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Article

A Motion Propagation Force Analysis of Multi-DoF Systems Using the Partial Lagrangian Method

by
Hironori Gunji
1,†,
Takashi Kusaka
2,*,† and
Takayuki Tanaka
2,†
1
Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0867, Japan
2
Faculty of Information Science and Technology, Hokkaido University, Sapporo 060-0867, Japan
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Robotics 2025, 14(5), 54; https://doi.org/10.3390/robotics14050054
Submission received: 5 December 2024 / Revised: 10 April 2025 / Accepted: 22 April 2025 / Published: 24 April 2025
(This article belongs to the Section Intelligent Robots and Mechatronics)
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Abstract

A partial Lagrangian method is proposed as an inverse dynamics analysis method for multi-link systems. This method, combined with automatic differentiation, allows for the derivation of equations of motion and analytical extraction of motion-induced torque components. We introduce the concept of motion propagation force to describe joint torque components generated by the motion of other joints. This concept aligns with existing notions such as interaction torque, while providing a novel analytical perspective. The effectiveness of the proposed method is confirmed through simulations using a three-DoF arm model, where motion propagation torques are visualized and validated. This method is useful for motion analysis and impedance control in complex robotic systems.
Keywords: Lagrange equation; automatic differentiation; motion propagation Lagrange equation; automatic differentiation; motion propagation

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MDPI and ACS Style

Gunji, H.; Kusaka, T.; Tanaka, T. A Motion Propagation Force Analysis of Multi-DoF Systems Using the Partial Lagrangian Method. Robotics 2025, 14, 54. https://doi.org/10.3390/robotics14050054

AMA Style

Gunji H, Kusaka T, Tanaka T. A Motion Propagation Force Analysis of Multi-DoF Systems Using the Partial Lagrangian Method. Robotics. 2025; 14(5):54. https://doi.org/10.3390/robotics14050054

Chicago/Turabian Style

Gunji, Hironori, Takashi Kusaka, and Takayuki Tanaka. 2025. "A Motion Propagation Force Analysis of Multi-DoF Systems Using the Partial Lagrangian Method" Robotics 14, no. 5: 54. https://doi.org/10.3390/robotics14050054

APA Style

Gunji, H., Kusaka, T., & Tanaka, T. (2025). A Motion Propagation Force Analysis of Multi-DoF Systems Using the Partial Lagrangian Method. Robotics, 14(5), 54. https://doi.org/10.3390/robotics14050054

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