•In order to obtain a series of quadrangular prisms deployable units (QPDUs) which can be folded into a straight line, a topology structure synthesis and analysis method based on graph theory is ...proposed in this paper.•Graphs of statically determinate QPDUs are synthesized.•Combined with graph properties, a procedure for synthesizing conceptual configurations of QPDUs is obtained.•All 78 kinds of QPDUs are discovered by using synthesis approach mentioned in this paper.
This study proposes a conceptual configuration synthesis method based on graph theory to obtain a series of quadrangular prismatic deployable units (QPDUs) which can be folded into a straight line. Firstly, according to graph theory, graphs of statically determinate QPDUs are synthesized. Secondly, in order to establish the conceptual configuration of QPDUs, weighted graph, weighted adjacency matrix and some rules are analyzed. Combined with graph properties, a procedure for synthesizing conceptual configuration of QPDUs is obtained. Finally, all 78 kinds of QPDUs are discovered by using synthesis approach mentioned above. These QPDUs are then used to build large deployable space mechanisms, such as mast, planar and hoop mechanisms, in different construction methods. This study expands the deployable unit configuration library, and the method can provide experience for the theoretical research in aerospace deployable mechanisms.
Structural synthesis plays an important role in the conceptual design of mechanisms. Based on the link assortment array, links are divided into binary links and multi-vertex links. From the relation ...of binary links and multi-vertex links, a new form of the adjacency matrix is introduced to illustrate planar kinematic chain. It enriches the representative form of the adjacency matrix, which can provide a new direction for rigid-chain detection and structural synthesis. Without auxiliary graph models, based on the link-path adjacency matrix, characteristic code, and Sudoku Crosswords, a computer-aided digitization method is proposed to synthesize the whole family of planar non-fractioned kinematic chains. Compared with most existing methods of structural synthesis, isomorphic kinematic chains and some rigid chains are identified and deleted in the generation of link-path adjacency matrix, which can improve the efficiency of structural synthesis. By synthesizing planar non-fractioned kinematic chains with up to 10 links and 5 degrees of freedom, results confirm that the proposed method is available.
•A systematic approach for the structural synthesis of two-loop mechanisms.•Mutual constraints generated by the coupling sub-chain between connected loops.•Constraint synthesis method for kinematic ...limbs and single-loop mechanisms.•A general procedure for synthesizing two-loop mechanisms.
The conventional parallel mechanism (CPM) is characterized by connecting serial kinematic limbs or chains to the moving platform or linkage. The mobility and motion pattern of the CPM may be further constrained by adding a coupling sub-chain to serial kinematic chains. That will result in a new class of mechanisms called generalized parallel mechanisms or GPMs for short. While the systematic mobility analysis and structural synthesis of GPMs are more challenging and have rarely been studied, the application of the coupling sub-chain possesses the potential for enhanced functionality and performance. This paper proposes a novel approach for synthesizing two-loop mechanisms with coupling sub-chains that form the basic building blocks for GPMs. The screw theory based constraint synthesis method is advocated. Examples are enumerated to demonstrate the feasibility of the proposed approach.
•A new algorithm of links labelling along with the binary code, is used for the isomorphism detection of kinematic chains.•Kinematic chains with simple and multiple joints, and also the Epicyclic ...gear chains have been tested very effectively.•Decoding of the binary codes for various kinematic chains is presented in a unique way.
Isomorphism of kinematic chains (KCs) has always been a critical issue for the researchers dealing with structural synthesis. Consequently, many researchers of repute presented various methods during the last eight decades for the KCs with either simple and/or multiple joints. Binary code is one of such various methods, but the major problem lies in the algorithm of links labelling, which becomes cumbersome, in particular, for large KCs. The paper presents a simple algorithm of links labelling used to find out a binary sequence which, in turn, provides a maximum binary code (chain invariant). The algorithm is tested for six, seven, eight, nine, ten, eleven, twelve and fifteen links with simple joints, seven and eight links KCs with multiple joints and finally, the Epicyclic gear trains (EGTs) with four, five and six links for its efficiency and reliability. The results are in full agreement with the references taken for the purpose. The paper discusses, in a unique way, the decoding of the binary codes of different KCs also.
