Deployable Polyhedral Mechanisms Research Articles

Sarrus-inspired deployable polyhedral mechanisms

Deployable polyhedral mechanisms (DPMs) have witnessed flourishing growth in recent years because of their potential applications in robotics, space exploration, structure engineering, and so forth. This paper firstly presents the construction, mobility and kinematics of a family of Sarrus-inspired deployable polyhedral mechanisms. By carrying out expansion operation and implanting Sarrus linkages along the straight-line motion paths, deployable tetrahedral, cubic and dodecahedral mechanisms are identified and constructed following tetrahedral, octahedral, and icosahedral symmetry, respectively. Three paired transformations with synchronized radial motion between Platonic and Archimedean polyhedrons are revealed, and their significant symmetric properties are perfectly remained in each work configuration. Subsequently, with assistant of equivalent prismatic joints, the equivalent analysis strategy for mobility of multiloop polyhedral mechanisms is proposed to significantly simplify the calculation process. This paper hence presents the construction method and equivalent analysis of the Sarrus-inspired DPMs that are not only valuable in theoretical investigation, but also have great potential in practical applications such as mechanical metamaterials, deployable architectures and space exploration.

Hamiltonian-path based constraint reduction for deployable polyhedral mechanisms

Most of the deployable polyhedral mechanisms (DPMs) are multi-loop overconstrained mechanisms that causes barriers for their applications due to the issues in assembly, operation and control. Yet, constraint reduction for these multi-loop overconstrained mechanisms is extremely challenging in kinematics. In this paper, by introducing the Hamiltonian path to investigate the 3D topological graphs of a group of Sarrus-inspired DPMs, we propose a systematic method for constraint reduction of multi-loop overconstrained DPMs. We demonstrate that through the removal of redundant joints with the assistant of tetrahedral Hamiltonian path, one equivalent simplest topological graph of tetrahedral mechanism is identified as a reduction basic unit. Subsequently, one simplest form of Sarrus-inspired cubic mechanism is obtained by investigating two Hamiltonian paths of its dual octahedron and sequentially arranging basic units. Furthermore, a total of nineteen simplest forms of Sarrus-inspired dodecahedral mechanisms are identified from seventeen Hamiltonian paths of its dual icosahedron. The overconstraints in each simplest Sarrus-inspired DPM are greatly reduced while preserving the original one-degree-of-freedom (DOF) motion behavior. The method proposed in this paper not only lays the groundwork for further research in wider deployable polyhedrons, but also inspires the reduction of other multi-loop overconstrained mechanisms, with potential applications in the fields of manufacturing, architecture and space exploration.

Deployable polyhedral mechanisms with radially reciprocating motion based on novel basic units and an additive-then-subtractive design strategy

This paper is to deal with the mechanism design problem for constructing deployable polyhedral mechanisms on the basis of novel basic units with an additive-then-subtractive design strategy. The aimed deployable polyhedral mechanisms can be, but are not limited to, Platonic and Archimedean solids. The basic units involved in the type synthesis process refer to one-degree-of-freedom regular polygonal prisms, whose deployable performance has been already proven to be excellent. To show the procedure of the type synthesis method, the case study on a deployable regular-tetrahedron mechanism is presented as a design example. The mobility properties of the proposed deployable regular-tetrahedron mechanism are then confirmed with the combination of screw theory and line geometry. In addition, the kinematic model is presented to study the deployable performance of deployable polyhedral mechanisms. By adopting the proposed type synthesis method, novel deployable Platonic and Archimedean polyhedral mechanisms are proposed with wider-margin radially reciprocating motion. This work not only provides the design and analysis method but also contributes new types of mechanisms, hoping to have a reference for the research of deployable polyhedral mechanisms.

