An improved algorithm for the construction of generalized kinematic chains

Yan, Hong Sen; Chiu, Yu Ting

doi:10.1016/j.mechmachtheory.2014.03.015

Cited by 37 publications

(9 citation statements)

References 18 publications

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“…4. This approach has been used for the development of applications such as finding the spatial structure for a specific task [33], or the generation of atlas for different planar mechanisms with a single union type [31], [32], [34]. In this work a novel technique for representing planar mechanisms by extended matrices is developed, the Santiago-Portilla Method (SPM), facilitating the design of mechanisms since it includes joint types, identification and size of bars and coupler points, spatial position of the overall system, and the identification of link types.…”

Section: B Santiago-portilla Methods (Spm) For Matrix Representation Of Planar Mechanismsmentioning

confidence: 99%

“…Spatial mechanisms are represented with graphs and their adjacency matrices in [33], to design hybrid and fractionated structure robots, although only considering revolute joints. In [34], three different algorithms are used in conjunction to the adjacency matrix to generate mechanisms by varying the number and type of the links, obtaining an atlas as a result. An elementary graph is used in [35] to represent the topology of planar and spatial mechanisms, also taking into account mobility criteria to produce unique representations including links with multiple unions.…”

Section: Introductionmentioning

confidence: 99%

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A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design

et al. 2019

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In this paper, a graph-theory-based approach for representing planar mechanisms is presented, the Santiago Portilla method (SPM). From the corresponding adjacency matrix, SPM generates an extended matrix containing the complete characterization of a planar mechanism, including all the information about both topology and geometry. This matrix representation can be used for the optimal design of mechanisms, allowing simultaneously the topological and dimensional synthesis by means of computational tools such as the metaheuristic algorithms. A case study corresponding to the design of a fixed-linear-trajectory tracker mechanism is included in order to test the efficiency of the proposed approach. It was carried out by addressing the design as an optimization problem and solving it with the differential evolution algorithm, representing the individuals in its population by the matrix form generated by the SPM. The results of the case study show that the SPM and its matrix representation constitute a useful and flexible tool for the solution of the real engineering problems involving the design of planar mechanisms.

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Section: B Santiago-portilla Methods (Spm) For Matrix Representation Of Planar Mechanismsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Graph-Theory-Based Method for Topological and Dimensional Representation of Planar Mechanisms as a Computational Tool for Engineering Design

et al. 2019

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“…The automatic sketching of kinematic chains has been constantly investigated during the following years [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68] and it is still an open and interesting problem.…”

Section: Automatic Sketching Of Kinematic Chainsmentioning

confidence: 99%

On Crossley's contribution to the development of graph based algorithms for the analysis of mechanisms and gear trains

Pennestrı̀

Belfiore

2015

Mechanism and Machine Theory

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This paper celebrates a particular branch of Crossley's early work dedicated to Mechanism Science, which deals with a rigorous introduction of Graph Theory to the study of some fundamental and intrinsic properties of kinematic chains and mechanisms. Although such idea gave its main outcome in Type and Number Synthesis (which has been much better and extensively described in another paper of the present special issue) some other intriguing side effects appeared, later in Mechanism Science, which yielded several results, and are still in the center of research and industrial world interest, such as, to name but a few, the automatic generation of the equations governing kinematic, static force and dynamic analysis of mechanisms and geared trains, the power flow analysis, the computation of the efficiency and, finally, the never fully explored structure-to-function mapping, which the present contribution points out to be still a challenge in the field

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“…In the 1960s, many researchers [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] demonstrated the feasibility of synthesizing the kinematic structure of mechanisms with closed chains by means of graph theory.…”

Section: Graph Theorymentioning

confidence: 99%

“…In which few of KCs have cut-links. In 2013, Yan and Chiu [34,35] proposed an enumeration algorithm for the construction of generalized KCs, based on graph theory, including the atlas of KCs for mechanisms and the atlas of rigid chains for structures. Furthermore, the numbers of generalized KCs with up to 16 links are listed.…”

Section: Graph Theorymentioning

confidence: 99%