A computational methodology for detection of distinct mechanisms from simple jointed kinematic chains

Manikandan, H.; Kaup, Vijayananda; Babu, Harish

doi:10.1063/5.0049931

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…The first step in this study is to enumerate chains containing up to 20 links and possessing up to 13 degrees of freedom [15]. Towards this end, the authors have used their own program for structural synthesis of SJKC structures.…”

Section: Results and Conclusionmentioning

confidence: 99%

“…Towards this end, the authors have used their own program for structural synthesis of SJKC structures. The isomorphism test used in [15] was based on the generation of an ordered set of N strings from an N link chain. Two chains were declared isomorphic if both yielded identical set of strings.…”

Section: Results and Conclusionmentioning

confidence: 99%

“…Manikandan et.al [16,17] used the methodology based on rooted tree structures to address isomorphism in simple jointed chains and multiple jointed kinematic chains. The generated isomorphism index was later used to identify the number of mechanisms possible from a given simple jointed kinematic chains [18]. Again, the same rooted tree structures were used to address isomorphism while synthesizing Baranov truss and 12-link & 3-d.o.f chains which established the robustness of the isomorphism index.…”

Section: Introductionmentioning

confidence: 99%

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Identification of Cospectral Simple Jointed Kinematic Chains using Characteristic Polynomial of Degree Matrix and Structural Matrix

Manikandan

Kaup²,

Babu³

2022

J. Phys.: Conf. Ser.

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Different methods to address the isomorphism in kinematic chains existed earlier and is well reported. In all the methods, link-adjacency matrix (LAM) represents the structural information of a given kinematic chain. Having gathered a large collection of co-spectral chains belonging to a large number of chain categories possessing (containing up to 20 links and up to 13 degrees of freedom), the present work aims at addressing the isomorphism by developing and implementing a methodology for isomorphism based on characteristic coefficients of the degree matrix and structural matrix representations of a specified Simple Jointed Kinematic Chain (SJKC) being computed and comparing. While the above two tests proved to be successful in most cases, two instances of cospectral cases were discovered wherein the above polynomial-based tests failed to detect dissimilarity in the chain structures. These cases are reported in the paper.

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Section: Results and Conclusionmentioning

confidence: 99%

Section: Results and Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identification of Cospectral Simple Jointed Kinematic Chains using Characteristic Polynomial of Degree Matrix and Structural Matrix

Manikandan

Kaup²,

Babu³

2022

J. Phys.: Conf. Ser.

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“…Also, the isomorphism test based on rooted tree structures (RTS) proposed by the authors [19,20] is implemented to avoid duplicate structures. RTS method was found to be robust as it can address isomorphism while synthesizing various structures reported by the same authors [21][22][23][24].…”

Section: Determination Of the Number Of Clutches And Brakes In Egtmentioning

confidence: 99%

A computational methodology for synthesis of epicyclic gear transmission system configurations with multiple planetary gear trains

Hariharan¹,

Kaup²,

Babu³

2022

FME Transactions

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Epicyclic Gear Transmission Systems (EGTs) find a wide variety of applications in automatic transmission systems due to their flexibility to deliver a variety of speed ratios. The design of EGT involves the enumeration of all possible layouts, typically called structural synthesis. Thus, the structural synthesis of an EGT consists of defining a topology for EGT with coupled planetary gear trains (PGTs) along with constraining elements such as connections, brakes, and clutches while delivering a definite transmission ratio between the input and output shafts. Given the number of PGTs, permanent connection, clutches, and brakes, the methodology systematically introduces these elements of PGTs to deliver the given number of distinct speed ratios. Determining the number of distinct speed ratios for a given combination of brakes and clutches has been expressed as a transformation of a graph representation of the EGT layout. A computer program has been developed for the structural synthesis of EGTs and validated against the 3 epicyclic, 6-speed EGT systems. The viability aspects of the synthesized structure are carried out. Also, an isomorphism test is addressed in the synthesis methodology to detect unique EGT structures at every synthesis stage.

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Synthesis of Assur groups via group and matroid theory

Morlin

Carboni

Martins

2023

Mechanism and Machine Theory

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A computational methodology for detection of distinct mechanisms from simple jointed kinematic chains

Cited by 3 publications

References 15 publications

Identification of Cospectral Simple Jointed Kinematic Chains using Characteristic Polynomial of Degree Matrix and Structural Matrix

Identification of Cospectral Simple Jointed Kinematic Chains using Characteristic Polynomial of Degree Matrix and Structural Matrix

A computational methodology for synthesis of epicyclic gear transmission system configurations with multiple planetary gear trains

Synthesis of Assur groups via group and matroid theory

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