Optimization Method for the Deployment Route of Generalized Scissor Linkages

Abstract

Scissor structures, widely used in kinetic architecture, have been researched for over six decades. However, most studies focus on the deployability of the scissor structures, often disregarding the potential transformability of scissor loops that allow changing the curvature. Three scissor units, namely, translational, polar, and angulated units, do not adhere to the trajectory of an arc suitable for a transformable canopy structure. Although the deployment route of the polar version aligns with this trajectory, it is impractical for achieving transformability due to deviations. Therefore, the paper presents a novel approach to optimize generalized scissor linkages (GSLs), consisting of symmetrical and identical scissor units. Defined by three variables, GSL is introduced to address the transformability issue, and the optimization method is developed. According to this method, the selected polar scissor is modified to synthesize the GSL version. It is demonstrated that no GSL is composed of identical and symmetrical units deploying precisely along the arc trajectory. Nevertheless, the proposed optimization method enables the output GSL to converge toward the desired route. Three basic scissor unit types can be represented by a single parameterized GSL, effectively unifying different scissor linkages under a single definition. Scissor linkages find extensive applications in kinetic architecture, such as domes, canopies, tents, emergency bridges, temporary shelters, and responsive facades. Existing studies on such linkages predominantly focus on deployed and contracted configurations of these mechanical structures. This study diverges by attempting to establish intermediate phases for designing such structures that can adapt to changing environmental conditions or user needs. To achieve the objective, the scissor linkage must move within a defined range, conceptualized as an arc of a circle. For instance, by tracking the movement of the sun, one can ensure a consistent positioning of shadowed areas beneath an architectural canopy. None of the existing scissor linkages composed of basic translational, polar, and angulated units in the literature moves along this trajectory precisely. Only polar linkages approximate the desired route despite their large deviations. The generalized scissor linkage (GSL) introduced in the paper with distinct parameters demonstrates fewer deviations. Hence, an attempt is made to synthesize the GSL as the optimized version of the polar linkages. The mathematical foundation of the optimization method is introduced. It is foreseen that this method holds the potential to evolve into a versatile design tool in the future.