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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

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...

Absolute Motion Analysis- General Plane Motion

Absolute Motion Analysis- General Plane Motion

Visualize a drone, with its propellers spinning rapidly, hovering mid-air. The fascinating movements and operations of this drone can be comprehended by applying the principle of general plane motion.
As the drone's propellers rotate, an upward force is generated that counteracts the force of gravity, enabling the drone to lift off from the ground. This initial movement of the drone is along a straight path, representing a form of translational motion. In this phase, every point on the drone...

Relative Motion Analysis using Rotating Axes - Acceleration

Relative Motion Analysis using Rotating Axes - Acceleration

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...

Relative Motion Analysis - Velocity

Relative Motion Analysis - Velocity

A stroke engine has a slider-crank mechanism that converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider.
When an external force is exerted, it sets the crank into a rotational movement. This, in turn, instigates the motion of the connecting rod, leading to what is referred to as a general plane motion. This process involves two key points - point A on the connecting rod...

Curvilinear Motion: Rectangular Components

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the time...

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Related Experiment Video

Updated: Jul 7, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Spatiotemporal approach for time-varying global image motion estimation.

W G Chen¹, G B Giannakis, N Nandhakumar

¹Microsoft Corp., Redmond, WA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 1, 1996

Summary

This study introduces new spatiotemporal algorithms for accurate image motion estimation, even with changing velocities. The developed methods improve accuracy by modeling time-varying motion using polynomial and trigonometric models.

Related Experiment Videos

Last Updated: Jul 7, 2026

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

Published on: February 12, 2014

Area of Science:

Computer Vision
Signal Processing
Image Analysis

Background:

Traditional spatiotemporal image motion estimation relies on constant velocity assumptions.
This assumption is inadequate when scene or camera velocity changes during acquisition.
Existing methods struggle with dynamic, time-varying motion scenarios.

Purpose of the Study:

To develop advanced spatiotemporal algorithms for accurate image motion estimation.
To address limitations of constant velocity assumptions in dynamic scenes.
To handle time-varying, space-invariant image motion effectively.

Main Methods:

Utilized polynomial and trigonometric polynomial models for time-varying image motion.
Formulated time-varying motion estimation as 1-D polynomial phase or phase-modulated signal parameter estimation.
Leveraged established radar signal processing techniques.

Main Results:

Developed novel spatiotemporal algorithms for time-varying motion estimation.
Demonstrated equivalence to 1-D signal parameter estimation problems.
Achieved more accurate motion estimates compared to alternative approaches.
Validated through simulation results.

Conclusions:

The proposed polynomial and trigonometric models effectively handle time-varying image motion.
The approach offers superior accuracy in motion estimation for dynamic scenes.
This work provides a robust framework for advanced image motion analysis.