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{{Userspace draft|source=ArticleWizard|date=October 2020}}[[File:Hoberman Mechanism.gif|thumb|Two dimensional Hoberman Mechanism made of 24 angulated bars and 36 revolute joints]]A Hoberman Mechanism, or Hoberman Linkage, is a deployable mechanism that turns linear motion into radial motion.
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[[File:Hoberman 16 centred.gif|thumb|An expanding and contracting 2D Hoberman sphere]]
The Hoberman Mechanism is made of two angulated ridged bars connected at a central point by a [[revolute joint]], making it move much like a [[Scissors mechanism|scissor mechanism]].<ref name=":0">{{Cite patent|title=Radial expansion/retraction truss structures|gdate=1990-04-06|url=https://patents.google.com/patent/US5024031A/en}}</ref> Multiple of these linkages can be joined together at the ends of the angulated bars by more revolute joints, expanding radially to make circle shaped mechanisms. The mechanism is a GAE (generalize angulated element) where the coupler curve is a radial straight line.<ref name=":1">{{Cite journal|last=You|first=Z.|last2=Pellegrino|first2=S.|date=1997-05-01|title=Foldable bar structures|url=http://www.sciencedirect.com/science/article/pii/S0020768396001254|journal=International Journal of Solids and Structures|language=en|volume=34|issue=15|pages=1825–1847|doi=10.1016/S0020-7683(96)00125-4|issn=0020-7683}}</ref>This allows the Hoberman Mechanism to act with a single degree of freedom, meaning that it is an [[Overconstrained mechanism|over-constrained mechanism]] because the mobility formula predicts that it would have a smaller degree of freedom than it does. as the mechanism has more [[Degrees of freedom (mechanics)|degrees of freedom]] than the [[Chebychev–Grübler–Kutzbach criterion|mobility formula]] predicts.<ref name=":2">{{Cite journal|date=2007-09-01|title=A kinematic theory for radially foldable planar linkages|url=https://www.sciencedirect.com/science/article/pii/S0020768307000923|journal=International Journal of Solids and Structures|language=en|volume=44|issue=18-19|pages=6279–6298|doi=10.1016/j.ijsolstr.2007.02.023|issn=0020-7683}}</ref>
The '''Hoberman mechanism''', invented by American architect, engineer, and artist [[Chuck Hoberman]], is a system enabling expandable structures such as self-building tents and certain children's toys, specifically his "[[Hoberman sphere]]"<ref name=":0">{{Cite news|last=Frauenfelder|first=Mark|date=1998-06-01|title=Transformer|work=Wired|url=https://www.wired.com/1998/06/hoberman/|access-date=2020-10-22|issn=1059-1028}}</ref>, to change in size significantly.


The kinematic theory behind the Hoberman Mechanism has been used to help further the understanding of mobility and foldability of deployable mechanisms.
Structures with this mechanism typically have rigid, identical parts linked together around pivots (rotation points). These individual parts can be made from numerous materials depending on the purpose of the structure. For example, the framework of a self-building tent would be made from hard, durable materials like aluminum or steel, and a Hoberman sphere designed for children would be made from a light, colorful material like plastic. This allows the structure to have the greatest range when the links are moved, and form a larger final shape, or fold into a smaller compact structure for storage. The overall structure, and its individual parts, can have any three-dimensional shape, allowing a variety of structures to be designed for different applications, such as screens and radio antennas.<ref>{{Cite patent|title=Reversibly expandable doubly-curved truss structure|gdate=1988-10-27|url=https://patents.google.com/patent/US4942700A/en}}</ref>


