Academic Journal
Mathematical modelling and kinematic validation of a six-degree-of-freedom industrial manipulator using the robotics toolbox for Python.
| Τίτλος: | Mathematical modelling and kinematic validation of a six-degree-of-freedom industrial manipulator using the robotics toolbox for Python. |
|---|---|
| Συγγραφείς: | Jai, Aashish Carmel, Sebastian, Sanjay, Krishnasamy, P., Kishor, T. N., Rajalakshmy, P., Kavitha, V., Stanley, Kingston, Sivasundaram, S. |
| Πηγή: | Mathematics in Engineering, Science & Aerospace (MESA); 2026, Vol. 17 Issue 2, p735-751, 17p |
| Θεματικοί όροι: | Robot kinematics, Jacobian matrices, Manipulators (Machinery), Kinematics, Software libraries (Computer programming) |
| Περίληψη: | Accurate kinematic modeling is fundamental to the performance of industrial manipulators operating in precision-critical environments. This paper presents a forward kinematic analysis of a six-degree-of-freedom (6-DoF) serial industrial manipulator. The Denavit--Hartenberg (DH) convention is used to derive the homogeneous transformation matrices for each joint. The analytical model is implemented and validated using the open-source Robotics Toolbox for Python, with DH parameters sourced from RoboDK. End-effector poses computed by the toolbox are compared against manual DH matrix multiplication for multiple joint configurations, yielding zero numerical error across all tested poses and a maximum Jacobian error of 3.44 x 10-7 (finite difference precision). The paper further extends the kinematic model to derive the geometric Jacobian matrix, perform singularity analysis via determinant and rank deficiency, compute Yoshikawa's manipulability index, formulate a least-squares kinematic calibration framework, and characterize the reachable workspace using geometric and numerical methods. An extended mathematical treatment covering rigid body transformations, adjoint maps, twist and wrench representations, Hessian-based kinematic analysis, redundancy resolution, and operational-space dynamics is also presented. The close correspondence between analytical and numerical results validates the correctness of the derived DH parameters and demonstrates the effectiveness of open-source Python tools for industrial robot modeling and simulation. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematics in Engineering, Science & Aerospace (MESA) is the property of Nonlinear Studies and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: edb DbLabel: Complementary Index An: 194662995 RelevancyScore: 1082 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1082.4189453125 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Mathematical modelling and kinematic validation of a six-degree-of-freedom industrial manipulator using the robotics toolbox for Python. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jai%2C+Aashish+Carmel%22">Jai, Aashish Carmel</searchLink><br /><searchLink fieldCode="AR" term="%22Sebastian%2C+Sanjay%22">Sebastian, Sanjay</searchLink><br /><searchLink fieldCode="AR" term="%22Krishnasamy%2C+P%2E%22">Krishnasamy, P.</searchLink><br /><searchLink fieldCode="AR" term="%22Kishor%2C+T%2E+N%2E%22">Kishor, T. N.</searchLink><br /><searchLink fieldCode="AR" term="%22Rajalakshmy%2C+P%2E%22">Rajalakshmy, P.</searchLink><br /><searchLink fieldCode="AR" term="%22Kavitha%2C+V%2E%22">Kavitha, V.</searchLink><br /><searchLink fieldCode="AR" term="%22Stanley%2C+Kingston%22">Stanley, Kingston</searchLink><br /><searchLink fieldCode="AR" term="%22Sivasundaram%2C+S%2E%22">Sivasundaram, S.</searchLink> – Name: TitleSource Label: Source Group: Src Data: Mathematics in Engineering, Science & Aerospace (MESA); 2026, Vol. 17 Issue 2, p735-751, 17p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Robot+kinematics%22">Robot kinematics</searchLink><br /><searchLink fieldCode="DE" term="%22Jacobian+matrices%22">Jacobian matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Manipulators+%28Machinery%29%22">Manipulators (Machinery)</searchLink><br /><searchLink fieldCode="DE" term="%22Kinematics%22">Kinematics</searchLink><br /><searchLink fieldCode="DE" term="%22Software+libraries+%28Computer+programming%29%22">Software libraries (Computer programming)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Accurate kinematic modeling is fundamental to the performance of industrial manipulators operating in precision-critical environments. This paper presents a forward kinematic analysis of a six-degree-of-freedom (6-DoF) serial industrial manipulator. The Denavit--Hartenberg (DH) convention is used to derive the homogeneous transformation matrices for each joint. The analytical model is implemented and validated using the open-source Robotics Toolbox for Python, with DH parameters sourced from RoboDK. End-effector poses computed by the toolbox are compared against manual DH matrix multiplication for multiple joint configurations, yielding zero numerical error across all tested poses and a maximum Jacobian error of 3.44 x 10<superscript>-7</superscript> (finite difference precision). The paper further extends the kinematic model to derive the geometric Jacobian matrix, perform singularity analysis via determinant and rank deficiency, compute Yoshikawa's manipulability index, formulate a least-squares kinematic calibration framework, and characterize the reachable workspace using geometric and numerical methods. An extended mathematical treatment covering rigid body transformations, adjoint maps, twist and wrench representations, Hessian-based kinematic analysis, redundancy resolution, and operational-space dynamics is also presented. The close correspondence between analytical and numerical results validates the correctness of the derived DH parameters and demonstrates the effectiveness of open-source Python tools for industrial robot modeling and simulation. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Mathematics in Engineering, Science & Aerospace (MESA) is the property of Nonlinear Studies and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edb&AN=194662995 |
| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 735 Subjects: – SubjectFull: Robot kinematics Type: general – SubjectFull: Jacobian matrices Type: general – SubjectFull: Manipulators (Machinery) Type: general – SubjectFull: Kinematics Type: general – SubjectFull: Software libraries (Computer programming) Type: general Titles: – TitleFull: Mathematical modelling and kinematic validation of a six-degree-of-freedom industrial manipulator using the robotics toolbox for Python. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jai, Aashish Carmel – PersonEntity: Name: NameFull: Sebastian, Sanjay – PersonEntity: Name: NameFull: Krishnasamy, P. – PersonEntity: Name: NameFull: Kishor, T. N. – PersonEntity: Name: NameFull: Rajalakshmy, P. – PersonEntity: Name: NameFull: Kavitha, V. – PersonEntity: Name: NameFull: Stanley, Kingston – PersonEntity: Name: NameFull: Sivasundaram, S. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 20413165 Numbering: – Type: volume Value: 17 – Type: issue Value: 2 Titles: – TitleFull: Mathematics in Engineering, Science & Aerospace (MESA) Type: main |
| ResultId | 1 |