Deployable scissor mechanisms derived from non-crossing angulated structural elements

This paper focuses on exploring and generalizing a scissor structural element, termed non-crossing angulated element (NCAE), in the context of unlocking its unexplored design potential and further broaden its applicability to deployable scissor mechanisms. Three types of NCAE assemblies are proposed and termed Types I, II, and III NCAE. The geometrical conditions of these NCAE assemblies are established to maintain an invariable subtended angle during motion. Based on Type I NCAE, a new construction method of double-ring mechanism that can transform the shape between two specified polygons with an equal number of sides is proposed. Owing to the scissor structure of NCAE, a novel deployable polyhedral mechanism with radially reciprocating motion but no singularity is synthesized. Relying on the advantage of the shape transformation property from NCAE, we incorporate this element with a straight scissor element and construct deployable polyhedral mechanisms with radial expansion motion to obtain a large deformation capability. To validate all the formed mechanisms, both computer model simulations and constructed prototype demonstrations are conducted. The results demonstrate the feasibility of the proposed mechanisms and synthesis approaches.

A class of N-sided antiprism deployable polyhedral mechanisms based on an asymmetric eight-bar linkage

An asymmetric eight-bar linkage is used as the basic unit to develop a group of N-sided antiprism (N⩾3) mechanisms. First, the geometric properties and kinematics equations of the asymmetric eight-bar linkage are investigated. When the kinematic conditions hold, an asymmetric eight-bar linkage and a single-plane or double-plane symmetric eight-bar linkage can be coupled. Second, the concept of axis groups is proposed, and virtual-center-based method is applied to construct a class of deployable polyhedral mechanisms based on N-sided antiprism polyhedrons; the motion bifurcation characteristics of the mechanisms are revealed by analyzing the singularity of the eight-bar linkages. These mechanisms may perform motion bifurcation in multiple different positions; therefore, these mechanisms are capable of having many different configurations that can increase their application potential for adapting to different tasks and working environments. Finally, the motion unit H is constructed based on the axis group and used as the deployable unit to synthesize a deployable mechanism with 120 loops based on a rhombic triacontahedron. Moreover, H can replace the double-plane symmetrical eight-bar linkage in other deployable polyhedral mechanisms to construct mechanisms with larger work space.

Design and Analysis of Reconfigurable Deployable Polyhedral Mechanisms With Straight Elements

Abstract This paper presents the construction method of a family of reconfigurable deployable polyhedral mechanisms (RDPMs) based on straight elements. First, reconfigurable straight element (RSE) is designed from two aspects: two prismatic-revolute-revolute-prismatic mechanisms aspect and reconfigurable angulated element aspect, and the kinematics and multifurcation of RSE are investigated. Then reconfigurable multiple straight elements (RMSEs) with n pairs of straight elements are proposed, RMSEs can reach two different transition configurations, the constraint conditions of RMSEs at transition configuration I and transition configuration II are analyzed with all link lengths identified. Finally, two typical polyhedra are used as a basis to construct RDPMs to verify the feasibility of the proposed construction method. A combination of half platforms and whole platforms for the first time is used in the construction of RDPMs, and the obtained mechanisms can switch between two kinds of conventional deployment configurations (the Hoberman sphere motion configuration and radially reciprocating motion configuration) and their compound configurations.

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

This paper, for the first time, presents an overconstrained spatial eight-bar linkage and its application to the synthesis of a group of Fulleroid-like deployable platonic mechanisms. Structure of the proposed eight-bar linkage is introduced, and constrain and mobility of the linkage are revealed based on screw theory. Then by integrating the proposed eight-bar linkage into platonic polyhedron bases, synthesis of a group of Fulleroid-like deployable platonic mechanism is carried out; which is demonstrated by the synthesis and construction of a Fulleroid-like deployable tetrahedral mechanism. Further, mobility of the Fulleroid-like deployable platonic mechanisms is formulated via constraint matrices by following Kirchhoff’s circulation law for mechanical networks, and kinematics of the mechanisms is presented with numerical simulations illustrating the intrinsic kinematic properties of the group of Fulleroid-like deployable platonic mechanisms. In addition, a prototype of the Fulleroid-like deployable spherical-shape hexahedral mechanism is fabricated and tested; verifying the mobility and kinematic characteristics of the proposed deployable polyhedral mechanisms. Finally, application of the proposed deployable platonic mechanisms is demonstrated in the development of a transformable quadrotor. This paper hence presents a novel overconstrained spatial eight-bar linkage and a new geometrically intuitive method for synthesising Fulleroid-like regular deployable polyhedral mechanisms that have great potential applications in deployable, reconfigurable and multifunctional robots.

