Geometrical universality of Truss-Z system

Abstract

Standardization and modularization are common means of simplification and economization of engineering structures. Extremely modular systems (EMS) are comprised of very few (ideally just one) types of modules and allow for creation of structurally sound free-form constructions. Truss-Z (TZ) is the EMS considered in this paper. It is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. TZ structures are composed of four variations of a single basic unit subjected to affine transformations (mirror reflection, rotation and their combination). A family of shapes including: isosceles quadrilaterals (concave and convex), regular and irregular kites and darts, isosceles triangles and trapezoids has been considered for the planar projection of Truss-Z modules (TZMs). It has been shown that isosceles triangles and trapezoids suit best TZ. The universality of TZM has been assessed by measurement of the regularity of distribution reachable points by given TZ built with several such TZMs. It has been shown that the vertex angle (θ) of 32.5° gives the most regularly distributed, thus universal TZ.