Analytical Kinematic Modeling and Simulation Verification of a Three-Link Planar Manipulator

Nuoyu Jiang

doi:10.62762/TICPS.2026.746937

Volume 1, Issue 1, ICCK Transactions on Intelligent Cyber-Physical Systems

Volume 1, Issue 1, 2025

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ICCK Transactions on Intelligent Cyber-Physical Systems, Volume 1, Issue 1, 2025: 26-37

Free to Read | Research Article | 13 February 2026

Analytical Kinematic Modeling and Simulation Verification of a Three-Link Planar Manipulator

Nuoyu Jiang 1 *

1 School of Electrical Engineering, Yancheng Institute of Technology, Yancheng 224051, China

* Corresponding Author: Nuoyu Jiang, [email protected]

DOI: 10.62762/TICPS.2026.746937

ARK: ark:/57805/ticps.2026.746937

Received: 06 January 2026, Accepted: 03 February 2026, Published: 13 February 2026

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Abstract

This paper establishes an analytical kinematic model for a three-degree-of-freedom planar manipulator with three serial links, and validates it through MATLAB numerical simulations and SolidWorks-ADAMS co-simulation. Based on the mechanism topology and the Denavit-Hartenberg (D-H) parameter method, coordinate frames are assigned, and homogeneous transformation modeling is performed, leading to a closed-form forward kinematics expression for the end-effector pose. By combining wrist-point decomposition, geometric approaches, and the law of cosines, an analytical inverse kinematics solution is derived, and the characteristics of multiple solution configurations are discussed. The simulation results show that the analytical forward and inverse kinematics are consistent with the numerical outputs from the Robotics Toolbox, and the inverse solution can reliably recover the joint angles. In the ADAMS simulation, joint responses follow a sinusoidal driving law, and the end-effector trajectory is continuous and smooth, satisfying the motion characteristics of planar mechanisms. These results confirm the correctness and engineering applicability of the proposed model.

Graphical Abstract

Keywords

three-link planar manipulator

D-H parameter method

forward kinematics

analytical inverse kinematics

MATLAB and ADAMS simulation validation

Data Availability Statement

Data will be made available on request.

Funding

This work was supported without any funding.

Conflicts of Interest

The author declares no conflicts of interest.

AI Use Statement

The author declares that no generative AI was used in the preparation of this manuscript.

Ethical Approval and Consent to Participate

Not applicable.

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APA Style

Jiang, N. (2026). Analytical Kinematic Modeling and Simulation Verification of a Three-Link Planar Manipulator. ICCK Transactions on Intelligent Cyber-Physical Systems, 1(1), 26–37. https://doi.org/10.62762/TICPS.2026.746937

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TY  - JOUR
AU  - Jiang, Nuoyu
PY  - 2026
DA  - 2026/02/13
TI  - Analytical Kinematic Modeling and Simulation Verification of a Three-Link Planar Manipulator
JO  - ICCK Transactions on Intelligent Cyber-Physical Systems
T2  - ICCK Transactions on Intelligent Cyber-Physical Systems
JF  - ICCK Transactions on Intelligent Cyber-Physical Systems
VL  - 1
IS  - 1
SP  - 26
EP  - 37
DO  - 10.62762/TICPS.2026.746937
UR  - https://www.icck.org/article/abs/TICPS.2026.746937
KW  - three-link planar manipulator
KW  - D-H parameter method
KW  - forward kinematics
KW  - analytical inverse kinematics
KW  - MATLAB and ADAMS simulation validation
AB  - This paper establishes an analytical kinematic model for a three-degree-of-freedom planar manipulator with three serial links, and validates it through MATLAB numerical simulations and SolidWorks-ADAMS co-simulation. Based on the mechanism topology and the Denavit-Hartenberg (D-H) parameter method, coordinate frames are assigned, and homogeneous transformation modeling is performed, leading to a closed-form forward kinematics expression for the end-effector pose. By combining wrist-point decomposition, geometric approaches, and the law of cosines, an analytical inverse kinematics solution is derived, and the characteristics of multiple solution configurations are discussed. The simulation results show that the analytical forward and inverse kinematics are consistent with the numerical outputs from the Robotics Toolbox, and the inverse solution can reliably recover the joint angles. In the ADAMS simulation, joint responses follow a sinusoidal driving law, and the end-effector trajectory is continuous and smooth, satisfying the motion characteristics of planar mechanisms. These results confirm the correctness and engineering applicability of the proposed model.
SN  - pending
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -

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@article{Jiang2026Analytical,
  author = {Nuoyu Jiang},
  title = {Analytical Kinematic Modeling and Simulation Verification of a Three-Link Planar Manipulator},
  journal = {ICCK Transactions on Intelligent Cyber-Physical Systems},
  year = {2026},
  volume = {1},
  number = {1},
  pages = {26-37},
  doi = {10.62762/TICPS.2026.746937},
  url = {https://www.icck.org/article/abs/TICPS.2026.746937},
  abstract = {This paper establishes an analytical kinematic model for a three-degree-of-freedom planar manipulator with three serial links, and validates it through MATLAB numerical simulations and SolidWorks-ADAMS co-simulation. Based on the mechanism topology and the Denavit-Hartenberg (D-H) parameter method, coordinate frames are assigned, and homogeneous transformation modeling is performed, leading to a closed-form forward kinematics expression for the end-effector pose. By combining wrist-point decomposition, geometric approaches, and the law of cosines, an analytical inverse kinematics solution is derived, and the characteristics of multiple solution configurations are discussed. The simulation results show that the analytical forward and inverse kinematics are consistent with the numerical outputs from the Robotics Toolbox, and the inverse solution can reliably recover the joint angles. In the ADAMS simulation, joint responses follow a sinusoidal driving law, and the end-effector trajectory is continuous and smooth, satisfying the motion characteristics of planar mechanisms. These results confirm the correctness and engineering applicability of the proposed model.},
  keywords = {three-link planar manipulator, D-H parameter method, forward kinematics, analytical inverse kinematics, MATLAB and ADAMS simulation validation},
  issn = {pending},
  publisher = {Institute of Central Computation and Knowledge}
}

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