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"Least squares optimization"

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Design and Performance Optimization of a Wire-spring Based Planar Gravity Compensation Mechanism for a Robotic Arm
Kyuna Park, Minhyo Kim, Sangrok Jin
J. Korean Soc. Precis. Eng. 2026;43(6):559-566.
Published online June 1, 2026
DOI: https://doi.org/10.7736/JKSPE.025.00020
This study introduces a wire-spring based planar gravity compensation mechanism and evaluates its performance through both analysis and experiments. The mechanism features three pulleys, one spring, and one wire, all arranged in a planar configuration for compact installation within a robotic arm. A linear approximation of the target gravitational torque was derived using the least-squares method, allowing for the determination of spring stiffness and initial tension. Experimental results indicated that the proposed mechanism reduced the maximum torque by approximately 63%. However, the measured slope was gentler than the theoretical model due to friction losses. Additional tests that varied spring stiffness (k) and initial wire tension (A) confirmed that k primarily influences the slope of the compensation torque, while A affects its intercept. This finding suggests that compensation performance can be tailored to specific requirements by adjusting these parameters. The study successfully demonstrates a compact and lightweight mechanism and experimentally validates its tunability through design adjustments. Future research will focus on reducing friction, extending the mechanism to multi-degree-of-freedom systems, and validating performance under dynamic conditions for applications in collaborative and medical robots.
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