A hinged dissection of a set of polygons S is a collection of polygonal pieces hinged together at vertices that can be rotated into any member of S. We present a hinged dissection of all edge-to-edge gluings of n congruent copies of a polygon P that join corresponding edges of P . This construction uses kn pieces, where k is the number of vertices of P . When P is a regular polygon, we show how...

Any two polygons of equal area can be partitioned into congruent sets of polygonal pieces, and in many cases one can connect the pieces by flexible hinges while still allowing the connected set to form both polygons. However it is open whether such a hinged dissection always exists. We solve a special case of this problem, by showing that any asymmetric polygon always has a hinged dissection to...

A review of contributions and views on the second spectrum of Timoshenko beam theory (TBT) over the past two decades, together with some new results, are presented. It is shown that the Timoshenko frequency equation factorises not solely for hinged–hinged end conditions, as is often claimed, but also for guided–guided and guided–hinged; these new cases may be regarded as portions of a multi-spa...

We have developed a new magnetic actuation process for hinged, surface micromachined structures to assemble threedimensional optical devices with high efficiency and high yield. Electroplated magnetic material (Permalloy) is integrated with two types of hinged microstructures and the magnetic actuation process has been experimentally characterized. Under a given external magnetic field, the ang...

This study compared the effects of solid and hinged ankle-foot orthoses (AFOs) on the gait of children with spastic diplegic cerebral palsy (CP) who ambulate with excessive ankle plantar flexion during stance. Twelve children with spastic diplegic CP wore no AFOs for an initial 2-week period, solid AFOs for 1 month, no AFOs for 2 weeks, and hinged AFOs for 1 month. Lower extremity muscle timing...