Configuration synthesis of linear foldable over-constrained deployable unit based on screw theory

https://doi.org/10.1016/j.mechmachtheory.2020.104163Get rights and content

Highlights

  • Configuration synthesis method for over-constrained deployable mechanisms is proposed.

  • Principles which the over-constrained deployable units should meet are summarized.

  • Configuration requirements of the kinematic pairs of deployable units are analyzed.

Abstract

According to a description of the topology structure of deployable antennas, this work proposes the configuration synthesis method of over-constrained deployable units on the basis of screw theory and conducts example analyses on the basis of an analysis method and certain design steps. First, the basics of screw theory are introduced in detail, and an over-constrained deployable unit is represented by a screw. Second, through over-constraint analysis, the kinematic pair configurations of the mechanism under over-constraint have been established. Third, according to the general process of the deployable unit with common over-constraints proposed in this paper, the example is analyzed in detail. Finally, the model is verified according to the obtained configuration synthesis results. The cubic deployable unit mechanism is obtained through 3D printing, and the folding function is tested to verify the correctness of the theoretical analysis, which can provide theoretical reference for the mechanism design of large deployable units.

Introduction

Since the first artificial satellite antenna was used in 1958, large space-borne antenna technology has rapidly been developed. Many application fields, such as space communication, space observation, electronic reconnaissance, and exploration, have proposed different functional requirements for space-borne antennas. Meanwhile, the demand and the technical performance requirements for these antennas are growing [1], [2]–-3]. The mechanisms of space antennas are important parts of antenna systems. They play a role in unfolding, forming, and supporting the reflection surfaces of antennas and provide sufficient stiffness and precision. The structure and performance of these mechanisms are critical for the performance of antenna systems. At present, mechanisms of satellite-borne antennas used in orbit usually have characteristics such as light weight, and high stability [4]. Large-diameter space antennas should be folded compactly as minimal stowed volumes are needed before launch, and deployed normally in orbit. [5], [6], [7]. In accordance with the compositions of the working surfaces of antennas, deployable antennas can be divided into three categories: solid reflector deployable antennas, inflatable deployable antennas, and metal mesh deployable antennas [8]. Metal mesh deployable antennas have become a research hotspot due to their high deployment accuracy, large diameter, and mature technology. The truss deployable antenna developed by the engineering test satellite ETS-VII and launched by Japan in December 2006 is a representative metal mesh deployable antenna. The outstanding feature of this antenna is that it comprises 14 hexagonal prism modules that have a diameter of 4.8 m and consists of six basic units [9–10]. Russia has successfully developed a tetrahedral modular deployable antenna. The basic unit of this kind of truss antenna is a tetrahedron that can be unfolded and folded. The vertices and undersides of multiple tetrahedral elements are inverted with each other to form a tetrahedral modular deployable antenna [11]. Furthermore, Canada's RADARSAT-1/2 satellite antenna support mechanism is composed of triangular pyramid units [12,13]. Launched at the end of 2000, Thuraya satellite, with a 12 m diameter, is an AstroMesh circular truss developable antenna; the developable antenna support structure mainly comprises interconnected quadrilateral units, each of which has a variable-length diagonal rod; the diagonal bars of adjacent units are arranged in reverse order, and this feature is used to achieve mechanism motion [14], [15], [16], [17]–18]. The advantage of annular truss deployable antennas is that their mass does not increase proportionally with any increase in diameter; moreover, these antennas have a large folding ratio and a small mass. However, when the diameter reaches or exceeds 100 m, all existing antenna forms cannot meet the required stiffness and folding ratio. The antenna support truss is composed of several identical modules or basic units. With the assumption that one module is composed of a plurality of units, the basic unit is deemed the minimum structural unit of the support truss. Therefore, basic units are the key factor in constructing a new large deployable structure, and the design of large spatial antennas is the innovative design of basic units.

