Robotic Spatial Deposition for Kirchhoff–Plateau Surfaces (KPS) on Pre-Tensioned Membranes

Kirchhoff–Plateau Surfaces (KPS) represent a class of form-active systems composed of elastic rods embedded in pre-stretched membranes. These hybrid structures derive their form from the interaction between the rods’ bending stiffness and the membrane’s tensile force, and the final forms are found when two forces reach an equilibrium. As a design strategy, KPS structure can be applied for lightweight and deployable architectural systems with embedded directional stiffness (via rods).
Previous studies have demonstrated KPS fabrication through planar rod deposition using filament-based 3D printers. Building on this foundation, this study proposes a spatial deposition approach that leverages a six-degree-of-freedom robotic arm to deposit rods directly onto pre-formed, three-dimensional KPS membranes. This approach introduces several advantages, for example, (1) the deposited rods follow continuous 3D toolpaths aligned with the equilibrium geometry, allowing them to inherit curvature and torsion naturally. This results in smoother, more accurate forms without the need for extensive post-processing. (2) rods are deposited in situ and residual stress is reduced, which improves bonding between rod and membrane; and (3) the spatial deposition accommodates non-uniform curvature and localized prestretching, which allows differentiated patterning over membrane surfaces. In this way, KPS can be developed as programmable systems where structural reinforcement and environmental performance are embedded directly into the surface geometry.