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6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra

6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012, MIT OCW). Instructor: Professor Erik Demaine. This course focuses on the algorithms for analyzing and designing geometric foldings. Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra. Applications to architecture, robotics, manufacturing, and biology are also covered in this course. (from ocw.mit.edu)

 Lecture 12 - Tensegrities & Carpenter's Rules

This lecture covers infinitesimal rigidity and motion, and tensegrity systems as an extension of rigidity theory. The rigidity matrix, equilibrium stress, and duality are introduced, and a proof to Carpenter's Rule Theorem is presented.

 Class 12 - Tensegrities

This class covers several examples of tensegrity structures and in Freeform software. A question on linear programming's application to the motions and stresses is addressed.

Go to the Course Home or watch other lectures:

 Lecture 01 - Overview Lecture 02 - Simple Folds Lecture 03 - Single-Vertex Crease Patterns Lecture 04 - Efficient Origami Design Lecture 05 - Artistic Origami Design Lecture 06 - Architectural Origami Lecture 07 - Origami is Hard Lecture 08 - Fold & One Cut Lecture 09 - Pleat Folding Lecture 10 - Kempe's Universality Theorem Lecture 11 - Rigidity Theory Lecture 12 - Tensegrities & Carpenter's Rules Lecture 13 - Locked Linkages Lecture 14 - Hinged Dissections Lecture 15 - General & Edge Unfolding Lecture 16 - Vertex & Orthogonal Unfolding Lecture 17 - Alexandrov's Theorem Lecture 18 - Gluing Algorithms Lecture 19 - Refolding & Smooth Folding Lecture 20 - Protein Chains Lecture 21 - HP Model & Interlocked Chains