The number of stroke patients is steadily increasing, highlighting the critical need for rehabilitation to restore motor function. The shortage of rehabilitation specialists and the repetitive nature of traditional exercises underscore the advantages of robotic systems. However, many existing rehabilitation robots are not adaptable to various therapeutic requirements. Modular robots, with their reconfigurability and ease of assembly, provide a practical solution. This study presents the design and development of a modular wrist rehabilitation robot, consisting of three identical modules that provide the necessary degrees of freedom for wrist movement. The modular structure allows for easy assembly, adjustment for different hand sizes, and adaptability to various configurations. To improve control performance, an impedance control strategy was implemented along with a gravity compensation method. Simulation results show that impedance control alone resulted in an RMS error of approximately 7 degrees, while adding gravity compensation reduced the maximum error to 0.79 degrees. The proposed controller was implemented on the robot and validated through experimental tests with individuals. The results confirmed that impedance control effectively facilitates interaction between the robot and the user, demonstrating the system's potential for improving rehabilitation outcomes.

Design of a passive spatial 2-DoF singularity-configurable gravity compensator for forearm and shank with roll-pitch motion

Gravity compensation for hardware-in-the-loop zero-gravity simulation system of spacecraft

The upper-limb exoskeleton is ergonomically designed to align with human arm motion and can be configured for deployment as a master tool manipulator (MTM) in teleoperation systems. However, existing teleoperated exoskeletons are limited by excessive weight and inadequate force feedback. This study proposes a novel lightweight exoskeleton with optimized shoulder and wrist joint structure, enabling full arm mobility and sufficient force feedback. In practical applications, gravitational forces can lead to muscle fatigue and degrade teleoperation performance, making compensation essential for ergonomic and safety. However, unknown system disturbance caused by unmodeled dynamics (such as internal compliance and cables) pose challenges for compensation precision. A theoretical dynamics model and a Bayesian neural network (BNN) trained on separate datasets to predict joint torques and their corresponding uncertainties were independently developed. Then a Bayesian fusion method was employed to combine model-based and data-driven estimates, using predicted standard deviations to assign fusion weights and produce a refined torque output. Compared to relying solely on the CAD model, the proposed fusion framework combines the physical consistency of model-based approaches with the adaptability of data-driven methods. Experiments ultimately demonstrate that the proposed algorithm effectively reduces modeling errors and enhances the accuracy and robustness of gravity compensation.

Abstract The gravity sag causes significant error in the shape of synchrotron mirrors. To counter this, a novel near-Bessel point (nBP) support for the deformable mirror is proposed. This method is proposed to eliminate the conventional gravity compensation arrangements. The proposed mirror system has been analysed using finite element method (FEM). The shape errors for the case of Bessel point (BP) and nBP supports are compared for the 112 mm, 225 mm, and 450 mm long mirrors using the FEM. By shifting one of the support points from BP to nBP, the root mean square (RMS) shape error reduces significantly. Thereafter, the shape error for four different profiles with change in the grazing incident angle for 225 mm long mirror is evaluated.It is observed that the shape error increases with the increase in the grazing incident angle. The effect of the change in the distance of focus from the center of the mirror on shape error is also analyzed. It is found that the shape error increases as the distance of focus from the center of the mirror decreases. Finally, the effect of the error in the support point on the shape error is analysed. The misalignment along the length has a significant adverse effect on the shape error, while along the thickness has a negligible effect on the shape error. The nBP support can be used for mechanical, piezoactuated, and hybrid deformable mirrors at Synchrotron Radiation beamlines.

Synergistic vibration control in heavy-duty helical gear systems through gravity compensation and coupled SCES-SFD dynamics

A novel gravity compensation mechanism for orthogonal DoFs with coupled springs

In this paper, we proposed a novel method for grinding trajectory planning on large-curved forgings to improve grinding performance and grinding efficiency. Our method consists of four main steps. Firstly, we conducted simulations and analyses on the contact state and contact pressure between the grinding tool and curved workpieces, and explored different grinding methods. Based on the Preston equation, a material removal model was established to analyze the grinding force. Secondly, we proposed an adaptive impedance control method based on grinding force analysis, which can control the contact force indirectly by adjusting the end position of the robot. To address the inability of impedance control to adjust impedance parameters in real time, a control strategy involving online estimation of environmental position and stiffness is adopted. Based on the Lyapunov asymptotic stability principle, an adaptive impedance control model is established, and the effectiveness of the adaptive algorithm is verified through simulation. Thirdly, Position correction is realized through gravity compensation of the grinding force and discretization of the impedance control model. Subsequently, a dynamic trajectory adjustment strategy is proposed, which integrates position correction for the current grinding point and position compensation for the next grinding point, to achieve the force control objective in the grinding process. Finally, a constant force grinding experiment was conducted on large-curvature blades using a robotic automatic grinding system. The grinding system effectively removed the knife marks on the blade surface, resulting in a surface roughness of 0.5146 μm and a grinding efficiency of approximately 0.89 cm2/s. The simulation and experimental results indicate that the smoothness and grinding efficiency of the blades are superior to the enterprise’s existing grinding technology, verifying the feasibility and effectiveness of our proposed method.

