Fig. 1: Evolution of reciprocal frame (RF) structures.

a Leonardo da Vinci’s woven bridge sketch in Codex Atlanticus represents one of the most famous RF concepts in the Western world, where components are supposed to be tied together at nodes. b In da Vinci’s weaving bridge, the node of the second component set is supported by the bending moment of the first set via vertical elements, and vice versa, achieving mutual reinforcement. c An early RF practice in the East is the Rainbow Bridge depicted in “Along the River During the Qingming Festival”, and the bridge achieved a span of approximately 19.4 meters. d The Rainbow Bridge also features reciprocal behavior between the first and second component sets through vertical elements. Its structural logic is relatively advanced as a realized application: components from one set (except the vertical elements) are connected as one. e Contemporary reciprocal frames have evolved into planar-like structural units, shifting the reciprocal behavior of components from reinforcement to maintaining equilibrium and adapting to more free-form shapes. f This evolution led to widespread RF applications, particularly in landscaped pavilions and residences. The shift sacrifices structural redundancy, resulting in instability if one single component fails.