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Relative Motion Analysis using Rotating Axes

Relative Motion Analysis using Rotating Axes

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 instrumental in...

Relative Motion Analysis using Rotating Axes-Problem Solving

Relative Motion Analysis using Rotating Axes-Problem Solving

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Kinematic Equations for Rotation

Kinematic Equations for Rotation

In mechanics, when one observes a rigid body in rotational motion with constant angular acceleration, it is possible to establish equations for its rotational kinematics. This process resembles how linear kinematics are dealt with in simpler motion studies.
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Relative Motion Analysis using Rotating Axes - Acceleration

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Gyroscope

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Related Experiment Video

Updated: May 28, 2026

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery

Published on: August 12, 2021

Rotor Attitude Estimation for Spherical Motors Using Geometry-Constrained Kalman Transformer Algorithm in Monocular

Fucong Liu^1,2,3, Baokaidi Tian^1,2, Faqiang Wen^1,2

¹School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China.

Sensors (Basel, Switzerland)

|May 27, 2026

Summary

This summary is machine-generated.

This study introduces a visual rotor attitude estimation (RAE) method for permanent-magnet spherical motors (PMSpMs) using a Kalman filter and geometric constraint Transformer (GK-TransT). The GK-TransT method offers high accuracy and real-time performance for precise motor control.

Keywords:

Kalman filter permanent magnet spherical motor rotor attitude estimation transformer visual tracking

Related Experiment Videos

Last Updated: May 28, 2026

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery

Published on: August 12, 2021

Area of Science:

Robotics and Control Systems
Computer Vision
Mechanical Engineering

Background:

Permanent-magnet spherical motors (PMSpMs) offer three-degree-of-freedom omnidirectional motion.
Accurate rotor attitude estimation (RAE) is critical for the closed-loop control of PMSpMs.
Existing RAE methods may lack robustness or real-time capabilities for complex spherical motor dynamics.

Purpose of the Study:

To propose and validate a novel visual RAE method for PMSpMs.
To enhance the accuracy, robustness, and real-time performance of RAE.
To compare the proposed method against existing algorithms and sensor technologies.

Main Methods:

Development of a visual RAE system using a monocular camera and a visual feature component (VFC) on the rotor.
Implementation of the Kalman filter and geometric constraint Transformer (GK-TransT) algorithm for enhanced tracking.
Comparative analysis with TransT, KCF, and CSRT algorithms, and validation against a MEMS sensor using a hydraulic rotary table benchmark.

Main Results:

The GK-TransT algorithm achieved high tracking precisions of 90.9% (main) and 94.4% (auxiliary) feature points.
The system demonstrated an average processing speed of 61.23 FPS with a single-frame latency of 16.33 ms.
The GK-TransT method outperformed MEMS sensors in accuracy and showed superior robustness under occlusion and motion blur.

Conclusions:

The proposed GK-TransT visual RAE method is highly applicable for PMSpMs due to its precision, speed, and robustness.
The developed RAE test bench validates the method's effectiveness and practicality.
This visual RAE approach provides a reliable alternative for controlling omnidirectional spherical motors.