Extending the method coined virtual-center-based (VCB) for synthesizing a group of deployable platonic mechanisms with radially reciprocating motion by implanting dual-plane-symmetric 8-bar linkages into the platonic polyhedron bases, this paper proposes for the first time a more general single-plane-symmetric 8-bar linkage and applies it together with the dual-plane-symmetric 8-bar linkage to the synthesis of a family of one-degree of freedom (DOF) highly overconstrained deployable polyhedral mechanisms (DPMs) with radially reciprocating motion. The two 8-bar linkages are compared, and geometry and kinematics of the single-plane-symmetric 8-bar linkage are investigated providing geometric constraints for synthesizing the DPMs. Based on synthesis of the regular DPMs, synthesis of semiregular and Johnson DPMs is implemented, which is illustrated by the synthesis and construction of a deployable rectangular prismatic mechanism and a truncated icosahedral (C60) mechanism. Geometric parameters and number synthesis of typical semiregular and Johnson DPMs based on the Archimedean polyhedrons, prisms and Johnson polyhedrons are presented. Further, movability of the mechanisms is evaluated using symmetry-extended rule, and mobility of the mechanisms is verified with screw-loop equation method; in addition, degree of overconstraint of the mechanisms is investigated by combining the Euler's formula for polyhedrons and the Grübler–Kutzbach formula for mobility analysis of linkages. Ultimately, singular configurations of the mechanisms are revealed and multifurcation of the DPMs is identified. The paper hence presents an intuitive and efficient approach for synthesizing PDMs that have great potential applications in the fields of architecture, manufacturing, robotics, space exploration, and molecule research.

This paper presents two integrated planar-spherical overconstrained mechanisms that are inspired and evolved from origami cartons with a crash-lock base. Investigating the crash-lock base of the origami cartons, the first overconstrained mechanism is evolved by integrating a planar four-bar linkage with two spherical linkages in the diagonal corners. The mechanism has mobility one and the overconstraint was exerted by the two spherical linkages. This mechanism is then evolved into another integrated planar-spherical overconstrained mechanism with two double-spherical linkages at the diagonal corners. The evolved mechanism has mobility one. It is interesting to find that the double-spherical linkage at the corner of this new mechanism is an overconstrained 6R linkage. The geometry evolution is presented and the constraint matrices of the mechanisms are formulated using screw-loop equations verifying mobility of the mechanisms. The paper further reveals the assembly conditions and geometric constraint of the two overconstrained mechanisms. Further, with mechanism decomposition, geometry and kinematics of the mechanisms are investigated with closed-form equations, leading to comparison of these two mechanisms with numerical simulation. The paper further proposes that the evolved overconstrained mechanism can in reverse lead to new origami folds and crease patterns. The paper hence not only lays the groundwork for kinematic investigation of origami-inspired mechanisms but also sheds light on the investigation of integrated overconstrained mechanisms.

Artificial muscles are promising in soft exoskeletons, locomotion robots, and operation machines. However, their performance in contraction ratio, output force, and dynamic response is often imbalanced and limited by materials, structures, or actuation principles. We present lightweight, high–contraction ratio, high–output force, and positive pressure–driven X-crossing pneumatic artificial muscles (X-PAMs). Unlike PAMs, our X-PAMs harness the X-crossing mechanism to directly convert linear motion along the actuator axis, achieving an unprecedented 92.9% contraction ratio and an output force of 207.9 Newtons per kilogram per kilopascal with excellent dynamic properties, such as strain rate (1603.0% per second), specific power (5.7 kilowatts per kilogram), and work density (842.9 kilojoules per meter cubed). These properties can overcome the slow actuation of conventional PAMs, providing robotic elbow, jumping robot, and lightweight gripper with fast, powerful performance. The robust design of X-PAMs withstands extreme environments, including high-temperature, underwater, and long-duration actuation, while being scalable to parallel, asymmetric, and ring-shaped configurations for potential applications.

This paper investigates the mobility and kinematics of the Hoberman switch-pitch ball, and particularly, its variant that does not resort to bevel gears. The ball variant is a general case of the Hoberman switch-pitch ball and constitutes the ball. This paper starts from examining the geometry of the ball variant and its composition, and decomposes it into loops containing eight-bar radially foldable linkages. To investigate the eight-bar radially foldable linkage, constraint matrices are developed using the screw-loop equation. This paper extends the study to the ball variant and investigates the singularity and various configurations based on the geometry and kinematics of the ball variant. This leads to the investigation of the Hoberman switch-pitch ball as a special case of the ball variant with bevel gears to simultaneously drive three joints in every vertex of the ball mechanism. The analysis is then followed by a numerical demonstration of the kinematic characteristics of the Hoberman switch-pitch ball.

This paper presents for the first time a novel two degrees of freedom (2-DOF) single-looped dual-plane-symmetric spatial eight-bar linkage with exact straight-line motion. Geometry and kinematics of the eight-bar linkage are investigated and closed-form equations are presented revealing the exact straight-line motion feature of the linkage on the condition that two symmetric inputs are given. In order to secure two symmetric inputs, a geared eight-bar linkage is then proposed converting the linkage into a 1-DOF linkage of exact straight-line motion. The direction of the straight-line motion produced by the proposed eight-bar linkage is changeable and is only dependent on the structure parameters of the two pairs of V-shaped R-R dyads of the linkage. Further, the proposed eight-bar linkage is applied to the synthesis and construction of a group of deployable Platonic mechanisms with radially reciprocating motion. The virtual-center-based (VCB) method is presented for the synthesis and prototypes of the deployable Platonic mechanisms are fabricated verifying the mobility and motion of the proposed mechanisms.