== History ==
== History ==
The Hoberman Mechanism originates from the idea of making something bigger become smaller. [[Chuck Hoberman]], a fine arts graduate from [[Cooper Union]] realized that his lack in knowledge of engineering was holding him back from creating the things he could picture in his head. He enrolled in [[Columbia University]] to get a masters in [[mechanical engineering]].<ref>{{Cite news|title=Transformer|language=en-us|work=Wired|url=https://www.wired.com/1998/06/hoberman/|access-date=2020-10-29|issn=1059-1028}}</ref> After this he started working with [[origami]], studying the way that it folded and changed shape. He soon realized that his interests lied in the expansion and shrinkage of the objects he was making. Hoberman started to experiment with different expanding mechanisms and started to create mechanisms of his own. He later patented a system that uses two identical bent rods connected in the middle by a joint; he called it the Hoberman Mechanism.<ref>{{Cite web|title=Chuck Hoberman {{!}} Lemelson|url=https://lemelson.mit.edu/resources/chuck-hoberman|access-date=2020-10-29|website=lemelson.mit.edu}}</ref> The creation of the Hoberman Mechanism has since helped with more mechanical discoveries and research concerning foldability and mobility of mechanisms.
Through experimentation, Hoberman invented ways for structures of a multitude of different shapes to grow and shrink in size simultaneously.


=== Early Days ===
== Mechanics ==
Beginning with his question of how to "make objects shrink in size", Hoberman experimented with [[origami]] and observed the way they folded and changed shape. He later worked with interwoven metal parts linked in pivots, which proved to increase the volume of the object significantly. Hoberman eventually patented some of the linkage systems he devised, and even manufactures them at his company Hoberman Associates.<ref name=":0" /><ref>{{Cite web|title=Chuck Hoberman {{!}} Lemelson|url=https://lemelson.mit.edu/resources/chuck-hoberman|access-date=2020-10-24|website=lemelson.mit.edu}}</ref>


=== Synchronized Ring Linkages ===
=== How it Works ===
The Hoberman Mechanism is made of two identical angulated rods joined together at their bends by one central [[revolute joint]]. Multiple of these mechanisms can be linked by connecting the ends of the pairs together with two more revolute joints. Due to the mechanism's design, however, the revolute joints act as if they are [[Prismatic joint|prismatic]]-[[Revolute joint|revolute]] joints because they move along a straight axis as the system changes shape. By pushing or pulling on any of the joints, the entire system moves and changes shape, gaining volume or folding into itself. These systems of linkages can be expanded to a full circle where it moves as one system, turning linear motion from a single axis of a joint into radial motion across the entire mechanism.
The ring linkage system was developed in 2004 and is made of at least six linkages connected into a ring-like shape. The structure can grow into a ring-like shape or shrink into a star-like shape with the linkages pushed close together for efficient space storage. These properties make ring linkages useful for structures that require its surface area to be changed.<ref>{{Cite patent|title=Synchronized ring linkages|gdate=2004-10-12|url=https://patents.google.com/patent/US7540215B2/en}}</ref>


=== Kinematic Theory ===
=== Folding Covering Panels for Expanding Structures ===
[[File:Single Actuated Element.png|thumb|Fig 1. Example of a single PRRP linkage]]
In 2005, Hoberman released a linkage system of bars interconnected into scissors-like pivots, whose overall structure is a triangle that can expand or contract. This structure is to be used with a foldable covering panel connected to the bars so that the cover can spread out with the structure, or compress into a smaller polygonal shape. Like the four-bar linkage system, the folding panel can be used to set up temporary shelters, in addition to foldable projection screens and transformable lighting products.<ref>{{Cite patent|title=Folding covering panels for expanding structures|gdate=2002-11-25|url=https://patents.google.com/patent/US6834465B2/en}}</ref>
[[File:Hoberman 6.gif|thumb|A Hoberman Mechanism made of12 angulated bars and 18 revolute joints ]]
The Hoberman Mechanism is a [[Degrees of freedom (mechanics)|single degree of freedom]] structure meaning that the system can be driven with a single [[actuator]]. The mechanism is made of two identical angulated rods joined together by a central revolute pivot and four end pivots constrained to move along a single line. Because the four end pivots are restrained in this way, the mechanism can be treated as pair of PRRP (prismatic-revolute-revolute-prismatic) mechanisms joined at a central point.<ref>{{Cite journal|last=Li|first=Ruiming|last2=Yao|first2=Yan-an|last3=Kong|first3=Xianwen|date=2017-10-01|title=Reconfigurable deployable polyhedral mechanism based on extended parallelogram mechanism|url=http://www.sciencedirect.com/science/article/pii/S0094114X17301672|journal=Mechanism and Machine Theory|language=en|volume=116|pages=467–480|doi=10.1016/j.mechmachtheory.2017.06.014|issn=0094-114X}}</ref> The two PRRP linkages trace a pair of identical straight lines from the origin of the mechanism to their coupler points, so they have the same coupler curve. The equation for the coupler curve of the PRRP linkages in a Hoberman Mechanism follows the coupler point ''B(x,y)'' in Fig 1:<ref name=":2" /><ref>{{Cite journal|last=Sun|first=Xuemin|last2=Yao|first2=Yan-An|last3=Li|first3=Ruiming|date=2020-03-01|title=Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes|url=https://doi.org/10.1007/s11465-019-0567-5|journal=Frontiers of Mechanical Engineering|language=en|volume=15|issue=1|pages=89–99|doi=10.1007/s11465-019-0567-5|issn=2095-0241}}</ref>


