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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.
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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.
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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.
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A slider-crank mechanism 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. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in...

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Related Experiment Video

Updated: Mar 31, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

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Studies on dynamic motion compensation and positioning accuracy on star tracker.

Zhang Jun, Hao Yuncai, Wang Li

|October 20, 2015

Summary

This study introduces a new method to reduce star tracker motion errors by modeling star spot velocity. The approach enhances location accuracy for both uniform motion and acceleration, improving dynamic performance.

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Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

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Area of Science:

Aerospace Engineering
Astrophysics
Navigation Systems

Background:

Motion error significantly limits star tracker dynamic performance.
Nonuniformity of star image velocity on the detector is a key motion error source.

Purpose of the Study:

To develop a general model for moving star spots.
To propose a novel method for motion compensation and location accuracy.
To analyze existing techniques like time-delayed integration.

Main Methods:

Building a general model for moving star spots.
Deriving motion compensation and location accuracy for uniform velocity and acceleration.
Theoretically analyzing time-delayed integration and similar techniques.

Main Results:

The proposed method demonstrates steadier performance than dynamic binning.
Positional error is negligible when smear length is significantly less than 3.464 times the star spot scale.
Accuracy can be maintained by adjusting frame-integration time inversely proportional to focal plane velocity.

Conclusions:

The novel method effectively minimizes velocity nonuniformity in star trackers.
Acceleration effects must be compensated to approach the Cramér-Rao lower bound for accuracy.
The findings suggest practical strategies for enhancing star tracker precision.