Planetary gear trains (PGTs) with one or more degrees of freedom (DOFs) have numerous uses in PGT-based mechanisms. The majority of the currently available synthesis methods have focused on 1-DOF ...PGTs, with only a few investigations on multi-DOF PGT synthesis. The method for synthesizing 7-link 3-DOF PGMs is outlined. All possible link assortments are produced, labeled spanning trees are generated, and potential geared graphs are constructed. The guidelines for including geared edges and how to synthesize geared graphs are outlined. Vertex-degree arrays are generated to validate the geared graphs. Isomorphic geared graphs are identified by comparing the isomorphic identification numbers of geared graphs with the same spanning tree. Fractionated geared graphs are identified using the reachability matrix method. The new method has a straightforward algorithm. In contrast to what is reported in the literature, the results of the synthesis of 7-link 3-DOF PGMs show that there are seven non-fractionated mechanisms. MATLAB programs are used to acquire the vertex-degree arrays.
Based on the modified Grübler–Kutzbach (G–K) criterion and relative degrees of freedom (RDOF) criterion, a novel method is proposed for structural synthesis of a class of kinematically redundant ...parallel manipulators (KR-PMs) with spherical joints attached to a moving platform. First, a formula that can be used to calculate the number of kinematic joints not limited to basic joints is proposed, which is affected by the number of links including fixed base, links with multi-node, compound hinges, and the INTERNAL independent loops in parallel manipulators. Furthermore, the sum degrees of all the kinematic joints possesses a direct relationship with the number of kinematic joints, the number of spherical joints, and the type combination of spherical joints attached to the moving platform. Then, the relationship between the mobility M and the RDOF with intermediate variables is derived based on modified G-K criterion and RDOF criterion, which is the base of the proposed synthesis procedure. Next, the proposed synthesis procedure is performed with the synthesis conditions RDOF = 3 or 4, and some typical KR-PMs are obtained. Finally, the condition for proper selection of actuators for KR-PM is revealed. And the reasons for large configuration randomness of the synthesized KR-PMs are discussed.
•A method for synthesizing all non-isomorphic Assur groups is proposed.•The complete set of Assur groups with up to 12 links is obtained.•Structures of Assur groups with 10 and 12 links are reported ...for the first time.•Three classified databases of all synthesized Assur groups are created.
The present study proposes a systematic method for synthesizing a complete set of Assur groups with different links. Moreover, the corresponding databases, including all classified topological structures of synthesized Assur groups, are created. In this regard, the structural correlation and the topological representation of Baranov trusses and Assur groups are initially reviewed. Then, the primary and the secondary vertex-classified sets are introduced to reduce the times of isomorphism identification in the Assur group synthesis. Based on the vertex-symmetry codes used for the isomorphism identification, the systematic synthesis procedure is proposed to achieve all non-isomorphic Assur groups derived from the corresponding Baranov trusses. Finally, a complete set of Assur groups with 2, 4, 6, 8, 10 and 12 links is obtained and three corresponding databases of all synthesized Assur groups are established in accordance with their classified structural characteristics.
Due to the large scale of AT planetary gear trains (PGTs) schemes with 4-5 degrees of freedom, the optimization time is too long. In order to be qualified for large-scale AT structural schemes ...synthesis, a link synthesis and isomorphism identification method based on string encoding is proposed. The characters of the links are defined according to each link type of the PGT, and the AT structure is converted into a string. By analyzing the characteristics of the brake links and interconnection links in the planetary gear set string, and using the combination principle to design a reasonable string synthesis algorithm, the isomorphism identification of the PGTs and the AT structures are realized respectively. During the synthesis of the AT structures, the PGT strings and AT structure strings that do not satisfy the link constraints are eliminated separately. The correctness and efficiency of the method are verified by five examples.
Compared with non-overconstrained deployable units, overconstrained deployable units are widely used in space missions for their higher stiffness characteristics. Besides the performance of a ...three-step topological structural analysis and design of the rectangular pyramid deployable truss unit (PDTU), conducting a structural synthesis of an overconstrained deployable unit requires the determination of the relative position and direction of each kinematic axis. The structural synthesis of an overconstrained deployable unit is investigated based on screw theory and its topological structure. The possible overconstrained cases of the rectangular PDTUs are analyzed, and corresponding screw expressions are obtained. Thus, the rectangular PDTUs, which can be folded into a plane, are synthesized systemically, and a series of overconstrained rectangular PDTUs is obtained. Furthermore, the feasibility of the folded and deployed motions under one degree of freedom for those deployable units is verified in dynamical simulation by using ADAMS 2010.
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