Systemics of Assur groups with multiple joints

Chu, Jinkui; Weiqing, Cao

doi:10.1016/s0094-114x(97)00117-1

Cited by 37 publications

(5 citation statements)

References 3 publications

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“…Additionally, Assur groups are used to generate minimal kinematic chains for several screw systems that are applied to the structural synthesis of robots [29][30][31]. Jinkui and Weiqing apply Assur groups to investigate chains with multiple joints [32]. Yannou et al use Assur groups as modular components for the design of platforms for planar mechanisms [33].…”

Section: Assur Groupmentioning

confidence: 99%

Differential kinematics of parallel manipulators using Assur virtual chains

Campos

Guenther

Martins

2009

Proceedings of the Institution of Mechanical Engineers, Part C:

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This article introduces the concept of Assur virtual chains and its applications in differential kinematics of parallel manipulators. Using Assur virtual chains, the differential kinematics has a simple matricial formulation and the choice between direct and inverse kinematics is reduced to select primary variables in a homogeneous linear system. Assur virtual chains are also useful for obtaining information about the relative movements or to imposing particular kinematic constraints between two links of a kinematic chain. Additionally, a new systematic algorithm is established to analytically eliminate passive joint velocities and calculate the Jacobian matrices. This elimination approach is based on screw theory concepts such as twist, wrench, and reciprocity; also, graph theory is used for kinematic chain representation. At the end of the article, the method is applied to a 3RRR planar parallel manipulator and a general universal-prismatic-spheric Stewart—Gough platform.

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Section: Assur Groupmentioning

confidence: 99%

Differential kinematics of parallel manipulators using Assur virtual chains

Campos

Guenther

Martins

2009

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…The Assur groups are used in literature for the analysis and enumeration of kinematic chains. Jinkui and Weiqing [10] apply Assur groups to investigate chains with multiple joints. Manolescu [11] uses Assur groups to create kinematic chains of eight, nine and ten links.…”

Section: Introductionmentioning

confidence: 99%

Determination of a fourth-class Assur group position diagram by means of the revision of the linkage condition of a closure link

Riaza

Calle

Henao

et al. 2016

J Braz. Soc. Mech. Sci. Eng.

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“…Rao and Deshmukh [8] developed a method of computer-aided structural synthesis of planar kinematic chains based on loop formation. Chu and Cao [9,10] used an improved graph to study type synthesis of 1DOF 6-bar and 8-bar linkages, including the use of component group or module of the AG [11], and the use of dyads was developed by Lulian and Dan [12]. Recently, Assur graphs were used by Shai [13] in topological synthesis.…”

Section: Introductionmentioning

confidence: 99%

Assur-Group Inferred Structural Synthesis for Planar Mechanisms

Wang

Dai

2015

Journal of Mechanisms and Robotics

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In order to obtain a comprehensive list of possible mechanisms with various choices of both R and P pairs and mechanism inversion of planar mechanisms, a new structural synthesis method is developed by integrating Assur groups (AGs) as elements in the newly developed group-based adjacency matrix. This extended adjacency matrix is proposed with the diagonal elements representing three fundamental elements as the frame link, driving link, AG and augmented AG (AAG) if metamorphic mechanisms are to be synthesized. The off-diagonal elements provide information on group combination and connection forms of the above three fundamental elements and that on the associated kinematic pairs. Based on the extended adjacency matrix, all assembly modes for the given AGs can be established and isomorphism mechanisms can be identified at the same time. Considering all types of the AGs in the extended adjacency matrix, group permutation and combination are used and connection forms are generated including variation of the driving link and mechanism inversion. The structural synthesis is then extending to generating a comprehensive list of types of mechanisms and illustrated by the synthesis for class II 6-bar planar mechanisms with both R and P pairs, generating a list of 588 types of mechanisms that are derived for the first time. The paper further applies the approach to metamorphic mechanisms, and obtained five connection forms of the 7-bar 2DOF metamorphic mechanisms.

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Systemics of Assur groups with multiple joints

Cited by 37 publications

References 3 publications

Differential kinematics of parallel manipulators using Assur virtual chains

Differential kinematics of parallel manipulators using Assur virtual chains

Determination of a fourth-class Assur group position diagram by means of the revision of the linkage condition of a closure link

Assur-Group Inferred Structural Synthesis for Planar Mechanisms

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