Publication: Development of algorithm for the formation of self-assembly structure using shape-changeable tetrahedron units
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Date
2023-05-01
Authors
Kang Seng Yiak
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Abstract
Self-assembly is a spontaneous process in which an aggregation of structure organized from individual component forms a stable ordered complex structure without external assistance. This study is a basic theoretical study on potential application of self-assembly process in architectural engineering. The main aims are the determination of suitable basic building block and formulation of algorithm for its movement during self-assembly process taking idea from self-assembly process in nature. The basic building block called Shape-Changeable Molecular Tetrahedron which is a combination of regular tetrahedron and tetrahedral molecular geometry has been firstly created and designed. It contains one centroid, four vertices (one air vertex, one behind vertex and two side vertices), four centroid-to-vertex actuators and six length-changeable vertex-to-vertex struts. The basic unit of shape-changeable molecular tetrahedron was created firstly using SOLIDWORKS and then imported into 3ds Max with certain simplifications for the purpose of simulation of self-assembly process. A simple rolling gait algorithm based on simple Euclidian geometry was formulated and developed to solve the movement of the molecular tetrahedron. The shape changeability of the molecular tetrahedron unit was an essential feature for the movement which was achieved by the extension and contraction of the actuators and struts. Every molecular tetrahedron underwent a complete rolling gait locomotion based on the simple basic rolling gait algorithm in the following five-step process involving changes in coordinates of vertices and centroid while observing strut length limit, actuator length limit and condition of vertex remaining on the plane of the site: i. movement of air vertex and centroid, ii. movement of behind vertex and centroid, iii. movement of air vertex, iv. movement of behind vertex and v. movement of centroid. Three types of rolling gaits were used for successful completion of self-assembly process: forward rolling gait, backward rolling gait for obstacle avoidance and climbing rolling gait. The following three conditions were specified for every unit to self-aware on the types of rolling gaits to execute: i. Condition I: checking of centroid-to-centroid distance of units for backward movement to avoid collision, ii. Condition II: checking of distance to target by behind vertex for forward movement, iii. Condition III: checking of units’ vertex-to-vertex distance for unit connection for climbing movement. Three different cases of final target assembled structures, namely Hexagon Form (Case 1), Arch Form (Case 2) and Tower Form (Case 3), were used to investigate the different pathways of rolling gait along which randomly located shape-changeable molecular tetrahedron units navigated freely to form successfully different final assembled structures. This basic study has yielded a workable basic unit and simple rolling gait algorithm for self-assembly which forms the first step towards application in architectural engineering.