A family of reconfigurable deployable polyhedral mechanisms based on semiregular and Johnson polyhedra

This paper proposes and designs reconfigurable double angulated element (RDAE) and reconfigurable multiple angulated element (RMAE). A family of reconfigurable deployable polyhedral mechanisms (RDPM) based on semiregular and Johnson polyhedra are synthesized by using RDAE and RMAE. The obtained RDPMs can deploy in Hoberman sphere motion (HSM) and Radially Reciprocating Motion (RRM). The constraint conditions and geometric parameters (angles and link lengths) of RDAE are identified by considering the constraints of two pairs of angulated elements and three intersected axes. The kinematics of RDAE in HSM mode and RRM mode are also analyzed. RMAE is further investigated with its constraints and parameters identified. The construction steps of RDPMs based on semiregular and Johnson polyhedra are introduced separately, and reconfigurable deployable triangular prismatic mechanism and reconfigurable deployable triangular cupola mechanism as two examples are constructed in computer as well as in reality to verify the feasibility of RDAE, RMAE and the proposed construction method.

Reconfigurable deployable polyhedral mechanism based on extended parallelogram mechanism

This paper dealt with the construction of a novel class of reconfigurable deployable polyhedral mechanisms (RDPMs). A parallelograms mechanism was designed by considering layers of links and size of revolute joints, and extended parallelogram mechanisms (EPaM) were constructed for the first time by inserting angulated elements and scissor-like elements into the parallelogram mechanism. The detailed parameters and magnification ratios of two kinds of EPaMs were calculated. A method was then proposed for constructing RDPMs based on EPaMs. The proposed method can provide more modular linkages for RDPMs, and all polyhedra constituted by regular polygons can be used to construct RDPMs. The obtained RDPMs can be reassembled by increasing or decreasing the number of basic elements to change the sizes beyond their deployment capacity. A prototype of reconfigurable deployable hexahedral mechanism based on EPaMs was fabricated to verify the feasibility of this class of RDPMs, and three reconfigurable deployable hexahedral mechanisms in three sizes based on the prototype were reassembled and tested.

A class of reconfigurable deployable platonic mechanisms

This paper deals with the design of a new class of reconfigurable deployable Platonic mechanisms (RDPMs). At first, reconfigurable angulated element (RAE) with four half-platforms is designed and analyzed based on the reconfigurable property of angulated element. Using RAE as module, a method of synthesizing RDPMs is then proposed and three RDPMs are constructed. Starting from Type I generalised angulated element (GAE), a reconfigurable generalised angulated element (RGAE) comprised of two GAEs is investigated with its reconfigurable conditions identified. n pairs of straight elements (SE) and n pairs of angulated elements (AE) are further inserted into 2-RGAEs to construct n-SEs-2-RGAEs and n-AEs-2-RGAEs. The fully-retracted state and fully-expanded state of n-SEs-2-RGAEs and n-AEs-2-RGAEs are also detailed. Using 1-AE-2-RGAEs, three RDPMs with large magnification ratio are constructed in 3D software and fabricated using aluminum to verify their feasibility. This work provides a systematic approach to the design of RDPMs which can switch between two kinds of conventional deployable polyhedral mechanisms, including deployable polyhedral mechanisms with radially reciprocating motion and Hoberman spheres.

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

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.

Double–link expandohedra: a mechanical model for expansion of a virus

Double–link expandohedra are introduced: each is constructed from a parent polyhedron by replacing all faces with rigid plates, adjacent plates being connected by a pair of spherically jointed bars. Powerful symmetry techniques are developed for mobility analysis of general double–link expandohedra, and when combined with numerical calculation and physical model building, they demonstrate the existence of generic finite breathing expansion motions in many cases. For icosahedrally symmetric trivalent parents with pentagonal and hexagonal faces only (fullerene polyhedra), the derived expandohedra provide a mechanical model for the experimentally observed swelling of viruses such as cowpea chlorotic mottle virus (CCMV). A fully symmetric swelling motion (a finite mechanism) is found for systems based on icosahedral fullerene polyhedra with odd triangulation number, T ⩽ 31, and is conjectured to exist for all odd triangulation numbers.