Perspectives on Euler angle singularities, gimbal lock, and the orthogonality of applied forces and applied moments

Hemingway, Evan; O’Reilly, Oliver M.

doi:10.1007/s11044-018-9620-0

Cited by 84 publications

(52 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results for this case are qualitatively similar to those for = R and little is gained by adding this additional feature to the model 8. Our perspective on coordinate singularities is based on the recent work[24].…”

supporting

confidence: 70%

Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Bronars

O’Reilly

2019

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

The celebrated mathematician John E. Littlewood noted that a hoop with an attached mass rolling on a ground plane may exhibit self-induced jumping. Subsequent works showed that his analysis was flawed and revealed paradoxical behaviour that can be resolved by incorporating the inertia of the hoop. A comprehensive analysis of this problem is presented in this paper. The analysis illuminates the regularity induced in the model of the hoop when its mass moment of inertia is incorporated, shows that the paradoxical motions of the hoop are consistent with the principles of mechanics and demonstrates the simplest example in the dynamics of rigid bodies that exhibits self-induced jumping.

show abstract

supporting

confidence: 70%

Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Bronars

O’Reilly

2019

Proc. R. Soc. A.

Self Cite

View full text Add to dashboard Cite

show abstract

“…ELAs are limited by a phenomenon called "gimbal lock" due to similarities between two phenomena, which prevents them from measuring orientation when the pitch angle approaches ± 90 degrees. Thus, QTRs are often used [34] and are included as features in this study for comparison. Nonetheless, the non-fusion MGF data do not show any obvious significance in describing gesture patterns [23]; thus, they were excluded from the analysis in this study.…”

Section: Data Preprocessingmentioning

confidence: 99%

Sensor Fusion of Motion-Based Sign Language Interpretation with Deep Learning

Lee

Chong

Chung

2020

Sensors

View full text Add to dashboard Cite

Sign language was designed to allow hearing-impaired people to interact with others. Nonetheless, knowledge of sign language is uncommon in society, which leads to a communication barrier with the hearing-impaired community. Many studies of sign language recognition utilizing computer vision (CV) have been conducted worldwide to reduce such barriers. However, this approach is restricted by the visual angle and highly affected by environmental factors. In addition, CV usually involves the use of machine learning, which requires collaboration of a team of experts and utilization of high-cost hardware utilities; this increases the application cost in real-world situations. Thus, this study aims to design and implement a smart wearable American Sign Language (ASL) interpretation system using deep learning, which applies sensor fusion that “fuses” six inertial measurement units (IMUs). The IMUs are attached to all fingertips and the back of the hand to recognize sign language gestures; thus, the proposed method is not restricted by the field of view. The study reveals that this model achieves an average recognition rate of 99.81% for dynamic ASL gestures. Moreover, the proposed ASL recognition system can be further integrated with ICT and IoT technology to provide a feasible solution to assist hearing-impaired people in communicating with others and improve their quality of life.

show abstract

“…To that end, there are three alternatives ( Figure 3): Euler angles, rotation matrices and quaternions [22]. The use of Euler angles leads to singularity problems when the angle of the second rotation (ψ) is 0 or π radians, leading to the so-called Gimbal lock [15]. In addition, these angles involve a combination of nonlinear sine and cosine functions, which mathematical treatment is laborious [16].…”

Section: Rotation Operatorsmentioning

confidence: 99%

Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method

et al. 2019

View full text Add to dashboard Cite

The Discrete Element Method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First or second order integration schemes based on a Taylor series are frequently used in this framework and showed to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the 4 th order Runge-Kutta scheme presented by Munjiza et al. and the predictor-corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a Velocity Verlet scheme for the translational in

show abstract

Perspectives on Euler angle singularities, gimbal lock, and the orthogonality of applied forces and applied moments

Cited by 84 publications

References 13 publications

Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Gliding motions of a rigid body: the curious dynamics of Littlewood's rolling hoop

Sensor Fusion of Motion-Based Sign Language Interpretation with Deep Learning

Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method

Contact Info

Product

Resources

About