<math>y = x \tan(\alpha/2 )</math>
=== Synchronized Four-Bar Linkages ===
In 2006, Hoberman developed a linkage system of interconnected linkages, with each one made up of four bars. Two of the bars are designed to lift and support the remaining two bars like pillars, forming a trapezoidal shape. The linkages are to be lined parallel to each other, so that when activated, the system would build itself into a tent frame, which is useful when one must rapidly set up temporary shelters.<ref>{{Cite patent|title=Synchronized four-bar linkages|gdate=2006-01-12|url=https://patents.google.com/patent/US7644721B2/en}}</ref>


<math>\tan(\alpha/2)=r_2/r_1</math>
=== Panel Assemblies Having Controllable Surface Properties ===
Made of at least one fixed panel and a minimum of two movable panels, Hoberman developed a design for controllable panel assemblies in 2010. With at least two drive links, each with its own pivot connected to the panels, the panels can move in a way that aligns them to the fixed panel, each other, or not align with any other panel. The panels can be perforated (filled with holes) or be made of a colorless material with an applied graphic pattern. The sheets can be transparent when aligned, and opaque when unaligned, helping control a building's internal temperature through shading. (see also [[passive cooling]])<ref>{{Cite patent|title=Panel assemblies having controllable surface properties|gdate=2010-03-23|url=https://patents.google.com/patent/US8615970B2/en}}</ref>


For parameters {r<sub>1</sub>,r<sub>2</sub>,α}, this equation of the coupler curve follows the equation for a strait line (y=mx). Because the two angulated rods that make up a Hoberman Mechanism are identical, they have the same r<sub>1</sub> and r<sub>2</sub> values and thus the same coupler curve.
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== Applications ==
Hoberman's mechanism is common in the toys he invented, namely the Hoberman sphere. Besides its use in toys, engineers are constantly discovering new ways to apply this system.


A pair of PRRP linkages that share a coupler curve at a common coupler point have a single degree of freedom, which is why the Hoberman Mechanism has a single degree of freedom. The motion that the Hoberman Mechanism produces is radial motion even though it looks like linear motion because the motion follows the coupler curve, which is a radial strait line.<ref>{{Cite journal|last=Li|first=Ruiming|last2=Yao|first2=Yan’an|last3=Kong|first3=Xianwen|date=2016|editor-last=Ding|editor-first=Xilun|editor2-last=Kong|editor2-first=Xianwen|editor3-last=Dai|editor3-first=Jian S.|title=A Method for Constructing Reconfigurable Deployable Polyhedral Mechanism|url=https://link.springer.com/chapter/10.1007/978-3-319-23327-7_86|journal=Advances in Reconfigurable Mechanisms and Robots II|series=Mechanisms and Machine Science|language=en|location=Cham|publisher=Springer International Publishing|pages=1023–1035|doi=10.1007/978-3-319-23327-7_86|isbn=978-3-319-23327-7}}</ref>
=== Children's Toys ===
[[File:Hoberman Sphere at Liberty Science Center, 2015.jpg|thumb|Original Hoberman Sphere displayed at the Liberty Science Center in 2015]]
While Hoberman's sphere is his most known toy, there are other toys that use the same mechanism.


