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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.

The study aims to investigate the nexus between total factor productivity and tourism growth in Latin American countries for time series data from 1995 to 2017.

Using the extension of the Granger noncausality test in the nonlinear time-varying of Ajmi et al. (2015), the study points out the interconnectedness between the variables during the period.

The study found nonlinear causality between the variables. Particularly, studying the conclusions for the time-varying Granger causality fashion, it can be noticed that the one-way causality from total factor productivity to tourism growth is obtained for Argentina, Bolivia, Brazil, Uruguay and Venezuela, while the vice versa is confirmed for Chile, Ecuador and Nicaragua. Lastly, the study dissected the plots of the curve causality.

In view of the results, some crucial policy implications could be suggested, such as, under certain circumstances and as an exceptional case, the use of policy instruments such as targeted investment, marketing and the support of tourism organizations focused on driving a tourism-led-based productivity and/or tourism programs and projects.

The current work is distinguished from the existing body of understanding in several substantial directions. This work explores, for the first time, the linkages between the total factor productivity index and tourism growth for Latin American countries. No single attempt has been known to investigate this interaction by using nonlinear causality, and this study determines the shape of the curve between the total factor productivity index and tourism growth for each country.

The purpose of this review is to comprehensively consider the material properties and processing of additive titanium alloy and provide a new perspective for the robotic grinding and polishing of additive titanium alloy blades to ensure the surface integrity and machining accuracy of the blades.

At present, robot grinding and polishing are mainstream processing methods in blade automatic processing. This review systematically summarizes the processing characteristics and processing methods of additive manufacturing (AM) titanium alloy blades. On the one hand, the unique manufacturing process and thermal effect of AM have created the unique processing characteristics of additive titanium alloy blades. On the other hand, the robot grinding and polishing process needs to incorporate the material removal model into the traditional processing flow according to the processing characteristics of the additive titanium alloy.

Robot belt grinding can solve the processing problem of additive titanium alloy blades. The complex surface of the blade generates a robot grinding trajectory through trajectory planning. The trajectory planning of the robot profoundly affects the machining accuracy and surface quality of the blade. Subsequent research is needed to solve the problems of high machining accuracy of blade profiles, complex surface material removal models and uneven distribution of blade machining allowance. In the process parameters of the robot, the grinding parameters, trajectory planning and error compensation affect the surface quality of the blade through the material removal method, grinding force and grinding temperature. The machining accuracy of the blade surface is affected by robot vibration and stiffness.

This review systematically summarizes the processing characteristics and processing methods of aviation titanium alloy blades manufactured by AM. Combined with the material properties of additive titanium alloy, it provides a new idea for robot grinding and polishing of aviation titanium alloy blades manufactured by AM.

Complex and exquisite patterns are sculpted on the surface to beautify the parts. Due to the thin-walled nature, the blank of the part is often deformed by the forming and clamping processes, disabling the nominal numerical control (NC) sculpting programs. To address this problem, a fast adaptive sculpting method of the complex surface is proposed.

The geometry of the blank surface is measured using on-machine measurement (OMM). The real blank surface is reconstructed using the non-uniform rational basis spline (NURBS) method. The angle-based flattening (ABF) algorithm is used to flatten the reconstructed blank surface. The dense points are extracted from the pattern on the image using the OpenCV library. Then, the dense points are quickly located on the complex surfaces to generate the tool paths.

By flattening the reconstructed surface and creating the mapping between the contour points and the planar mesh triangular patches, the tool paths can be regenerated to keep the contour of the pattern on the deformed thin-walled surface.

The proposed method can adjust the tool paths according to the deformation of the thin-walled part. The consistency of sculpting patterns is improved.