Mobile assemblies of four-spherical-4R-integrated linkages and the associated four-crease-integrated rigid origami patterns

Abstract

Rigid origami, which can be regarded as assemblies of spherical linkages, inspires a new paradigm of design for mechanical metamaterials and deployable structural systems with large deployable ratio. In this paper, the kinematic properties of assemblies of spherical 4R linkages are studied, and new origami patterns are obtained. Kinematics of a single loop spherical 4R linkage is firstly presented, and by assigning four specified values for the four twist angles, and defining four pairs of specified input and output angles, 16 maps between the input and output angles are obtained together with 256 types of special spherical 4R linkages. By merging four identical spherical 4R linkages into a single loop, three basic mobile assemblies are constructed and the one-degree-of-freedom kinematic compatibility condition is formulated. Through alteration of the four vertex linkages in the three basic assemblies, variations of the basic assemblies are generated. Consequently, by adding further geometric conditions, novel rigid origami patterns are obtained leading to the tessellation of the spherical-4R-linkageintegrated assemblies. Hence, this paper provides a novel approach for generating new rigid origami patterns which can lead to the development of foldable structures and tessellations with potential applications in robotics, smart architectures, and space exploration.

A Stiffness Variable Passive Compliance Device with Reconfigurable Elastic Inner Skeleton and Origami Shell

“…To alleviate above shortcomings, a tubular origami shell with Yoshimura pattern [31] is integrated to form an enclosed structure and prevent the device from twist, as shown in Figure 1. As an ancient Chinese and Japanese art of paper folding, origami is drawing more and more attention these years in the robotics field and origami robots can be defined as autonomous machines whose morphology and function are created using folding [32][33][34][35]. The Yoshimura pattern is a cylindrical folding origami that supports bending and axial folding [36][37][38].…”

Rigid foldability and mountain-valley crease assignments of square-twist origami pattern

“…The rigid origami around each vertex is treated as a spherical linkage in which the axes of all joints meet at a point [13] [14]. An origami pattern with multiple vertices is then regarded as an assembly of spherical linkages [15][16][17]. Therefore, the rigid foldability of origami patterns can be analyzed based on spherical linkages.…”