The Euler-Lagrange Equations of Motion for the Three-Link Planar RPR Robotic Arm

Year 2025, Volume: 8 Issue: 6, 1856 - 1863, 15.11.2025

Onur Denizhan

https://doi.org/10.34248/bsengineering.1771804

Abstract

Robot design, motion planning, controller design, simulation and animation require dynamic modeling of robots. Several research studies demonstrate different methods for various mechanism configurations through their formulations and applications. However, the literature lacks any existing formulation or application of different methods for a three-link planar revolute-prismatic-revolute (RPR) robotic arm. This research introduces the Euler-Lagrange motion equations for a three-link planar RPR robotic arm. The Euler-Lagrange formulation uses kinetic and potential energy of mechanisms to establish its variational approach. The first step involves deriving the Lagrange equations together with their necessary derivatives. This study presents the Euler-Lagrange motion equations through sequential steps. The numerical examples are also provided and serve to validate the presented equations. This research adds knowledge to the dynamic modeling analysis of the three-link planar RPR robotic arm mechanism.

Keywords

Euler-Lagrange equations , Equations of motion , Robotic arm , Three-link planar RPR robot , Dynamic modeling

Ethical Statement

Ethics committee approval was not required for this study because there was no study on animals or humans.

Thanks

The author wishes to express his gratitude to Prof. Meng-Sang Chew, which indirectly made this work possible.

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