This study deals with a review of planar scissor structural mechanisms (SSMs) and reports on how they can be easily transformed from a stowed to a deployed configuration. These mechanisms have an important transformation capacity of their extension and rotation properties, and many examples have been proposed that vary in size, type and geometry. Although there are many studies dealing with designing new planar or spatial SSMs and their calculation methods, there is no systematic study demonstrating the basic typologies, geometric principles, design rules and constraints of such SSMs. Further, current calculation methods are based on the inductive approach in which the dimension of one scissor unit (SU) is given, but the span of the whole structure is found later according to the number of SUs that are used to assemble the structure. However, this approach is not convenient for architectural applications, because it requires a deductive approach in which the dimensions and required number of SUs are calculated according to defined span length. On the basis of this concept, this article, first, analyses the geometric design of SSMs systematically in terms of their possible configurations and then develops trigonometric calculation methods for different types of SSMs, using a deductive approach.

In this paper, a novel two-dimensional scissor structure that transforms between concave and convex configurations is presented. The structure is designed by a method of assembling kite or anti-kite loops in the flat configuration. Angulated units are generated from the assembled loops. Finally, a new angulated scissor unit is introduced in order to design the novel scissor structure.

Double curved geometries including hyperbolicparaboloids (hypars) have become a trend in contemporary architecture. However, most of the constructed architectural examples of the hypars are static and cannot offer any form variability. In this paper, a 2-DOF 8R linkage mechanism is introduced to buildtransformable hypar structures. It is inspired from the basic design principles of Bennett linkage. By its distinctive connection details and additional links, this novel mechanism can change its form fromplanar geometries to various hypars. The paper begins with the brief summary of the applications of hypar structures in architecture. Secondly, main principles and deficiencies of the Bennett linkage are presented. According to these deficiencies, structural synthesis of the novel mechanism is considered. Finally, advantages and potential uses of the proposed novel mechanism are explained.

When the existing literature on the research of scissor structures is thoroughly investigated, it is seen that different researchers use different terminologies and classifications especially for the definition of the primary units and the motion type. Some of the studies define the whole geometry based on the geometric properties of the primary scissor units and the unit lines while some other studies define it according to the loops. All these studies use different names for similar elements. This article aims to review the literature on the classification and terminology of scissor structures and represent the state of art on the studies. Tables are represented showing all approaches in the literature. In addition, the article criticizes the missing points of each terminology and definition, and proposes some new terminology. In order to arrive at this aim, different definitions of the primary scissor units and motion types used in key studies in the literature are investigated thoroughly. With several examples, it is demonstrated that naming the scissor units according to the resulting motion type might be misleading and it is better to specify the motion type for the whole structure. A classification for transformation of planar curves is presented.

A novel structural mechanism (SM) that is capable of transforming itself into various hyperbolic paraboloid (hypar) geometries is introduced in this paper. Composed of straight bars and novel joint types, the SM is designed based on the ruled surface generation method. Thus, the paper first investigates the geometrical properties and morphology of the hypar surface. Second, it constructs the SM and discusses its transformation capability with respect to its kinematic properties. Then, it presents a parametric model not only to analyze the geometry and possible configurations of the SM but also to prepare a model for the structural analysis. Finally, a transformable shelter structure is proposed as an architectural application of the SM and its feasibility is tested based on the structural analysis conducted in different configurations of the structure. According to the results of the structural analysis, the strength, and the stiffness of the structure are discussed in detail.