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The purpose of this paper is to propose a smooth double-spline interpolation method for six-degree-of-freedom rotational robot manipulators, achieving the global C2 continuity of the robot trajectory.

This paper presents a smooth double-spline interpolation method, achieving the global C2 continuity of the robot trajectory. The tool center positions and quaternion orientations are first fitted by a cubic B-spline curve and a quartic-polynomial-based quaternion spline curve, respectively. Then, a parameter synchronization model is proposed to realize the synchronous and smooth movement of the robot along the double spline curves. Finally, an extra u-s function is used to record the relationship between the B-spline parameter and its arc length parameter, which may reduce the feed rate fluctuation in interpolation. The seven segments jerk-limited feed rate profile is used to generate motion commands for algorithm validation.

The simulation and experimental results demonstrate that the proposed method is effective and can generate the global C2-continuity robot trajectory.

The main contributions of this paper are as follows: guarantee the C2 continuity of the position path and quaternion orientation path simultaneously; provide a parameter synchronization model to realize the synchronous and smooth movement of the robot along the double spline curves; and add an extra u-s function to realize arc length parameterization of the B-spline path, which may reduce the feed rate fluctuation in interpolation.

Non-uniform rational B-splines (NURBSs) are the de facto standard for representing objects in computer-aided design (CAD). The purpose of this paper is to discuss how to stick to this standard in all phases of the additive manufacturing (AM) workflow, from the CAD object to the final G-code, bypassing unnecessary polygonal approximations.

The authors use a commercial CAD system (Rhino3D along with its programming environment Grasshopper) for direct slicing of the model, offset generation and trimming. Circular arcs are represented as quadratic NURBSs and free-form geometry as quadratic or cubic polynomial B-splines. Therefore, circular arcs are directly expressible as G2/G3 G-code commands, whereas free-form paths are rewritten as a succession of cubic Bézier curves, thereby admitting exact translation into G5 commands, available in firmware for AM controllers, such as Marlin.

Experimental results of this paper confirm a considerable improvement in quality over the standard AM workflow, consisting of an initial polygonization of the object (e.g. via standard tessellation language), slicing this polygonal approximation, offsetting the polygonal sections and, finally, generating G-code made up of polyline trajectories (G1 commands).

A streamlined AM workflow is obtained, with a seamless transfer from the initial CAD description to the final G-code. By adhering to the NURBS standard at all steps, the authors avoid multiple representations and associated errors resulting from approximations.

This paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator.

When a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method.

Simulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits.

Currently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking.

Through a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time.

With the help of multi-body dynamics software UM, the paper uses Kik–Piotrowski model to simulate wheel-rail contact and Archard wear model for rail wear.

The CRH5 vehicle-track coupling dynamics model is constructed for the wear study of rails of small radius curves, namely 200 and 350 m in Guangzhou East EMU Depot and those 250 and 300 m radius in Taiyuan South EMU Depot.

Results show that the rail wear at the straight-circle point, the curve center point and the circle-straight point follows the order of center point > the circle-straight point > the straight-circle point. The wear on rail of small radius curves intensifies with the rise of running speed, and the wearing trend tends to fasten as the curve radius declines. The maximum rail wear of the inner rail can reach 2.29 mm, while that of the outer rail, 10.11 mm.

With the increase of the train passing number, the wear range tends to expand. The rail wear decreases with the increase of the curve radius. The dynamic response of vehicle increases with the increase of rail wear, among which the derailment coefficient is affected the most. When the number of passing vehicles reaches 1 million, the derailment coefficient exceeds the limit value, which poses a risk of derailment.

The supercritical design of tail rotor drive shaft has attracted more attention in helicopter design due to its high power–weight ratio and low maintenance cost. However, there exists excessive vibration when the shaft passes through the critical frequency. Dry friction damper is the equipment applied to the drive shaft to suppress the excessive vibration. In order to figure out the damping mechanism of the dry friction damper and improve the damping efficiency, the dynamic model of the shaft/damper system is established based on the Jeffcott rotor model.

The typical frequency response of the system is studied through bifurcation diagrams, amplitude-frequency characteristic curves and waterfall frequency response spectrum. The typical transient responses under frequency sweeps are also obtained.

The results show that the response of the system changes from periodic no-rub motion to quasi-periodic rub-impact motion, and then to synchronous full annular rub-impact, and finally, back to periodic no-rub motion. The slip of the rub-impact ring improves the stability of the system. Besides, the effects of the system parameters including critical dry friction force, rub-impact friction coefficient, initial clearance on the stability and the vibration damping capacity are studied. It is observed that the stability changes significantly varying the three parameters respectively. The vibration damping capacity is mainly affected by the critical dry friction force and the initial clearance.

Presented results provide guidance for the design of the dry friction damper.