Academic Journal
Mathematical modelling and kinematic validation of a six-degree-of-freedom industrial manipulator using the robotics toolbox for Python.
| Title: | Mathematical modelling and kinematic validation of a six-degree-of-freedom industrial manipulator using the robotics toolbox for Python. |
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| Authors: | Jai, Aashish Carmel, Sebastian, Sanjay, Krishnasamy, P., Kishor, T. N., Rajalakshmy, P., Kavitha, V., Stanley, Kingston, Sivasundaram, S. |
| Source: | Mathematics in Engineering, Science & Aerospace (MESA); 2026, Vol. 17 Issue 2, p735-751, 17p |
| Subject Terms: | Robot kinematics, Jacobian matrices, Manipulators (Machinery), Kinematics, Software libraries (Computer programming) |
| Abstract: | 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] |
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| Database: | Complementary Index |
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