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This document presents a revised translation to the English language work developed more than 40 years ago by the first author. It further summarizes a common misinterpretation of the method and succinctly describes a graphical procedure to correctly determine the derived displacement volume of a pump or a motor. The original work contains a directive for the determination of the derived displacement volume of hydrostatic positive displacement pumps and motors, from volumetric (flow and speed) measurements. The procedure is based on the definition of the derived displaced volume, defined as: The volumetric flow pushed or admitted by hydrostatic positive displacement pumps and motors per (shaft) revolution, at zero internal and external leakage flow conditions.

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Purpose An Autodesk Ember three-dimensional (3D) printer was used to print optical components from Clear PR48 photocurable resin. The cured PR48 was characterized by the per cent of light transmitted and the index of refraction, which was measured with a prism spectrometer. Lenses and diffraction gratings were also printed and characterized. The focal length of the printed lenses agreed with predictions based on the thin lens equation. The periodicity and effective slit width of the printed gratings were determined from both optical micrographs and fits to the Fraunhofer diffraction equation. This study aims to demonstrate the advantages offered by a layer-by-layer DLP printing process for the manufacture of optical components for use in the visible region of the electromagnetic spectrum. Design/methodology/approach A 3D printer was used to print both lenses and diffraction gratings from Standard Clear PR48 photocurable resin. The manufacturing process of the lenses and the diffraction gratings differ mainly in the printing angle with respect to the printer x-y-axes. The transmission diffraction gratings studied here were manufactured with nominal periodicities of 10, 25 and 50 µm. The aim of this study was to optically determine the effective values for the distance between slits, d, and the effective width of the slits, w, and to compare these values with the printed layer thickness. Findings The normalized diffraction patterns measured in this experiment for the printed gratings with layer thickness of 10, 25 and 50 µm are shown by the solid dots in Figures 8(a)-(c). Also shown as a red solid line are the fits to the experimental diffraction data. The effective values of d and w obtained from fitting the data are compared to the nominal layer thickness of the printed gratings. The effective distance between slits required to fit the diffraction patterns are well approximated by the printed layer thickness to within 14, 4 and 16 per cent for gratings with a nominal 10, 25 and 50 µm layer thickness, respectively. Research limitations/implications Chromatic aberration is present in all polymer lenses, and the authors have not attempted to characterize it in this study. These materials could be used for achromatic lenses if paired with a crown-type material in an achromatic doublet configuration, because this would correct the chromatic aberration issues. It is worthwhile to compare the per cent transmission in cured PR48 resin (approximately 80 per cent) to the percent transmission found in common optical materials like BK7 (approximately 92 per cent) over the visible region. The authors attribute the lower transmission in PR48 to a combination of surface scattering and increased absorption. At the present time, the authors do not know what fraction of the lower transmission is related to the surface quality resulting from sample polishing. Practical implications There are inherent limitations to the 3D manufacturing process that affect the performance of lenses. Approximations to a curved surface in the design software, the printing resolution of the Autodesk Ember printer and the anisotropy due to printing in layers are believed to be the main issues. The performance of the lenses is also affected by internal imperfections in the printed material, in particular the presence of bubbles and the inclusion of debris like dust or fibers suspended in air. In addition, the absorption of wavelengths in the blue/ultraviolet produces an undesirable yellowing in any printed part. Originality/value One of the most interesting results from this study was the manufacture of diffraction gratings using 3D printing. An analysis of the diffraction pattern produced by these printed gratings yielded estimates for the slit periodicity and effective slit width. These gratings are unique because the effective slit width fills the entire volume of the printed part. This aspect makes it possible to integrate two or more optical devices in a single printed part. For example, a lens combined with a diffraction grating now becomes possible.