Kinetics and Design of Semi-Compliant Grid Mechanisms

Abstract

The research of transformable structures has fascinated architects, engineers, and mathematicians (e.g. E. Piniero, C. Hoberman, F. Otto, S. Finsterwalder). Their potential to adapt to environmental conditions and user’s needs, or to aid the erection process has produced beautiful and complex designs (e.g. Hoberman sphere, Multihalle Mannheim). We can distinguish between conventional, discrete rigid-body-mechanisms and so-called compliant mechanisms, which utilize the elasticity of members to perform controlled elastic deformations (Howell (2001)). Recent developments in elastic gridshell construction have utilized this kinetic behaviour for the construction process and transformation (X-Shells, G-Shells, Inside/-Out). This paper aims to unravel the categories of such kinetic gridshells, and presents fundamental principles of semi-compliant quadrilateral grid structures with uniaxial rotational (scissor) joints built from initially straight, continuous beams. We use specific lamella profiles that restrict the elastic deformability, disabling at least one of the three local bending axes. Depending on the orientation of the profiles, we can categorize three families – doubly ruled (straight), geodesic and asymptotic networks – each exhibiting distinct kinetic properties with limited degrees of freedom. We verify our theory using a matrix of 3 x 2 basic/fundamental grid configurations. By controlling the structure’s parameters, we can design their shape and behaviour. Introducing the curvature-square diagram further allows us to understand and predict their kinetic performance. We present architectural applications of both experimental and built structures and apply our theory to a novel design for the kinetic umbrella, a transformable asymptotic gridshell.