Khushbu Kshirsagar
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HEX-FLEX

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Hands-on explorations with hexagons, their properties and mechanical movements 
THE CONCEPT

In an attempt to find mathematical connections in making and fabricating, I accidentally happened to explore interesting properties of hexagons creating some fun mechanical movements. This design was inspired by the Hoberman sphere - an isokinetic sculpture that resembles a geodesic dome but is capable of folding down to a fraction of its normal size. 

MATHEMATICAL CONNECTIONS

This kinetic sculpture draws fascinating connection with math as a part of it making and designing process. It's almost unbelievable how easily one could prototype something complex with easy math.
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Designing the base
  • In the image to the left, 'r' is the radius of the circle inscribed in the hexagon (note that a polygon with increasing sides eventually forms a circle).
  • The slot dimensions (length of the slot) for the movement of the other hexagons is the diameter of the "inscribed circle" which equals '2r'.
  • Assuming the linkages connecting the hexagons be of 'x' thickness.
    In the initial position, the linkages are clasped tightly with each other. This points towards the distance between the slot and the central hexagon to be
    'x + x' which is '2x'.
  • The distance between the central hexagon's centre and the slot is therefore equal to '2x + r'.

  • The linkages connecting the consecutive hexagons are made by keeping the hexagon as the base.
    Joining every other vertex of the hexagon gives the shape to the linkage. Each of the links are 120 degrees apart from each other.
  • When two 'Y-shaped' linkages connect two consecutive hexagons, their periphery forms another hexagon (clearly visible when the sculpture is fully turned).
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Designing the elements

UNDERSTANDING THE MOTION

The knob on the central hexagon offers a 180 degree rotation instead of the full 360 degree turn.
This is because while designing this sculpture, the length of he slot in the base was '2r'. Since there is a hexagon translating within the slot, which also has a circle of radius 'r' inscribed within itself and the rotation of the central hexagon (with another inscribed circle with radius 'r'); thus making the rotation restricted within the slot and only upto a 180 degrees.

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Central knob with a restriction of rotating to a 180 degrees
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Translation motion of the corresponding hexagons
NEXT STEPS

The next steps for this project are to use this sculpture as a tool for open-ended knowledge construction targeting audiences of all age groups.

I imagine the kinetic sculpture to be a part of a public installation. With the sculpture in motion in front of the visitors eyes, there would be spaces for open-ended explorations using the pieces of the sculpture.

In an attempt to do that, I'm looking at origami-based designs of a 'Flexagon'.
In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.

I'm looking at two-dimensional making spaces with flat flexagons and three dimensional making spaces with 3D hexa-flexagons as building units.
EXPLORATIONS IN THE 2D SPACE


​I imagine the 2D space as a place to play with elements present in the existing sculpture. This could be flat pieces of hexa-flexagons which can be turned into the 'Y-linkages' (similar to the main sculpture) and back into a flat hexagon.
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​This space also envisions on consisting of puzzle pieces which would be serve as geometric pieces in building.
This ensures a wide range of age groups to engage with the tangible pieces of the sculpture.

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EXPLORATIONS IN THE 3D SPACE

In the 3D space, a three-dimensional flexagon as a building unit of a larger open-ended sculpture can be constructed. This is a zone running completely on freely flowing creativity. Here are some building unit prototypes.
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3D building Flexagon and linkage units
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Constructing a 3D Flexagon
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Open-ended exploration with different materials


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NOTE:
The kinetic sculpture won the first prize in the
'Art Exhibition' category at the 'Graduate Students Research Symposium' conducted by Tufts University.
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  • projects
    • Morphblox
    • Twist-Yay!
    • Zine Machine
    • Moving Squares
    • Illustrations
    • SIGH!
    • Senses and Art
    • STEM toys >
      • Hex-flex
      • tea dipper
      • Knock 'em off!
      • Inertial bugs
    • Breathe
    • Non-sense machines >
      • Gravity-powered record player
      • The Mask
    • Drag-On
    • 3Doodle
    • 20-second smiley timer
    • Kali's Secret Weapon
    • Lazy Bird
    • SECMOL
    • rubberband joineries
    • Fun Builds
  • Research
  • About
  • CONTACT