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This paper aims to study the motion trajectory of the oil seal for shaft in eccentric state and derive equation of lip motion trajectory.

This paper analyzes the force during the motion of the eccentric lip by considering the material viscoelasticity, and a cam-plate mechanism is established as an equivalent model for the motion between the shaft and the lip; according to this, the equation of lip motion trajectory is derived.

The trajectory of the lip lags that of the shaft in the eccentric state because the viscoelasticity-affected lip recovery velocity is lower than the shaft recovery speed. The lip trajectory enters the lag phase earlier and the lag phase’s duration is longer with the increase of the eccentricity and rotational speed, because the deviation of the recovery velocities between the lip and the shaft will be exacerbated.

Innovatively, by considering the viscoelasticity of the material, the cam-plate mechanism is used to equivalent the motion of the shaft-lip to derive the equation for the radial motion trajectory of the eccentric lip. The regularity of lip motion is the key to determining the performance of oil seals, and the eccentric lip trajectory research method revealed in this paper provides a research basis for the performance research and optimization of eccentric oil seals.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-06-2023-0161/

The purpose of this paper is to maximize the speed of industrial robots by obtaining the minimum‐time trajectories that satisfy various constraints commonly given in the application of industrial robots.

The method utilizes the dynamic model of the robot manipulators to find the maximum kinematic constraints that are used with conventional trajectory patterns, such as trapezoidal velocity profiles and cubic polynomial functions.

The experimental results demonstrate that the proposed method can decrease the motion times substantially compared with the conventional kinematic method.

Although the method used a dynamic model, the computational burden is minimized by calculating dynamics only at certain points, enabling implementation of the method online. The proposed method is tested on more than 40 different types of robots made by Hyundai Heavy Industries Co. Ltd (HHI). The method is successfully implemented in Hi5, a new generation of HHI robot controller.

The paper shows that the method is computationally very simple compared with other minimum‐time trajectory‐planning methods, thus making it suitable for online implementation.

The purpose of this paper is to design a new trajectory error compensation method to improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction motion.

A trajectory error compensation method based on admittance-extended Kalman filter (AEKF) error fusion for human–exoskeleton interaction control. The admittance controller is used to calculate the trajectory error adjustment through the feedback human–exoskeleton interaction force, and the actual trajectory error is obtained through the encoder feedback of exoskeleton and the designed trajectory. By using the fusion and prediction characteristics of EKF, the calculated trajectory error adjustment and the actual error are fused to obtain a new trajectory error compensation, which is feedback to the knee exoskeleton controller. This method is designed to be capable of improving the trajectory tracking performance of the knee exoskeleton and enhancing the compliance of knee exoskeleton interaction.

Six volunteers conducted comparative experiments on four different motion frequencies. The experimental results show that this method can effectively improve the trajectory tracking performance and compliance of the knee exoskeleton in human–exoskeleton interaction.

The AEKF method first uses the data fusion idea to fuse the estimated error with measurement errors, obtaining more accurate trajectory error compensation for the knee exoskeleton motion control. This work provides great benefits for the trajectory tracking performance and compliance of lower limb exoskeletons in human–exoskeleton interaction movements.

Humanoid robots should have the ability of walking in complex environment and overcoming large obstacles in rescue mission. Previous research mainly discusses the problem of humanoid robots stepping over or on/off one obstacle statically or dynamically. As an extreme case, this paper aims to demonstrate how the robots can step over two large obstacles continuously.

The robot model uses linear inverted pendulum (LIP) model. The motion planning procedure includes feasibility analysis with constraints, footprints planning, legs trajectory planning with collision-free constraint, foot trajectory adapter and upper body motion planning.

The motion planning with the motion constraints is a key problem, which can be considered as global optimization issue with collision-free constraint, kinematic limits and balance constraint. With the given obstacles, the robot first needs to determine whether it can achieve stepping over, if feasible, and then the robot gets the motion trajectory for the legs, waist and upper body using consecutive obstacles stepping over planning algorithm which is presented in this paper.

