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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 - 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.
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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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Gyroscope

Gyroscope

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Gyroscope: Precession

Gyroscope: Precession

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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.
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Related Experiment Video

Updated: May 20, 2026

An Inertial Measurement Unit Based Method to Estimate Hip and Knee Joint Kinematics in Team Sport Athletes on the Field

An Inertial Measurement Unit Based Method to Estimate Hip and Knee Joint Kinematics in Team Sport Athletes on the Field

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Angular motion estimation using dynamic models in a gyro-free inertial measurement unit.

Ezzaldeen Edwan¹, Stefan Knedlik, Otmar Loffeld

¹Center for Sensor Systems (ZESS), University of Siegen, Paul Bonatz-Str. 9-11, 57068 Siegen, Germany. edwan@zess.uni-siegen.de

Sensors (Basel, Switzerland)

|July 11, 2012

Summary

This summary is machine-generated.

This study introduces dynamic models for gyro-free inertial measurement units (GF-IMUs) using accelerometers. It enhances angular motion estimation by accounting for bias parameters within a Kalman filter framework.

Keywords:

GF-IMU angular motion estimation dynamic models

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Area of Science:

Navigation and Guidance Systems
Sensor Fusion and Estimation Theory
Inertial Measurement Unit (IMU) Technology

Background:

Gyro-free inertial measurement units (GF-IMUs) infer angular motion using only accelerometers.
Estimating angular velocity in GF-IMUs is challenging as it's not directly measured.
Accelerometer biases introduce errors in angular information vector (AIV) estimations.

Purpose of the Study:

To describe the time evolution of the state vector for angular motion estimation in GF-IMUs.
To address accelerometer bias issues for accurate angular motion estimation.
To determine conditions for an observable state space model for GF-IMUs.

Main Methods:

Utilizing dynamic models from tracking theory to describe state vector evolution.
Employing a Kalman filter approach to estimate the angular velocity vector.
Augmenting the state vector to include and estimate accelerometer bias parameters.
Performing observability analysis to ensure state space model observability.

Main Results:

Dynamic models enable the estimation of angular motion in GF-IMUs.
Augmenting the state vector with bias parameters allows for unbiased angular motion estimation.
Observability analysis defines conditions for accurate state estimation.
Simulations compare models with and without bias parameters, highlighting the impact of bias.

Conclusions:

Dynamic models and Kalman filtering effectively estimate angular motion in GF-IMUs.
Accounting for accelerometer biases is crucial for accurate GF-IMU performance.
The proposed method enhances the reliability of angular motion estimation in accelerometer-only IMUs.