Invention & Innovation (MPU 3252) Chapter 4: Impacts of Invention & Innovation.
MIT Class 6.S080 (AUS) Mechanical Invention through...
Transcript of MIT Class 6.S080 (AUS) Mechanical Invention through...
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MIT Class 6.S080 (AUS) Mechanical Invention through Computation 3-dimensional Expanding Structures
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Mechanism – relation to base geometry
Linkages orthogonal to 3D surface
Linkages tangential to 3D surface
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Transformable Typology: Expanding Shapes
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Kinematic mode
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Icosahedron
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Radial expansion Points on expanding shape move radially outwards.
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Turning surfaces into mechanisms
Helicoid
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Surface terminology
Positive curvature
Zero curvature Negative
curvature
Surface normals
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Original patent: angulated scissor
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Original patent: expanding polygon
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Original patent: 3d loop linkage (3-sided)
link hub
Hubs create out of plane connections between linkages
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Original patent: 3d loop linkage (4-sided)
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Original patent: 3d loop linkage (6-sided)
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Original patent: expanding sphere
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Original patent: expanding icosahedron
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Mini Sphere
Mini sphere works with double scissor between hubs
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Angulated scissor construction - review
Projection of scissor (angulated line) scales as scissor folds
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Scissor frequency (between hubs)
As additional scissors are added, ratio of folded to unfolded size decreases
Greater Packing
efficiency
Increased Part count
(complexity) =>
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Hub and link assemblies (4-sided)
Hub pair
Hub pair
To maintain symmetry, distance from hub to center scissor connection must be equal for all links going into a single hub.
Circles formed by center scissor connections
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Hub and link assembly (3-sided)
Hub pair
Hub pair
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Base geometry
For structures with single scissors between adjacent hubs, circle tangency is required.
Hubs are located at center of circles
Core polyhedron
Dual figure gives location of scissors
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Surface made up of tangential circles
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Link construction from base geometry
Construct links as shown
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Wireframe
Centerline geometry of scissors
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Scissors shown without hubs
Need to allow space for hubs to avoid interferences
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Method to set hub geometry
Scaling method 1. Scale original
link length (A%) 2. Add line
extension (B%)
3. Insert scaled version back into base geometry
where A% + B% = 100%
Original version
Scaled version
Original version
Scaled version
(end points of construction line are same as original)
Red lines give wireframe hub geometry
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Mini Sphere – single scissor version
Hub construction
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Hub construction (alternate method)
B%
A%
Core polyhedron
Dual of core polyhedron
decompose => scale => recompose
Lines represent scissors (these expand/contract in physical mechanism)
Polygons represent hubs (these do not expand/contract in physical mechanism)
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Double scissor construction
Construct a line whose end-points lie on original angulated line
Segments (composed as shown) provide wireframe geometry of links
Mid-point of constructed line
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Mini sphere construction with double scissor
Mid-point of constructed line construct links
from line segments as shown Original base
geometry (single scissor)
Modified base geometry (double scissor)
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Establish hub geometry
Original version Scaled version
For structures with 2 or more scissors between adjacent hubs, circle tangency is not required.
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Wireframe
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Product
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Surface geometry => structural mechanism
• Surface Shape
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Surface geometry => structural mechanism
• Surface Shape • Tessellation
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Surface geometry => structural mechanism
• Surface Shape • Tessellation • Normal Vectors
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Surface geometry => structural mechanism
• Surface Shape • Tessellation • Normal Vectors • Intersections
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Surface geometry => structural mechanism
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Surface geometry => structural mechanism
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Korean Aerospace Institute
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Korean Aerospace Institute
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Expanding Sphere, CBIT Conference, Hanover, 2010
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Expanding Sphere, CBIT Conference, Hanover, 2010
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Expanding
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Expanding Helicoid
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Museo Interactivo Mirador, Chile
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Bordeaux, France Smith Haut Lafitte
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Suspended
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Detroit Auto Show 2012
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Hyperbolic parabaloid
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Hyperbolic parabaloid