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Coordination Number and Geometry

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In most main group element compounds, the valence electrons of the isolated atoms combine to form chemical bonds that satisfy the octet rule. For instance, the four valence electrons of carbon overlap with electrons from four hydrogen atoms to form CH4. The one valence electron leaves sodium and adds to the seven valence electrons of chlorine to form the ionic formula unit NaCl (Figure 1a). Transition metals do not normally bond in this fashion. They primarily form coordinate covalent bonds, a...
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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Calibration Procedures for Orthogonal Superposition Rheology
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Determine turntable coordinate system considering its non-orthogonality.

Xiaoting Guo1, Jun Tang1, Jie Li1

  • 1National Key Laboratory for Electronic Technology, School of Instrument and Electronics, North University of China, Taiyuan 030051, People's Republic of China.

The Review of Scientific Instruments
|April 1, 2019
PubMed
Summary

This study presents a fast method for calibrating three-axis turntables using 3D point cloud data. The technique accurately determines the turntable

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Area of Science:

  • Metrology and Measurement Science
  • Robotics and Automation
  • Computer Vision and 3D Reconstruction

Background:

  • Three-axis turntables are crucial in industrial and laboratory settings for object measurement.
  • Accurate calibration of turntable coordinate systems is essential for precise measurements.
  • Existing calibration methods can be complex and time-consuming.

Purpose of the Study:

  • To develop a fast and practical method for determining the coordinate system of a three-axis turntable.
  • To enable precise calibration using spatial coordinate point cloud data.
  • To validate the method's effectiveness through experimental results.

Main Methods:

  • Utilizing sphere fitting, plane fitting, and point projection to process scattered point cloud data.
  • Employing least two pairs of skew lines to compute the approximate turntable center, accounting for non-orthogonality.
  • Optimizing direction vectors based on the approximate sphere center and initial rotation vectors.

Main Results:

  • Successfully computed initial direction vectors and approximate turntable center.
  • Quantified non-orthogonality through intersection angles and distances between axes.
  • Demonstrated a reduction in total attitude errors across all three axes after calibration.

Conclusions:

  • The proposed method is effective and practical for calibrating three-axis turntables.
  • Spatial point cloud data analysis provides a robust approach to coordinate system determination.
  • Experimental validation confirms the significant improvement in measurement accuracy.