6.849: Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2010)

Prof. Erik Demaine


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[+] Locked linkages: Algorithms for unfolding 2D chains, pseudotriangulation, energy; rigid folding of single-vertex origami; locked trees, infinitesimally locked linkages, Rules 1 and 2; locked 3D chains, knitting needles.

This lecture is about locked linkages. Continuing on from the Carpenter's Rule Theorem from last lecture, which says that 2D chains can't lock, we'll see three different algorithms for folding 2D chains. Each algorithm has varying levels of expansiveness, symmetry, and efficiency, with applications to 2D robot-arm motion planning. We'll also see an application of a spherical version of the Carpenter's Rule Problem to rigid folding of single-vertex origami. Then we'll tour the world of locked 2D trees, which has had significant progress recently. To this end, I'll describe the extensive technology for proving 2D linkages to be locked. Finally we'll briefly look at locked 3D chains, which relates to protein folding.

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Handwritten notes, page 1/9[previous page][next page][PDF]

Handwritten notes, page 1/9[previous page][next page][PDF]

Slides, page 1/21[previous page][next page][PDF]

Figure 6.22 of GFALOP

Slides, page 1/21[previous page][next page][PDF]

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