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Method to determine the tracking angles of heliostats.

ABSTRACT: The heliostats with two tracking axes are considered, and the method is presented to find the tracking angles for reflection of sun light to a given target. An important advantage of the method is that the tracking axes are not required to be orthogonal like in azimuth-elevation, tilt-roll or target-aligned heliostats. All of these configurations are covered in a unified way, and the presented solution is valid even for arbitrary orientation of tracking axes. The ability to have such a general solution is very valuable, because the orthogonality condition may not hold precisely for manufacturing reasons or due to degradation of heliostats. These deviations need to be corrected properly to achieve a high concentration of sun light. The offsets between tracking axes are also taken into account. However, the targeting problem for heliostats in this case becomes considerably different from the inverse kinematic problems for robotic arm manipulators. It is shown that the tracking angles can be found iteratively, and the convergence of results is very fast for a typical set of parameters used in solar thermal plants. To simplify the use of the method, a Python-library HelioK was developed, and it is demonstrated how to work with it in a Jupyter-notebook. To explain the kinematics of heliostats better, a 3D model of heliostat is provided, which was made and animated in an open-source 3D editor Blender. The main highlights of the method:•The tracking axes and the facet of heliostat can have an arbitrary orientation, and there can be offsets between them.•The tracking problem is solved both for targets attached to heliostat (local aiming) and for separated targets (global aiming).•The single-axis trackers are included as a limiting case.

SUBMITTER: Grigoriev V

PROVIDER: S-EPMC8374198 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:Neuromuscular electrical stimulation (NMES) has been used to increase muscle strength and physical function. However, NMES induces rapid fatigue, limiting its application. To date, the effect of quadriceps femoris (QF) muscle length by knee and hip joint manipulation on NMES-induced contraction fatigability is not clear. We aimed to quantify the effects of different muscle lengths on NMES-induced contraction fatigability, fatigue index, and electromyographic (EMG) activity for QF muscle. QF maximum evoked contraction (QMEC) was applied in a 26 min protocol (10 s on; 120 s off; 12 contractions) in 20 healthy participants (24.0 ± 4.6 years old), over 4 sessions on different days to test different conditions. The tested conditions were as follows: supine with knee flexion of 60° (SUP60), seated with knee flexion of 60° (SIT60), supine with knee flexion of 20° (SUP20), and seated with knee flexion of 20° (SIT20). Contraction fatigability (torque decline assessed by maximal voluntary contraction [MVC] and during NMES), fatigue index (percentage reduction in MVC), and EMG activity (root mean square [RMS] and median frequency) of the superficial QF' constituents were assessed. After NMES, all positions except SUP20 had an absolute reduction in MVC (p < .001). Fatigue index was greater in SIT20 than in SIT60 (p < .001) and SUP20 (p = .01). There was significant torque reduction across the 12 QMEC in SUP60 and SIT60, up to 10.5% (p < .001-.005) and 9.49% (p < .001-.033), respectively. There was no torque reduction during NMES in SUP20 and SIT20. Fatigue was accompanied by an increase in RMS (p = .032) and a decrease in median frequency for SUP60 (p < .001). Median frequency increased only in the SUP20 condition (p = .021). We concluded that QF NMES-induced contraction fatigability is greater when the knee is flexed at 60° compared to 20°. In addition, a supine position promotes earlier fatigue for a 60° knee flexion, but it delays fatigue onset for a 20° knee flexion compared to the seated position. These results provide a rationale for lower limb positioning during NMES, which depends on training objectives, e.g., strengthening or task-specific functionality training.

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Method to determine the tracking angles of heliostats.

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