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Rotation with Constant Angular Acceleration - II01:16

Rotation with Constant Angular Acceleration - II

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Kinematics is the description of motion. The kinematics of rotational motion discusses the relationships between rotation angle, angular velocity, angular acceleration, and time. One can describe many things with great precision using kinematics, but kinematics does not consider causes. For example, a large angular acceleration describes a very rapid change in angular velocity without any consideration of its cause. Thus, rotational kinematics does not represent the laws of nature.
The first...
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Rotation with Constant Angular Acceleration - I01:37

Rotation with Constant Angular Acceleration - I

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If angular acceleration is constant, then we can simplify equations of rotational kinematics, similar to the equations of linear kinematics. This simplified set of equations can be used to describe many applications in physics and engineering where the angular acceleration of a system is constant.
Using our intuition, we can begin to see how rotational quantities such as angular displacement, angular velocity, angular acceleration, and time are related to one another. For example, if a flywheel...
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Adjusting a Traverse01:12

Adjusting a Traverse

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In the site survey of a four-sided traverse, internal angles are essential to ensure geometric accuracy. The survey revealed that the sum of the measured internal angles was 359 degrees and 48 minutes, which is 12 minutes less than the expected 360 degrees. This discrepancy signals an error likely arising from measurement inaccuracies during the fieldwork.To rectify this error, the adjustment process involved distributing the 12-minute shortfall equally across the four internal angles. By...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
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Relative Motion Analysis using Rotating Axes01:25

Relative Motion Analysis using Rotating Axes

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x'y', is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it...
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Relative Motion Analysis using Rotating Axes - Acceleration01:22

Relative Motion Analysis using Rotating Axes - Acceleration

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...
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Related Experiment Video

Updated: Sep 9, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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A Method for Measuring Angular Orientation with Adaptive Compensation of Dynamic Errors.

Dimitar Dichev1,2, Iliya Zhelezarov1,2, Borislav Georgiev1,2

  • 1Department of Machine and Precision Engineering, Technical University of Gabrovo, 4 H. Dimitar Str., 5300 Gabrovo, Bulgaria.

Sensors (Basel, Switzerland)
|August 28, 2025
PubMed
Summary

This study introduces a novel method for measuring object orientation, using adaptive Kalman filtering to correct dynamic errors in real-time. This system accurately determines roll and pitch for moving objects, validated against international standards.

Keywords:
MEMS sensorsadaptive Kalman filtrationangular orientation measurementevaluation of measurement uncertainty in dynamic measurements

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Area of Science:

  • Engineering
  • Measurement Science
  • Robotics

Background:

  • Accurate angular orientation measurement is critical for dynamic systems.
  • Existing methods often struggle with instrumental and dynamic errors.
  • Inertial element stabilization can be complex and error-prone.

Purpose of the Study:

  • To develop an integrated method for measuring the angular orientation of moving objects.
  • To reduce instrumental errors through a simplified mechanical structure.
  • To achieve adaptive compensation of dynamic errors using a hardware-software platform.

Main Methods:

  • An adaptive Kalman structure was employed for real-time error correction, avoiding inertial element stabilization.
  • A two-channel measurement model with independent signals and MEMS sensors was used.
  • A metrologically based methodology for quantitative assessment, including error and uncertainty theories, was developed.

Main Results:

  • A system for measuring roll and pitch was developed and implemented.
  • Experimental validation confirmed system accuracy in static and dynamic modes against a high-accuracy reference system.
  • The developed methodology provides objective, reproducible, and traceable evaluation.

Conclusions:

  • The integrated method offers a robust solution for angular orientation measurement of dynamic objects.
  • The adaptive Kalman approach effectively compensates for dynamic errors.
  • The system's accuracy and the assessment methodology are validated and traceable to international standards.