fighting energy of one ten times softer, and softening it gives up only 8 per cent of how firmly that crease is held, because the first actuator already holds it ten times over through the gearing. On the tightest pair softening saves four times the energy and gives up 68 per cent of the hold. Compliance is cheap exactly where the fight is expensive.
Named alongside it
The objects these essays reach for when they reach for this one.
ActuationRigid foldingSelf-foldingActuatorDegrees of freedomMiuraPropagation