The mobility formula for a single degree of freedom M = 3(n - 1) - 2j, where M is the degrees of freedom, n is is the number of moving elements, and j is the number of joints, predicts that a Hoberman Mechanism of 12 bars and 18 joints would have -3 degrees of freedom. That makes the Hoberman Mechanism a [[Overconstrained mechanism|over-constrained mechanism]] because all Hoberman Mechanisms have a single degree of freedom.<ref name=":2" /><ref>{{Cite web|last=Agrawal|first=Sunil K|date=|title=Polyhedral Single Degree-of-freedom Expanding Structures|url=https://www.seas.upenn.edu/~modlab/publications/icra01sunil.pdf|url-status=live|archive-url=|archive-date=|access-date=|website=}}</ref>
==== Hoberman Sphere ====
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== Applications ==
In contrast to its name, the [[Hoberman sphere]] has a polyhedral structure, or is three-dimensional and made up of smaller individual triangles, and can expand or contract at a constant speed due to its linkage system. When the sphere contracts or expands, the distance between each pivot decreases or increases, allowing the structure's individual parts as well as the whole sphere to change size with the same speed. The Original Hoberman Sphere, one of the largest of its kind, was displayed at the central exhibit of the atrium of the [[Liberty Science Center]] in [[New Jersey]]. First installed in 1992, then moved to the museum's new entrance hall in 2007, the 317 kilogram (700 pound) sphere is hung by cables and automatically expands and contracts.<ref>{{Cite web|title=Original Hoberman Sphere – Hoberman Associates|url=https://www.hoberman.com/portfolio/original-hoberman-sphere/|access-date=2020-10-25|language=en-US}}</ref>
The Hoberman Mechanism has been used in many different parts of everyday life.


==== Switch Pitch Toy ====
=== Art ===
[[File:Hoberman Sphere maintenance.jpg|thumb|Hoberman Sphere featured at the Liberty Science Center<ref>{{Cite web|title=Hoberman Sphere|url=https://lsc.org/explore/exhibitions/hoberman-sphere|access-date=2020-10-29|website=Liberty Science Center|language=en}}</ref>]]
Beginning production in 2001, the [https://www.hoberman.com/portfolio/switch-pitch-toy/ Switch Pitch toy] is a ball made to switch the inner and outer layers of the sphere when thrown into the air, thus changing its color. This toy won the Oppenheim Platinum Award for Design and was featured on the [[HBO]] comedy series [[Silicon Valley (TV series)|''Silicon Valley'']].<ref>{{Cite web|title=Switch Pitch Toy – Hoberman Associates|url=https://www.hoberman.com/portfolio/switch-pitch-toy/|access-date=2020-10-31|language=en-US}}</ref>
The Hoberman Mechanism is featured in works of art, mostly made by artist and inventor of the Hoberman Mechanism, [[Chuck Hoberman]]. Structures designed by Chuck Hoberman that included the Hoberman Mechanism were featured in The [[Elaine Dannheisser]] Projects Series from MoMA.<ref>{{Cite web|title=Projects 45: Chuck Hoberman {{!}} MoMA|url=https://www.moma.org/calendar/exhibitions/3080|access-date=2020-10-29|website=The Museum of Modern Art|language=en}}</ref> A Hoberman Sphere also was on display at the [[Museum of Modern Art|MoMA]] in [[New York City|New York]] as a part of the ''Century of the Child'' exhibit.<ref>{{Cite web|title=Century of the Child: Growing by Design, 1900–2000 {{!}} MoMA|url=https://www.moma.org/calendar/exhibitions/1222|access-date=2020-10-29|website=The Museum of Modern Art|language=en}}</ref> More large Hoberman Spheres featuring the Hoberman Mechanism are scattered around the world; they can be found anywhere from science centers around the US to wineries in [[France]].<ref>{{Cite web|last=Campbell-Dollaghan|first=Kelsey|date=2012-09-28|title=A Giant, Working Hoberman Sphere Made From Aluminum|url=https://www.fastcompany.com/1670878/a-giant-working-hoberman-sphere-made-from-aluminum|access-date=2020-10-29|website=Fast Company|language=en-US}}</ref>


