Geometric Design of Deployable Spatial Structures Made of Three-Dimensional Angulated Members
Publication: Journal of Architectural Engineering
Volume 26, Issue 3
Abstract
During their early development, deployable structures were constructed using translational and polar scissor units. The discovery of angulated units revolutionized the field and popularized radially deployable geometries. This paper presents a geometric design method for axisymmetric grid structures made of three-dimensional angulated scissor units on a regular polygonal base. The method is applied to a series of forms, namely: positive, zero, and negative curvature shapes, and validated using a graphical procedure. The paper also describes the kinematic analysis of deployable planar rings and three-dimensional axisymmetric grids. Position, velocity, and acceleration (PVA) analyses provided insights into the structures' motion characteristics and the influence of geometric parameters on their deployment and folding.
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Acknowledgments
The authors are grateful to the School of Architecture at the University of Illinois at Urbana-Champaign for making its resources available for this research.
Notations
The following symbols are used in this paper:
- a
- acceleration of a point;
- hi
- height of the ith tier;
- k
- shorter dimension of a scissor member in a polar unit;
- l
- semi-length of an angulated member; longer dimension of a scissor member in a polar unit;
- N
- number of tiers along the vertical;
- Ni
- ith tier;
- n
- number of polygonal sectors in plan;
- O
- center of polygon;
- pi
- hinge-point between angulated members of the ith tier;
- qi
- end point of angulated member of the ith tier;
- R
- outer radius of polygon formed by angulated units;
- Ri
- outer radius of polygon in the ith tier;
- r
- inner radius of polygon formed by angulated units;
- ri
- inner radius of polygon in the ith tier;
- V
- velocity of a point;
- αi
- subtended angle of an angulated unit in the ith tier;
- β
- deployment angle;
- γ
- deployment angle;
- θCi
- kink angle of between the semi-lengths a circumferential member of the ith tier;
- θi
- kink angle between the semi-lengths of an angulated member of the ith tier;
- θMi
- kink angle between the semi-lengths of a meridional member of the ith tier;
- λ
- angle between semi-lengths of angulated members in a scissor unit;
- φi
- joint angle in the ith tier; and
- ω
- angular velocity.
References
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Information & Authors
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Published In
Journal of Architectural Engineering
Volume 26 • Issue 3 • September 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: May 1, 2019
Accepted: Jan 28, 2020
Published online: Jun 16, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 16, 2020
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