Abstract The application of focus-tunable lenses (FTL) has significantly expanded in the field of photonics in the last decade, establishing these devices as fundamental optoelectronic components in most experimental setups. An electrically-addressed FTL allows fine, continuous, and dynamic power adjustment within a range of diopters. In many applications, the FTL is oriented horizontally, with vertical optical axis. However, those applications requiring alternative orientations are prone to be affected by aberrations due to the gravitational force effects on the optical fluid and elastic membrane of this device. A new FTL introduces a compensation for gravity, aiming to compensate for the induced coma. This study focuses on the optical performance of a gravity-compensated FTL, Optotune EL-16-40-GTC-VIS-5D (Optotune Switzerland AG). A comprehensive experimental wavefront characterization was conducted across the addressable power range (5 D) by measuring and analyzing the induced primary astigmatism, coma and spherical aberrations in a 6 mm-diameter aperture, with 530 nm illumination, with the lens in both horizontal (i.e., parallel to laboratory ground) and vertical (upright) lens orientations. A detailed comparison with two uncompensated standard models of the same brand (Optotune EL-16-40-TC-VIS-5D and EL-16-40-TC-VIS-5D-E) is presented in terms of measured wavefront error. The results showed the gravity-compensated FTL effectively corrected induced vertical coma when used upright. In contrast, the astigmatism induced (0.06 μm in both horizontal and vertical orientations) exceeded the observed vertical coma (around 0.030 μm) of the upright standard models. Additionally, such astigmatism (0.06 μm) is approximately three times greater than the astigmatism induced by the standard models in both positions. These results provide a valuable insight about induced aberrations, which can be particularly relevant for vision testing experiments and adaptive optics applications, both requiring precise aberration control. The astigmatism introduced by gravity-compensated FTLs, as well as other induced aberrations, can be significant, potentially masking the effects of other optical components or acting as confounding factors.

Amidst the global proliferation and sustained expansion of industrial robotics, the advancement of robot performance stands as a paramount scientific and technological pursuit commanding significant international attention. Enhancing robotic capabilities is not only pivotal for augmenting productivity but also constitutes a critical technology underpinning national strategic initiatives and industrial transformation. This paper reviews the enduring challenges in high-precision control of industrial manipulators, specifically examining four key issues: the tension between uncertainty robustness and real-time processing constraints; excessive latency in servo drive responses; inefficient energy recuperation from gravitational potential, which compromises overall system efficiency; and trajectory tracking inaccuracies arising from strong kinematic joint coupling inherent in conventional PID control frameworks. By rigorously examining the mathematical formulations and hardware implementation methodologies underpinning three core control algorithms PD control with gravity compensation, inversion control, and adaptive control this work quantifies the constraint boundaries imposed by these controllers on servo drive parameters. Furthermore, it proposes a holistic Pareto-optimization strategy targeting the energy consumption-precision-real-time performance triad. Finally, the paper outlines the emerging research trajectory of employing digital twin platforms for validating learning-enhanced backstepping control methodologies.

A Gravity Compensation Device to Reduce Workload for Indirect Live Line Workers

This paper presents a real-time framework for bilateral gait reconstruction and adaptive joint control using sparse inertial sensing. The system estimates full lower-limb motion from a single-side inertial measurement unit (IMU) by applying a pipeline that includes signal smoothing, temporal alignment via Dynamic Time Warping (DTW), and motion modeling using Gaussian Mixture Models with Regression (GMM-GMR). Contralateral leg trajectories are inferred using both ideal and adaptive symmetry-based models to capture inter-limb variations. The reconstructed motion serves as reference input for joint-level control. A classical Proportional–Integral–Derivative (PID) controller is first evaluated, demonstrating satisfactory results under simplified dynamics but notable performance loss when virtual stiffness and gravity compensation are introduced. To address this, an adaptive fuzzy PID controller is implemented, which dynamically adjusts control gains based on real-time tracking error through a fuzzy inference system. This approach enhances control stability and motion fidelity under varying conditions. The combined estimation and control framework enables accurate bilateral gait tracking and smooth joint control using minimal sensing, offering a practical solution for wearable robotic systems such as exoskeletons or smart prosthetics.