=== Hoberman Arch ===
=== Toys ===
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[[File:Hoberman Sphere.jpg|thumb|Mega Sphere with 6 rings of Hoberman Mechanisms]]
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[[File:SL Cauldron park arch (cropped).JPG|thumb|Hoberman arch used in the 2002 Winter Olympics at Salt Lake City, Utah]]
The most commonly seen form of the Hoberman Mechanism is in the toy made by Chuck Hoberman called the Mega Sphere or Hoberman Sphere. The Mega Sphere is a plastic, sphere shaped toy that expands and retracts as it is pushed and pulled on. The toy is made of six full rings of Hoberman Mechanisms that are all connected to each other so as one piece of it retracts or expands, the entirety of the structure follows. They are multicolored and range in size from a meter to just a few inches.<ref>{{Cite web|title=Hoberman Sphere Toy – Hoberman Associates|url=https://www.hoberman.com/portfolio/hoberman-sphere-toy/|access-date=2020-11-16|language=en-US}}</ref>
In the [[2002 Winter Olympics]] at [[Salt Lake City]], [[Utah]], the [[Hoberman Arch|Hoberman arch]] was used as a screen to be opened before revealing the stage for awarding medals.<ref>{{Cite web|title=Retractable arch will take center stage in Salt Lake - ProQuest|url=https://search.proquest.com/openview/499e479323ce11891751af5e5b4cc01b/1?pq-origsite=gscholar&cbl=42415|access-date=2020-10-24|website=search.proquest.com|language=en}}</ref>


=== POLA Ginza Façade ===
=== Architecture ===
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[[File:HobermanArchLit.JPG|thumb|Hoberman Arch featured at the 2002 winter Olympics in Utah]]
At the request of POLA, a Japanese cosmetics manufacturer, Hoberman designed a shading system with help from design architect Yasuda Atelier and executive architect [[Nikken Sekkei|Nikken Seikei]], for its new building in the [[Ginza]] district in [[Tokyo]]. Opening in 2009, the fourteen-story complex has 185 controlled panel mechanisms inside the double windows of the building's front side. Each panel is roughly 1 meter (3.28 feet) by 3 meters (9.84 feet) and is made from a curved acrylic sheet.<ref>{{Cite web|title=POLA Ginza Facade Tokyo – Hoberman Associates|url=https://www.hoberman.com/portfolio/pola-ginza-facade-tokyo/|access-date=2020-11-05|language=en-US}}</ref>
The Hoberman Mechanism has also been used in larger scale architectural projects. One of these structures is the [[Hoberman Arch]] featured the 2002 winter [[Olympic Games|Olympics]] in [[Utah]]. The Arch was designed by Chuck Hoberman; it was built to open and close using many interlocked Hoberman Mechanisms, acting as a mechanical curtain on the award ceremony stage.<ref>{{Cite web|date=2008-12-02|title=World's Largest Unfolding Arch To Form Centerpiece Of Winter Olympics' Medal Plaza|url=https://web.archive.org/web/20081202140853/http://www.burohappold.com/BH/NWS_2001WorldsLargestUnfoldingArchToFormCe.aspx|access-date=2020-11-16|website=web.archive.org}}</ref>

=== Microwave Antennas ===
[[File:POLA Ginza Buildings.JPG|thumb|Front of the POLA Ginza building]]
The properties of a microwave antenna can be changed if its surface area changes, enabling one antenna to perform multiple functions, specifically by tuning its frequency. This design has two partially rigid pieces linked together with pin joints that adjust the two actuation (operation) rings' surface area when necessary.<ref>{{Cite journal|last=Nassar|first=Ibrahim T.|last2=Weller|first2=Thomas M.|last3=Lusk|first3=Craig P.|date=2013-05|title=Radiating Shape-Shifting Surface Based on a Planar Hoberman Mechanism|url=http://ieeexplore.ieee.org/document/6420888/|journal=IEEE Transactions on Antennas and Propagation|volume=61|issue=5|pages=2861–2864|doi=10.1109/TAP.2013.2243094|issn=0018-926X}}</ref>


== References ==
== References ==
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{{Reflist}}
{{Reflist}}

== External links ==

*https://patents.google.com/patent/US4942700A/en
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Revision as of 06:17, 16 November 2020

Two dimensional Hoberman Mechanism made of 24 angulated bars and 36 revolute joints

A Hoberman Mechanism, or Hoberman Linkage, is a deployable mechanism that turns linear motion into radial motion.

