Fig. 4: Design and kinematic optimization of thick-panel origami structures with a seamless surface.
From: Thick-panel origami structures forming seamless surfaces
a Modification of the top layer pattern, removing green panels with valley creases from the top layer and the extension of adjacent yellow and blue panels to fill the space. Green panels with mountain creases remain intact. b The corresponding modifications for thick panels. The yellow panel is extended, represented by a transparent block, while the blue panel is adjusted to fit. Material from the bottom layer is selectively removed to prevent motion interference. c A modified unit with a seamless top surface and its folding process. Virtual joints M and N guide the consistent rotation of the yellow and blue panels, ensuring symmetric motion about the perpendicular bisector of line MN. d A detailed view of motion interference between the yellow and blue panels. The coordinate system X1NY1 is fixed to the blue panel as the base, and the coordinate system X2MY2 to the yellow panel as the moving platform. Points P and Q coincide at the flat state, while the motion path of P in X1NY1 is represented as a solid gray line. e The effect of panel extension length, i.e., t/d, on the panel design. For t/d = 0.5, the angularity of the tangent line remains zero, so the design parameter must also be zero, which is incompatible with thick-panel structures. Thus, asymmetrical extensions of the yellow and blue panels are essential. f The relationship between panel thickness h/d and the angularity of the tangent line. Decreasing h/d increases, with approaching as h/d nears zero.
