Synthesis, Mobility, and Multifurcation of Deployable Polyhedral Mechanisms With Radially Reciprocating Motion

Abstract

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.

A New Approach to the Generation of Retractable Plate Structures Based on One-Uniform Tessellations

“…Triangle on graph represents a subchain or a 2R joints. If RPS is constructed with subchains numbered (34,10,9), (33,19,18), (31,16,30), (28,14,37), (26,25,36), and (23,22,35), only one subchain is enough to prevent the movement. If RPS is constructed with six extra R joints, the plates numbered 28, 31, 19, 10, 23, and 26 have two 2R joints, respectively, (aj, af), (am, al), (t, v), (z, t) (aa, ab) (ae, ac) instead of three R joints.…”

“…Both types were overconstrained linkages [14]. Wei and Dai proposed a more general single plane symmetric eight-bar linkage to be used in the synthesis and construction of a group of deployable platonic mechanism with radially reciprocating motion [15,16]. Gazi and Korkmaz combined polygonal plates and bars by benefiting tessellation technique to reach an expandable structure [17].…”

A Sarrus-like overconstrained eight-bar linkage and its associated Fulleroid-like platonic deployable mechanisms

“…Overconstrained mechanisms, from the simple four-bar Bennet linkage (1) to the very complex deployable truncated icosahedral mechanism (2), have never lost their fascination to researchers in the science and engineering research communities. In most of the cases, the topology of an overconstrained mechanism might indicate rigidity but it is movable, or it has more mobility than the one its topology predicts.…”

Mechanism Design with Singularity Avoidance of Crystal-Inspired Deployable Structures

“…Because a crystal-inspired deployable structure can be gradually deployed to cover a large area, it has a potential engineering application as a macroscopic or mesoscale structure.Crystals 2019, 9, 421 2 of 9 the singular point and maintaining external forces on certain joints. Wei et al [17] and Ding et al [2] proposed different types of polyhedral linkages, and proposed different types of deployable structures and further explored kinematic mobility and bifurcation behavior of these symmetric deployable structures. Recently, based on group representation theory, Chen et al [18] utilized symmetry to investigate singularity of deployable structures, and extracted new mechanisms with lower-order symmetries.…”