Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandAufsatz in KonferenzbandForschungPeer-Review

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OriginalspracheEnglisch
Titel des SammelwerksAdvances in Robot Kinematics 2022
Herausgeber/-innenOscar Altuzarra, Andrés Kecskeméthy
Seiten198-207
Seitenumfang10
ISBN (elektronisch)978-3-031-08140-8
PublikationsstatusVeröffentlicht - 18 Juni 2022

Publikationsreihe

NameSpringer Proceedings in Advanced Robotics
Band24 SPAR
ISSN (Print)2511-1256
ISSN (elektronisch)2511-1264

Abstract

Functional redundancy for parallel manipulators (PM) with 3T1R degrees of freedom (DoF) presents an untreated niche regarding a general and systematic kinematic description. For an efficient formulation of the inverse kinematics problem (IKP) an existing approach using intrinsic Z- Y - X ′ ′ Tait-Bryan angles for the rotational kinematic constraints is transferred from 3T3R PMs to 3T1R PMs. The adaption of the kinematics model for the five-DoF leg chains of symmetric 3T1R PMs is elaborated in detail. The presented application in a Newton-Raphson IK scheme with nullspace projection is validated within a dimensional synthesis of such PMs, already exploiting the redundancy. The framework is able to reproduce existing PMs from literature. Results show the dimensioning of PMs for an exemplary task.

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Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints. / Schappler, Moritz.
Advances in Robot Kinematics 2022. Hrsg. / Oscar Altuzarra; Andrés Kecskeméthy. 2022. S. 198-207 (Springer Proceedings in Advanced Robotics; Band 24 SPAR).

Publikation: Beitrag in Buch/Bericht/Sammelwerk/KonferenzbandAufsatz in KonferenzbandForschungPeer-Review

Schappler, M 2022, Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints. in O Altuzarra & A Kecskeméthy (Hrsg.), Advances in Robot Kinematics 2022. Springer Proceedings in Advanced Robotics, Bd. 24 SPAR, S. 198-207. https://doi.org/10.1007/978-3-031-08140-8_22, https://doi.org/10.1007/978-3-031-08140-8_22
Schappler, M. (2022). Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints. In O. Altuzarra, & A. Kecskeméthy (Hrsg.), Advances in Robot Kinematics 2022 (S. 198-207). (Springer Proceedings in Advanced Robotics; Band 24 SPAR). https://doi.org/10.1007/978-3-031-08140-8_22, https://doi.org/10.1007/978-3-031-08140-8_22
Schappler M. Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints. in Altuzarra O, Kecskeméthy A, Hrsg., Advances in Robot Kinematics 2022. 2022. S. 198-207. (Springer Proceedings in Advanced Robotics). doi: 10.1007/978-3-031-08140-8_22, 10.1007/978-3-031-08140-8_22
Schappler, Moritz. / Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints. Advances in Robot Kinematics 2022. Hrsg. / Oscar Altuzarra ; Andrés Kecskeméthy. 2022. S. 198-207 (Springer Proceedings in Advanced Robotics).
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title = "Inverse Kinematics for Functional Redundancy of Symmetric 3T1R Parallel Manipulators Using Tait-Bryan-Angle Kinematic Constraints",
abstract = "Functional redundancy for parallel manipulators (PM) with 3T1R degrees of freedom (DoF) presents an untreated niche regarding a general and systematic kinematic description. For an efficient formulation of the inverse kinematics problem (IKP) an existing approach using intrinsic Z- Y ′ - X ′ ′ Tait-Bryan angles for the rotational kinematic constraints is transferred from 3T3R PMs to 3T1R PMs. The adaption of the kinematics model for the five-DoF leg chains of symmetric 3T1R PMs is elaborated in detail. The presented application in a Newton-Raphson IK scheme with nullspace projection is validated within a dimensional synthesis of such PMs, already exploiting the redundancy. The framework is able to reproduce existing PMs from literature. Results show the dimensioning of PMs for an exemplary task. ",
keywords = "3T1R, Dimensional synthesis, Euler angles, Functional redundancy, Kinematic constraints, Parallel manipulator, Parallel robot, Tait-Bryan angles",
author = "Moritz Schappler",
note = "Funding Information: The author acknowledges the support by the Deutsche Forschungsgemeinschaft (DFG) under grant number 341489206. Matlab code to reproduce the results is available at GitHub under free license at github.com/SchapplM/ robotics-paper ark2022 3T1R.",
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N1 - Funding Information: The author acknowledges the support by the Deutsche Forschungsgemeinschaft (DFG) under grant number 341489206. Matlab code to reproduce the results is available at GitHub under free license at github.com/SchapplM/ robotics-paper ark2022 3T1R.

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N2 - Functional redundancy for parallel manipulators (PM) with 3T1R degrees of freedom (DoF) presents an untreated niche regarding a general and systematic kinematic description. For an efficient formulation of the inverse kinematics problem (IKP) an existing approach using intrinsic Z- Y ′ - X ′ ′ Tait-Bryan angles for the rotational kinematic constraints is transferred from 3T3R PMs to 3T1R PMs. The adaption of the kinematics model for the five-DoF leg chains of symmetric 3T1R PMs is elaborated in detail. The presented application in a Newton-Raphson IK scheme with nullspace projection is validated within a dimensional synthesis of such PMs, already exploiting the redundancy. The framework is able to reproduce existing PMs from literature. Results show the dimensioning of PMs for an exemplary task.

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KW - Euler angles

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