The Hoberman Mechanism is made of two angulated ridged bars connected at a central point by a revolute joint, making it move much like a scissor mechanism.[1] Multiple of these linkages can be joined together at the ends of the angulated bars by more revolute joints, expanding radially to make circle shaped mechanisms. The mechanism is a GAE (generalize angulated element) where the coupler curve is a radial straight line.[2]This allows the Hoberman Mechanism to act with a single degree of freedom, meaning that it is an over-constrained mechanism because the mobility formula predicts that it would have a smaller degree of freedom than it does. as the mechanism has more degrees of freedom than the mobility formula predicts.[3]

The kinematic theory behind the Hoberman Mechanism has been used to help further the understanding of mobility and foldability of deployable mechanisms.

History

The Hoberman Mechanism originates from the idea of making something bigger become smaller. Chuck Hoberman, a fine arts graduate from Cooper Union realized that his lack in knowledge of engineering was holding him back from creating the things he could picture in his head. He enrolled in Columbia University to get a masters in mechanical engineering.[4] After this he started working with origami, studying the way that it folded and changed shape. He soon realized that his interests lied in the expansion and shrinkage of the objects he was making. Hoberman started to experiment with different expanding mechanisms and started to create mechanisms of his own. He later patented a system that uses two identical bent rods connected in the middle by a joint; he called it the Hoberman Mechanism.[5] The creation of the Hoberman Mechanism has since helped with more mechanical discoveries and research concerning foldability and mobility of mechanisms.

Mechanics

How it Works

The Hoberman Mechanism is made of two identical angulated rods joined together at their bends by one central revolute joint. Multiple of these mechanisms can be linked by connecting the ends of the pairs together with two more revolute joints. Due to the mechanism's design, however, the revolute joints act as if they are prismatic-revolute joints because they move along a straight axis as the system changes shape. By pushing or pulling on any of the joints, the entire system moves and changes shape, gaining volume or folding into itself. These systems of linkages can be expanded to a full circle where it moves as one system, turning linear motion from a single axis of a joint into radial motion across the entire mechanism.

Kinematic Theory

Fig 1. Example of a single PRRP linkage
A Hoberman Mechanism made of12 angulated bars and 18 revolute joints

The Hoberman Mechanism is a single degree of freedom structure meaning that the system can be driven with a single actuator. The mechanism is made of two identical angulated rods joined together by a central revolute pivot and four end pivots constrained to move along a single line. Because the four end pivots are restrained in this way, the mechanism can be treated as pair of PRRP (prismatic-revolute-revolute-prismatic) mechanisms joined at a central point.[6] The two PRRP linkages trace a pair of identical straight lines from the origin of the mechanism to their coupler points, so they have the same coupler curve. The equation for the coupler curve of the PRRP linkages in a Hoberman Mechanism follows the coupler point B(x,y) in Fig 1:[3][7]

For parameters {r1,r2,α}, this equation of the coupler curve follows the equation for a strait line (y=mx). Because the two angulated rods that make up a Hoberman Mechanism are identical, they have the same r1 and r2 values and thus the same coupler curve.

A pair of PRRP linkages that share a coupler curve at a common coupler point have a single degree of freedom, which is why the Hoberman Mechanism has a single degree of freedom. The motion that the Hoberman Mechanism produces is radial motion even though it looks like linear motion because the motion follows the coupler curve, which is a radial strait line.[8]

The mobility formula for a single degree of freedom M = 3(n - 1) - 2j, where M is the degrees of freedom, n is is the number of moving elements, and j is the number of joints, predicts that a Hoberman Mechanism of 12 bars and 18 joints would have -3 degrees of freedom. That makes the Hoberman Mechanism a over-constrained mechanism because all Hoberman Mechanisms have a single degree of freedom.[3][9]

Applications

The Hoberman Mechanism has been used in many different parts of everyday life.

