Design Method for Radially Retractable Single DOF Plate Structure Based on Regular 1-Uniform Regular Tessellations

Abstract

Aylin GAZİ, Koray KORKMAZThis paper is concerned with a method of designing single degree of freedom (DOF) radially retractable planar plate structures (RRPS). The shape of the plates are desired to be regular polygons and they are not allowed to overlap in any configuration and no gaps in the closed configuration. The method has been developed by translating geometric knowledge of tessellation in math. Therefore the paper firstly introduces the fundamentals of tessellations and then their classification based on polygon shape. After that it proposes a method of designing RRPS by using 1-uniform regular tessellations. The method identifies the plate types, shape and the way of connecting the plates with only revolute joints. Composed of various plates and joints, the proposed RRPSs based on 1-uniform regular tessellations are single DOF multi-loop planar mechanisms. Mobility analysis is made to prove the single DOF. After various mobility analysis, a theorem is developed to find the number of excessive plates. It is also introduced that there are passive joints besides excessive plates. When more plates and revolute joints are used in architectonic applications, the excessive plates and passive joints can be removed and reassembled if necessary for aesthetic or functional reasons. Finally, a single DOF radially retractable plate structure is proposed for a building façade as a sun shade to reduce the energy consumption. ABSTRACT ÖZ ARTICLE

A New Approach to the Generation of Retractable Plate Structures Based on One-Uniform Tessellations

“…Triangle on graph represents a subchain or a 2R joints. If RPS is constructed with subchains numbered (34,10,9), (33,19,18), (31,16,30), (28,14,37), (26,25,36), and (23,22,35), only one subchain is enough to prevent the movement. If RPS is constructed with six extra R joints, the plates numbered 28, 31, 19, 10, 23, and 26 have two 2R joints, respectively, (aj, af), (am, al), (t, v), (z, t) (aa, ab) (ae, ac) instead of three R joints.…”

“…Research on the calculation of mechanism mobility is also important in understanding the accuracy of the design process. Gazi and Korkmaz investigated the mobility analysis of the RPSs [18].On the other hand, Sareh and Guest presented a number of novel concepts and definitions, which help to apply systematic variations on Miura-ori pattern. They reduced the symmetry of the Miura-ori to obtain new patterns [19,20].…”