A review of planar scissor structural mechanisms: geometric principles and design methods

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.