Currently, the commonly used units of deployable mechanisms can be divided into the following types: scissor type, polyhedron deployable type, and space over-constrained type. You and Pellegrino[19,20], Tanaka et al.[21], Zhao et al.[22], and Lu et al.[23] proposed a set of deployable structures composed of scissor mechanisms. However, as the diameter of the deployable mechanisms increases, the mass of scissor mechanisms becomes excessively large to meet the mass limit of spacecraft. Therefore, scissors are unsuitable for large deployable structures. Wohlhart[24], Gosselin and Gagnon–Lachance[25], Kiper[26,27]. Ding et al. [28,29] have studied polyhedral deployable units. By placing planar linkages into regular polyhedral surfaces and combining various planar polygonal linkages, polyhedral deployable structures are obtained. However, few networking methods are available for building large deployable mechanisms by connecting multiple polyhedral deployable units. In addition, existing polyhedral deployable units have a small folding ratio, which is unsuitable for large space deployable mechanisms. Space over-constrained units has become a research hotspot for their high folding ratio and large stiffness. You and Chen proposed modified Bennett, Myard, and Bricard linkages and various space closed-loop over-constrained deployable mechanisms [30], [31], [32]–33] on the basis of single-loop over-constrained space linkages. They have collaborated with Liu [34], Song [35], Chai[36], Yoda[37], Lengyel[38], and Baker[39] to study the kinematics and exotic configurations of over-constrained deployable mechanisms. Dai and Wei have proposed several over-constrained deployable mechanisms [40], [41], [42], [43], [44]–45]. Other researchers have also done a lot of research and achieved remarkable results[46], [47], [48], [49], [50], [51]–52]. The folding motions of the existing over-constrained units are often space motions due to the specific geometric requirements, thereby resulting in inconvenient folding. In general, the deployment motion of the common units of the spatial deployable mechanism is a simple plane motion. In summary, basic units of deployable mechanisms have various types. The linear folding type deployable unit is in a straight line after folding. It has a small size and can effectively increase the volume ratio. Thus, it is suitable for large diameter antennas. However, no existing suitable over-constrained linear folding deployable unit exists that can be used to build large double-loop deployable antennas. Therefore, a new over-constrained linear folding mechanism unit should be constructed. The analysis method of the configuration synthesis of the deployable mechanism is the key to the innovative design of the configuration.

Space multi-loop structure synthesis is an effective innovative design method of mechanism; however, the latest research on space multi-loop structure synthesis in recent years primarily focuses on parallel mechanism, which is divided into five categories[53], namely, displacement subgroup method [54], motion synthesis method [55,56], Gf set theory[57], screw theory [58], [59], [60], [61], [62]–63], and Li's group theory [64,65]. The synthesis method of Parallel mechanisms has a reference value for deployable mechanisms. Therefore, in this study, the synthesis theory of parallel mechanisms is applied to a deployable mechanism to obtain a new deployable mechanism. In configuration synthesis theory, graph theory is suitable for the configuration synthesis of planar deployable mechanisms. However, it cannot handle the over constraint in space mechanisms and the configuration synthesis of space deployable mechanisms. The Lie group theory also has its own limitations. Particularly, a large part of the motion subsets of space rigid body motion do not have a displacement subgroup structure, and Lie groups cannot describe and analyze such motion. The principle of screw theory is clear and easy to understand, the description of over-constraint in mechanisms is well defined, and great achievements have been made in mechanism configuration synthesis. Therefore, in this study, the configuration synthesis method of basic units of mechanisms is researched on the basis of screw theory.

The rest of this paper is as follows. The screw representation of an over-constrained deployable unit is presented in Section 2. Kinematic pairs of over-constrained mechanism are configured in Section 3. The configuration synthesis of deployable units in the presence of common constraints is discusses in Section 4. The linear folding over-constrained triangular pyramid and quadrangular prism are used as examples to verify the deployable performance of the unit.

Section snippets

Screw representation of kinematic pairs

Screws can conveniently describe the kinematic pairs of mechanisms. Revolute pairs (R) are usually described by lines (zero-pitch screws), whereas prismatic pairs (P) are described by couples (infinite-pitch screws)[66]. According to the kinematics, the lower kinematic pairs, including spherical pairs (S), universal pairs (U), and other pairs, can be simplified to combination of R, P and H pairs(Helical pair). The common kinematic pairs in the deployable unit mechanism include revolute,

Kinematic pair configuration under over-constraint

According to the Eqs. (2-16) and (2-21), the axes of the kinematic pairs that can realize continuous folding motion under the common constraint and the conditions which their spatial positions must meet are deduced.

Process of configuration synthesis

The process of establishing the configuration synthesis of a deployable unit with common over-constraints is shown in Fig. 2.

Analysis of examples

Taking the linear folding triangle pyramid and quadrangular prism as examples, the process of the configuration synthesis of deployable units with common over-constraints proposed is introduced in detail.

Conclusions

Based on a description of topological structure, a screw theory-based synthesis method for over-constrained deployable mechanisms is proposed. First of all, the screw representation of the kinematic pair of a deployable mechanism unit is presented. Then, based on the virtual work principle, the sufficient and necessary conditions that the deployable unit can achieve continuous folding under constraints are obtained. The basic principles which the configuration of kinematic pair of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This project is supported by Self-Planned Task (NO. SKLRS202004C of State Key Laboratory of Robotics and System (HIT), Open Project of Space Structure and Mechanism Technology Laboratory of China Aerospace Science and Technology Group Co. Ltd, the National Natural Science Foundation of China (51835002 & 51675114), the Joint Funds of the National Natural Science Foundation of China (Grant No. U1637207) and the College Discipline Innovation Wisdom Plan in China (Grant No. B07018). These supports

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