Actuators

This study presents a review of passive linear gravity compensation (GC) mechanisms. Linear GC is defined as the realization of a displacement-independent constant upward force along a vertical axis to balance the gravitational load over the entire stroke. This paper focuses on passive systems that counteract gravity solely through mechanical or magnetic energy storage elements, without relying on external power sources. The main energy sources in passive systems—springs, permanent magnets, counterweights, and fluid pressure—are surveyed with emphasis on their ability to generate a constant force. Representative spring-based constant-force mechanisms, cam–spring linkages, and quasi-zero-stiffness magnetic gravity compensators are summarized, together with their applications in vibration isolation systems. Finally, reported performance data are compiled to outline the practical operating envelope of passive linear GC in terms of force level, stroke, and equivalent stiffness. This review reveals that permanent-magnet-based approaches are advantageous for short-stroke, high-precision applications, whereas spring-based mechanisms offer superior suitability for long-stroke requirements due to their greater design flexibility. Consequently, this review provides a strategic selection guideline based on the inherent trade-offs of energy-storage elements to meet specific application requirements.

In this paper, we study the leader-following time-varying formation (TVF) tracking control of general linear multi-agent systems (MASs) with nonzero control input of the leader, and the followers which have magnitude and rate saturation (MRS) and unknown disturbances. Under the assumption that only the followers connecting to the leader have access to the leader’s input and state, an output feedback controller incorporating a distributed extended state observer (ESO) is developed to ensure the asymptotic convergence of the formation errors without input saturation. Then, a saturation model is inserted to each follower’s dynamics to constrain the magnitude and rate of the control input, with consideration of MRS. Anti-windup protection loops are applied to compensate for the saturated signals to improve the closed-loop performance. Finally, the theoretical findings are demonstrated via a series of numerical simulations.

Effective and intelligent fault diagnosis is essential for ensuring the operational safety and reliability of gearbox systems. In practical engineering environments, however, weak fault-related features are often obscured by strong background noise, pronounced nonstationarity, and time-varying operating conditions, which significantly degrade the performance of conventional feature extraction techniques. To address these challenges, this paper proposes an adaptive feature extraction approach that integrates the complementary advantages of variational mode decomposition (VMD), Teager energy operator (TEO), and multi-scale permutation entropy (MPE) to enhance the characterization of weak and transient fault signatures. Vibration signals associated with different fault conditions are first adaptively decomposed into a series of intrinsic mode functions (IMFs) using VMD, enabling the effective separation of fault-sensitive components and enrichment of fault-related information. Subsequently, an enhanced multi-scale permutation entropy (EMPE) method is developed to emphasize transient impulsive characteristics and capture fault-induced complexity variations across multiple temporal scales. By jointly exploiting instantaneous energy modulation and multi-scale dynamical complexity analysis, the proposed approach exhibits improved sensitivity to weak fault signatures and enhanced robustness against variable operating conditions. The effectiveness and generalization capabilities of the proposed framework are validated using three experimental datasets involving gearboxes and rolling bearings under diverse operating conditions. Comparative results demonstrate that the proposed method outperforms conventional entropy-based approaches in terms of fault feature separability and diagnostic performance, highlighting its potential for practical condition monitoring and fault diagnosis of rotating machinery.