The purpose of the research is to develop a mathematical model, analyze the interaction of the elements of a three- link electromechanical system of a rehabilitation exoskeleton of the lower extremities and predict the driving forces. Methods. The presented article discusses an electromechanical multi-link system of a rehabilitation exoskeleton of the lower extremities. The analysis was performed using the decomposition method, which is the dismemberment of the system into its component parts and the study of the functioning of each part separately. Based on the developed mathematical model of a multi-link system, a computational experiment was conducted. The animation method is used, which creates a virtual trajectory of the ankle joint movement of a human-machine system. The proposed approach makes it possible to predict the behavior of the system, determine its configuration and, importantly, evaluate the values of control actions in the form of torque of electric drives that ensure the functioning of the system as part of rehabilitation measures. Results. A mathematical model of the functioning of the rehabilitation skeleton system of the lower extremities has been obtained, which makes it possible to predict the interaction of elements of an electromechanical multilink system. Based on the data from the computational experiment, it was found that the control of the hybrid drive affects the functioning of the links of the system under consideration. An animation method has been developed that creates a virtual trajectory of the ankle joint based on video motion capture and anthropomorphic parameters. The simulation results demonstrate that the gravity compensator of the hybrid drive creates an auxiliary torque that compensates for part of the gravitational forces from the elements of the electromechanical system. The effect of using a hybrid drive in the femoral joint on the functioning of the remaining links of the electromechanical system is shown, manifested in the exclusion of high-frequency vibrations of the knee and ankle links. Conclusion. The results of mathematical modeling make it possible to predict the interaction of the elements of the electromechanical system and to effectively control the robot's drive system over time. The discovered effect of the use of a hybrid drive in the femoral sphere on the functioning of the remaining links of the electromechanical system will make it possible to create a device capable of performing its functions in various operating conditions and providing motion parameters close to anthropomorphic.

Self-folding gravity compensation mechanism for a supplementary folding robot arm: Design, analysis and implementation

The article examines the prospects for the development of mass measurement systems in the low mass range (less than 1 g) based on the Planck constant. The focus is on new measurement methods, including watt balance with electromagnetic and electrostatic gravity compensation. These systems are based on fundamental physical principles and provide an opportunity to avoid the accumulation of errors specific to traditional methods of transferring a unit of mass through weights. The author describes in detail the principles of operation of watt balance, including design features such as the use of laser interferometers to measure displacements and voltage control systems. The article emphasizes the relevance of developing domestic low mass measuring systems in Russia, which is due to the need to improve the accuracy of measurements in such areas as analytical chemistry, biotechnology and nanotechnology. It is noted that the transition to methods based on fundamental physical constants will significantly improve metrological support, minimize errors and create a new generation of weighing equipment. The work carried out at VNIIM is aimed at developing and researching small mass measurement systems based on new principles that are not inferior in characteristics to the best foreign analogues. The author highlights the importance of calibrating such systems through standards of electrical quantities, which ensures their reliability and validity. The proposed solutions represent a significant contribution to the development of metrology.

Robotic devices offer assistance to individuals with upper-limb impairments. Among different control strategies, assistance should specifically account for the weight of both the device and the wearer's arm without introducing any distortion to the kinematic behaviour. This study investigates how varying weight support levels in the Harmony exoskeleton impact hand spatio-temporal features and inter-joint coordination during a pick-and-place task. Eight healthy subjects performed the selected functional movement across five distinct levels of arm support. Results indicated that movement smoothness and planning in the Cartesian space were not influenced by the Harmony exoskeleton. A decreased accuracy was noted only at high levels of weight support for movements against gravity, while movements propelled by gravity suffered an overall drop. Consistent inter-joint coordination was observed across different support levels, except for shoulder intra-extra rotation during movements against gravity. This study shed light on the effect of gravity compensation provided by the Harmony exoskeleton on kinematic performance, providing valuable insights for optimizing assistive devices for individuals with upper-limb impairments.

Gravity compensation mechanisms are essential for reducing energy losses in mechanical systems, with cable-pulley-spring units being a common implementation. Theoretical analysis of a classic unit reveals a fundamental trade-off: increasing spring elongation allows for reduced stiffness, which is particularly advantageous for systems requiring low spring stiffness and/or with limited motion ranges. However, systematic methods to achieve such elongation amplification remain underexplored. This study addresses this gap by proposing a spring elongation expansion method, derived from a reformulated elastic potential energy expression. Furthermore, the method is implemented through five proposed solutions, each corresponding to a novel mechanism. Each solution is systematically analyzed to establish kinematic and functional principles, supported by case studies and simulations. The proposed gear-based, X-type unit-based, and iris-based mechanisms achieve significant elongation improvements of 108.67%, 100.37%, and 83.87%, respectively. By synthesizing their parametric characteristics, this work provides a generalized design framework for high-performance gravity compensation systems, advancing energy-efficient mechanical design.

Design optimization and validation of a permanent-magnet array for gravity compensation in long-stroke linear motion

Development of Two-DOF Simultaneous Gravity Compensator for Mobile Manipulator

Abstract This article presents a nonlinear gear-spring design for gravity balancing of robotic manipulators with variable payloads. Three design methods based on the compact gear-spring mechanism are proposed for serial manipulators: (i) direct installation, (ii) integration with parallelogram linkages, and (iii) integration with a pulley-belt system. The significance of the proposed methods is that they enable compact designs with high performance, accommodate variable payloads, and incorporate gear friction losses into the performance analysis. In this work, numerical examples are illustrated to demonstrate the effectiveness of the proposed methods, showing that both the parallelogram and pulley-belt configurations can fully eliminate the actuator torques of the robotic manipulators under varying payloads, while the direct installation achieves partial gravity compensation. Furthermore, a prototype of a robot arm with a 1-kg payload capacity and 540-mm reach has also been developed by adopting a pulley-belt system. Experimental results showed average reductions of 72.8% in torque, 57.5% in power, and 89.3% in energy consumption.