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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 19 - Refolding & Smooth Folding

This lecture begins with a problem involving unfolding and refolding. Examples of smooth foldings and unfoldings are given, followed by a problem involving the wrapping of a sphere and a proof that the wrappings are contractive.


Class 19 - Refolding & Kinetic Sculpture

This class first covers research findings involving common unfoldings of boxes. Several examples of kinetic sculptures and machines are shown, including Theo Jansen's Strandbeests and Arthur Ganson's works at the MIT Museum.


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