Art

Hoberman Sphere featured at the Liberty Science Center[10]

The Hoberman Mechanism is featured in works of art, mostly made by artist and inventor of the Hoberman Mechanism, Chuck Hoberman. Structures designed by Chuck Hoberman that included the Hoberman Mechanism were featured in The Elaine Dannheisser Projects Series from MoMA.[11] A Hoberman Sphere also was on display at the MoMA in New York as a part of the Century of the Child exhibit.[12] More large Hoberman Spheres featuring the Hoberman Mechanism are scattered around the world; they can be found anywhere from science centers around the US to wineries in France.[13]

Toys

Mega Sphere with 6 rings of Hoberman Mechanisms

The most commonly seen form of the Hoberman Mechanism is in the toy made by Chuck Hoberman called the Mega Sphere or Hoberman Sphere. The Mega Sphere is a plastic, sphere shaped toy that expands and retracts as it is pushed and pulled on. The toy is made of six full rings of Hoberman Mechanisms that are all connected to each other so as one piece of it retracts or expands, the entirety of the structure follows. They are multicolored and range in size from a meter to just a few inches.[14]

Architecture

Hoberman Arch featured at the 2002 winter Olympics in Utah

The Hoberman Mechanism has also been used in larger scale architectural projects. One of these structures is the Hoberman Arch featured the 2002 winter Olympics in Utah. The Arch was designed by Chuck Hoberman; it was built to open and close using many interlocked Hoberman Mechanisms, acting as a mechanical curtain on the award ceremony stage.[15]

References

  1. ^ [1], "Radial expansion/retraction truss structures", issued 1990-04-06 
  2. ^ You, Z.; Pellegrino, S. (1997-05-01). "Foldable bar structures". International Journal of Solids and Structures. 34 (15): 1825–1847. doi:10.1016/S0020-7683(96)00125-4. ISSN 0020-7683.
  3. ^ a b c "A kinematic theory for radially foldable planar linkages". International Journal of Solids and Structures. 44 (18–19): 6279–6298. 2007-09-01. doi:10.1016/j.ijsolstr.2007.02.023. ISSN 0020-7683.
  4. ^ "Transformer". Wired. ISSN 1059-1028. Retrieved 2020-10-29.
  5. ^ "Chuck Hoberman | Lemelson". lemelson.mit.edu. Retrieved 2020-10-29.
  6. ^ Li, Ruiming; Yao, Yan-an; Kong, Xianwen (2017-10-01). "Reconfigurable deployable polyhedral mechanism based on extended parallelogram mechanism". Mechanism and Machine Theory. 116: 467–480. doi:10.1016/j.mechmachtheory.2017.06.014. ISSN 0094-114X.
  7. ^ Sun, Xuemin; Yao, Yan-An; Li, Ruiming (2020-03-01). "Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes". Frontiers of Mechanical Engineering. 15 (1): 89–99. doi:10.1007/s11465-019-0567-5. ISSN 2095-0241.
  8. ^ Li, Ruiming; Yao, Yan’an; Kong, Xianwen (2016). Ding, Xilun; Kong, Xianwen; Dai, Jian S. (eds.). "A Method for Constructing Reconfigurable Deployable Polyhedral Mechanism". Advances in Reconfigurable Mechanisms and Robots II. Mechanisms and Machine Science. Cham: Springer International Publishing: 1023–1035. doi:10.1007/978-3-319-23327-7_86. ISBN 978-3-319-23327-7.
  9. ^ Agrawal, Sunil K. "Polyhedral Single Degree-of-freedom Expanding Structures" (PDF).{{cite web}}: CS1 maint: url-status (link)
  10. ^ "Hoberman Sphere". Liberty Science Center. Retrieved 2020-10-29.
  11. ^ "Projects 45: Chuck Hoberman | MoMA". The Museum of Modern Art. Retrieved 2020-10-29.
  12. ^ "Century of the Child: Growing by Design, 1900–2000 | MoMA". The Museum of Modern Art. Retrieved 2020-10-29.
  13. ^ Campbell-Dollaghan, Kelsey (2012-09-28). "A Giant, Working Hoberman Sphere Made From Aluminum". Fast Company. Retrieved 2020-10-29.
  14. ^ "Hoberman Sphere Toy – Hoberman Associates". Retrieved 2020-11-16.
  15. ^ "World's Largest Unfolding Arch To Form Centerpiece Of Winter Olympics' Medal Plaza". web.archive.org. 2008-12-02. Retrieved 2020-11-16.
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