The consecutive stepping over problem is proposed in this paper. First, the paper defines two consecutive stepping over conditions, sparse stepping over (SSO) and tight stepping over (TSO). Then, a novel feasibility analysis method with condition (SSO/TSO) decision criterion is proposed for consecutive obstacles stepping over. The feasibility analysis method’s output is walking parameters with obstacles’ information. Furthermore, a modified legs trajectory planning method with center of mass trajectory compensation using upper body motion is proposed. Finally, simulations and experiments for SSO and TSO are carried out by using the XT-I humanoid robot platform with the aim to verify the validity and feasibility of the novel methods proposed in this paper.

In the industry, there is always a demand to shorten the task completion durations to maximize the efficiency of the operation. This work focuses on making use of a special type of kinematic redundancy, macro–micro manipulation, to minimize the task completion duration. The purpose of this paper is to develop the most convenient trajectory planner to be integrated with industrial computerized numerical control (CNC) systems to resolve kinematic redundancy for task duration minimization.

A special type of kinematic redundancy is devised by using two kinematically different mechanisms that have different advantages, which are named as macro and micro mechanisms. In this case, the control design including the trajectory planning should be devised taking into account the distinct advantages of both mechanisms. A new trajectory planning algorithm is designed and used for the constructed planar laser-cutting machine, and some benchmark pieces are cut.

Offline method has practical limitations for employment in a real case scenario such as assuming infinite jerk limits for each axis motion. This limitation was removed by using an online trajectory generation technique. Experimental test results indicate that the online trajectory planning technique developed for the macro–micro mechanism to shorten the task duration was successful.

Although the new trajectory planning algorithm is implemented for a laser-cutting machine, it can also be used for other manufacturing systems that require higher acceleration and accuracy levels than the conventional machines. The new algorithm is compatible with the commercially available CNC systems.

In this work, a new approach to reducing the task duration for planar machining operations was introduced by making use of macro–micro manipulation concept. The core novelty of the work is devising trajectory planning algorithms to get the most efficiency in terms of acceleration limits from a macro–micro manipulation while making these algorithms deployable to most of the CNC systems.

Automated robotic assembly on a moving workpiece, referred to as assembly in motion, demands that an assembly robot is synchronised in all degrees of freedom to the moving workpiece, on which assembly parts are installed. Currently, this requirement cannot be met due to the lack of robust estimation of 3D positions and the trajectory of the moving workpiece. The purpose of this paper is to develop a camera system that measures the 3D trajectory of the moving workpiece for robotic assembly in motion.

For the trajectory estimation, an assembly robot-guided, monocular camera system is developed. The motion trajectory of a workpiece is estimated, as the trajectory is considered as a linear combination of trajectory bases, such as discrete cosine transform bases.

The developed camera system for trajectory estimation is tested within the robotic assembly of a cylinder block in motion. The experimental results show that the proposed method is able to reconstruct arbitrary trajectories of an assembly point on a workpiece moving in 3D space.

With the developed technology, a point trajectory can be recovered offline only after all measurement images are acquired. For practical assembly tasks in real production, this method should be extended to determine the trajectory online during the motion of a workpiece.

For practical, robotic assembly in motion, such as assembling tires, wheels and windscreens on conveyed vehicle bodies, the developed technology can be used for positioning a moving workpiece, which is in the distant field of an assembly robot.

Besides laser trackers, indoor global positioning systems and stereo cameras, this paper provides a solution of trajectory estimation by using a monocular camera system.

This purpose of the paper is to examine the multi-channel cyclone created at the Vilnius Gediminas Technical University (VGTU) Research Institute of Environmental Protection. The paper aims to predict the possible trajectories of solid particle motion in the cyclone with reference to the mechanical forces only.

The numerical calculations were performed on the basis of experimental results. The system of differential equations describing particle motion in the cyclone is analysed and numerically solved using Runge–Kutta–Fehlberg method. Research consists of three examples that illustrate the impact of particle density and velocity on collection and analyses the particle motion trajectories in the first and second channels of the cyclone.

