Methodology for Designing Kinetic Planar Surface through Tessellation

Abstract

This paper illustrates the creation of kinetic planar surface by tessellation method. Tessellation is a traditional technique to usually cover a plane without gaps and create a decorative pattern. As we talk about kinetic design, it is an attractive strategy to solve the adaptive and responsive environmental architectural problems. Mathematical tessellation are the techniques to be used to design a surface. The purpose of this study is to develop a methodology for designing the kinetic planar surface with the help of regular tessellation technique in the area of architecture, mechanical and mathematical interdisciplinary approach. Her the method comprises of repetition of interconnected geometry, whose design derive from the symmetry that is taken from the original reference tessellation.

Introduction

I. INTRODUCTION

This paper deals with the study to develop a methodology for designing of kinetic planar surface by the use of mathematical tessellation in the area of architecture and mechanical an interdisciplinary approach. As surface design is one of the important interest for both artist and architects throughout the history.  Static architecture has been the only medium of relation between architecture and mathematics. But due to rapid change in modern activities and society the need of adaptation has emerged and kinetic architecture has gained importance b y developing in technical and construction properties. As the result of literature review, researchers and designers have considered a particular mechanism type in kinetic architecture. Therefore, the mechanism structure , number of joints and the links can be easily controlled at the same time. However, researchers design varies building with many control elements. As kinetic architecture needs a methodology to enhance the ability on various elements of building in a more easy and rapid way. This paper develops the relation between design process and architecture by kinetic means upon developing the method for kinetic planar surface. Tessellation is a common mathematical technique that is use to cover a plane without any gaps or overlaps. As it has been used to design planar surface as the facades of building. In literature tessellation usually means “tilling”. For example “portraying human begins and natural scenes are the concern of Mediterranean peoples in intricate mosaics” ”(Grunbaum and shepherd, 1986). The definition “ in mathematical approach, tilling means that accountability condition excludes families in which every tile has zero area(such as point or line segment) but nevertheless the definition admits tilling in which some tiles have bizarre shapes and properties”[1]. In mathematical approach first remarkable study was conducted by Johannes kepler in the book”Harmonice Mundi in (1619). Another important study was done by the Russian crystallographer E.S.Fedorov in 1891; he proved that every tessellation of the plane is constructed in accordance to one of the seventeen different groups of isometrics (Thinkquest, 2010). Moreover, Grünbaum and Shephard (1986) explained in their book that in the past there have been many attempts that try to describe and systematize the notation of tessellation. For instance “Bourgoin (1873, 1880, 1883, 1901), Day (1903), Dresser (1862), Edwards (1932), Meyer (1888)(figure 1).

Schauermann (1892), Wersin (1953) is noteworthy mainly for the extraordinary extent, which it plagiarizes Bourgouin (1883)[2].

Conclusion

As per the above studies and properties of methedolgy following conclusions are founded,as one of the concept of kinetic architecture is to fulfil the rapid changing of life conditions, and the result of this , the kinetic building parts should be constructed easily and cheap. this methedology can be used. the regular kinetic tessellation method, form, sixze and placement of platforms and links can easily be determined and it help in designing more comples pattern with simple construction fastly.Many architects and researchers deals with kinetic structures ends up covering the kinetic structure usually by textile or flexible material.Kinetic architecture is an interdiciplinary controversial approach between mechanism science and architecture. the rapid changes in environmental conditions effected human sourcs and architecture traditional aspect. there are few examples in application of structure as building parts .Finally the relationship between mathematical knowledge, mechanism science and building parts dereves more serious considderation in kinetic architecture.

References

[1] Alizade, Rasim. and Ca?das. Bayram. 2004. Structural Synthesis of Parallel Manipulators. Mechanism and Machine Theory 39 (8): 857-870. [2] Decagon periodic and non-periodic Tessellation. Accessed November 12, 2010 http://local.wasp.uwa.edu.au/~pbourke/texture_colour/nonperiodic [3] Grünbaum, Branko and G.C. Shephard. 1986. Tilings and Patterns. New York: W. H. Freeman and Company. [4] Grünbaum, Branko. 2006. What Symmetry Groups Are Present in the Alhambra. Notices Of the AMS 53(6): 670-673. [5] Khaira, Jaspreet. 2009. What a re Tiling and Tessellation and How a re They Used in Architecture. Young Scientist Journal 2 (7): 35-46. [6] Kinsey, L.C. and Moore, T.E. 2002. Symmetry, Shape and Space: An Introduction to Mathematics Through Geometry. New York: Key College Publishing [7] Norton, Robert.L. 2004. Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanism and Machines. Third Edition. Singapore.:McGraw-Hill. [8] Semiregular tessellations. Accessed September 24, 2009 http://mathworld.wolfram.com/SemiregularTessellation.html [9] Seymour, Dale and Jill.Britton. 1989. Introduction to Tessellations. United States of America: Dale Seymour Publications. [10] Tesselation surface. Accessed December, 14, 2009, www.5cense.com/Granada_Seville.htm. [11] Totally Tessellated: In Mathematics and Science. 1998. ThinkQuest Library: Oracle [12] ThinkQuest Library Accessed July 10 2010 http://library.thinkquest.org/16661/history/math.html [13] YAN, Hong-SEN.1998. Creative Design of Mechanical Devices. Singapore: Springer- Verlag Singapoure Pte.Ltd. [14] Zuk,William and Roger H.Clark. 1970. Kinetic Architecture NewYork: Van Nostrand Reinhold Comp.

Copyright

Copyright © 2023 Kashmika Bose, Neelam Khushwa, Nitya Durve. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.