Numerical calculations were performed according to the data from Vilnius Gediminas Technical University Research Institute of Environmental Protection. The particulate matter of wood ash and granite were used. The collection of solid particles of different size was examined when the air inflow velocity varies from 10 to 20 m/s. The possible motion trajectories of the solid particles are defined and the parameters of collected particles have been discussed.

The obtained results can be used for the analysis of air cleaning efficiency and particulate matter removal from air in a multi-channel cyclone.

The results lead us to improve the structure of the cyclone so as to effectively collect the solid particles of different size.

This paper presents the results obtained for the multi-channel cyclone created at the Vilnius Gediminas Technical University Research Institute of Environmental Protection.

The purpose of this paper is to improve control performance and safety of a real two-wheeled inverted pendulum (TWIP) robot by dealing with model uncertainty and motion restriction simultaneously, which can be extended to other TWIP robotic systems.

The inequality of lumped model uncertainty boundary is derived from original TWIP dynamics. Several motion restriction conditions are derived considering zero dynamics, centripedal force, ground friction condition, posture stability, control torque limitation and so on. Sliding-mode control (SMC) and model predictive control (MPC) are separately adopted to design controllers for longitudinal and rotational motion, while taking model uncertainty into account. The reference value of the moving velocity and acceleration, delivered to the designed controller, should be restricted in a specified range, limited by motion restrictions, to keep safe.

The cancelation of model uncertainty commonly existing in real system can improve control performance. The motion commands play an important role in maintaining safety and reliability of TWIP, which can be ensured by the proposed motion restriction to avoid potential movement failure, such as slipping, lateral tipping over because of turning and large fluctuation of body.

An inequation of lumped model uncertainty boundary incorporating comprehensive errors and uncertainties of system is derived and elaborately calculated to determine the switching coefficients of SMC. The motion restrictions for TWIP robot moving in 3D are derived and used to impose constraints on reference trajectory to avoid possible instability or failure of movement.

Nondestructive testing based on cooperative twin-robot technology is a significant issue for curved-surface inspection. To achieve this purpose, this paper aims to present a kinematic constraint relation method relative to two cooperative robots.

The transformation relation of the twin-robot base frame can be determined by driving the two robots for a series of handclasp operations on three points that are noncollinear in space. The transformation relation is used to solve the cooperative motion problem of the twin-robot system. Cooperative motions are divided into coupled and combined synchronous motions on the basis of the testing tasks. The position and orientation constraints for the two motion modes are also explored.

Representative experiments between two industrial robots are conducted to validate the theoretical developments in kinematic constraint analysis. Artificial defects are clearly visible in the C-scan results, thereby verifying the validity and the effectiveness of the proposed method.

The transformation relation of the twin-robot base frame is built under a series of handclasp operations. The position and orientation constraints for the coupled and combined synchronous motions are explored. Theoretical foundations of trajectory planning method for the transmitting and receiving transducers of the cooperative twin-robot system are presented.

The purpose of this paper is to propose an automatic interpolation algorithm for robot spraying trajectories based on cubic Non-Uniform Rational B-Splines (NURBS) curves, to solve the problem of sparse and incomplete trajectory points of the head and heel of the shoe sole when extracting robot motion trajectories using structured-light 3D cameras and to ensure the robot joints move smoothly, so as to achieve a good effect of automatic spraying of the shoe sole with a 7-degree-of-freedom (DOF) robot.

Firstly, the original shoe sole edge trajectory position points acquired by the 3D camera are fitted with NURBS curves. Then, the velocity constraint at the local maximum of the trajectory curvature is used as the reference for curve segmentation and S-shaped acceleration and deceleration planning. Immediately, real-time interpolation is performed in the time domain to obtain the position and orientation of each point of the robot motion trajectory. Finally, the inverse kinematics of the anthropomorphic motion of the 7-DOF robot arm is used to obtain the joint motion trajectory.

The simulation and experiment prove that the shoe sole spraying trajectory is complete, the spraying effect is good and the robot joint movement is smooth, which show that the algorithm is feasible.

This study is of good practical value for improving the quality of automated shoe sole spraying, and it has wide applicability for different shoe sole shapes.