Alternative Representation of the Shoulder Orientation Based on the Tilt-and-Torsion Angles

2020 ◽  
Vol 142 (7) ◽  
Author(s):  
Alexandre Campeau-Lecours ◽  
Dinh-Son Vu ◽  
Frédéric Schweitzer ◽  
Jean-Sébastien Roy
Keyword(s):  
Euler Angle ◽  
Test Subject ◽  
Euler Angles ◽  
Torsion Angles ◽  
Alternative Representation ◽  
Human Movements ◽  
Measurement Units ◽  
Arm Elevation ◽  
Gimbal Lock ◽  
Shoulder Elevation

Abstract The International Society of Biomechanics (ISB) has proposed standardized recommendations for recording human joint motion. The Euler angles—the orientation representation currently proposed by the ISB—have two drawbacks, namely, the issue of singularities (gimbal lock) and the difficulty to obtain clinical and interpretable orientation representation for compound movements. The orientation representation of the shoulder joint with the Euler angles is particularly challenging due to its broad range of motion. This paper proposes and evaluates an alternative orientation representation for shoulder movement based on the tilt-and-torsion representation, a method that aims at providing a more clinically interpretable solution for describing joint movements compared to the standard Euler angles. Three studies were performed to compare the different orientation representation methods. The first two studies consist in simulations of arm elevation in different planes. The third study is an experiment using inertial-measurement-units with one test subject performing shoulder elevation movements in different planes. The tilt-and-torsion representation is then compared with different Euler angle conventions. The results show that Euler angles are biased or clinically uninterpretable for compound movements. Conversely, tilt-and-torsion representation does not suffer from these limitations. Although not extensive, the experiments suggest that the tilt-and-torsion representation has the potential to better represent human movements and provide more clinically interpretable results than the Euler angles.

scholarly journals A Fusion Method for Combining Low-Cost IMU/Magnetometer Outputs for Use in Applications on Mobile Devices

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2616 ◽  
Author(s):  
Photis Patonis ◽  
Petros Patias ◽  
Ilias N. Tziavos ◽  
Dimitrios Rossikopoulos ◽  
Konstantinos G. Margaritis
Keyword(s):  
Mobile Devices ◽  
Low Cost ◽  
Mathematical Formulation ◽  
Computational Cost ◽  
Three Dimensional ◽  
Fusion Method ◽  
Augmented Reality Application ◽  
Measurement Units ◽  
Gimbal Lock ◽  
Software Utility

This paper presents a fusion method for combining outputs acquired by low-cost inertial measurement units and electronic magnetic compasses. Specifically, measurements of inertial accelerometer and gyroscope sensors are combined with no-inertial magnetometer sensor measurements to provide the optimal three-dimensional (3D) orientation of the sensors’ axis systems in real time. The method combines Euler–Cardan angles and rotation matrix for attitude and heading representation estimation and deals with the “gimbal lock” problem. The mathematical formulation of the method is based on Kalman filter and takes into account the computational cost required for operation on mobile devices as well as the characteristics of the low-cost microelectromechanical sensors. The method was implemented, debugged, and evaluated in a desktop software utility by using a low-cost sensor system, and it was tested in an augmented reality application on an Android mobile device, while its efficiency was evaluated experimentally.

scholarly journals Assessing Shoulder Biomechanics of Healthy Elderly Individuals During Activities of Daily Living Using Inertial Measurement Units: High Maximum Elevation Is Achievable but Rarely Used

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Ryan M. Chapman ◽  
Michael T. Torchia ◽  
John-Erik Bell ◽  
Douglas W. Van Citters
Keyword(s):  
External Rotation ◽  
Shoulder Function ◽  
Measurement Unit ◽  
Clinical Settings ◽  
Healthy Individuals ◽  
Inertial Measurement ◽  
Healthy Elderly ◽  
Maximum Elevation ◽  
Measurement Units ◽  
Shoulder Elevation

Current shoulder clinical range of motion (ROM) assessments (e.g., goniometric ROM) may not adequately represent shoulder function beyond controlled clinical settings. Relative inertial measurement unit (IMU) motion quantifies ROM precisely and can be used outside of clinic settings capturing “real-world” shoulder function. A novel IMU-based shoulder elevation quantification method was developed via IMUs affixed to the sternum/humerus, respectively. This system was then compared to in-laboratory motion capture (MOCAP) during prescribed motions (flexion, abduction, scaption, and internal/external rotation). MOCAP/IMU elevation were equivalent during flexion (R2 = 0.96, μError = 1.7 deg), abduction (R2 = 0.96, μError = 2.9 deg), scaption (R2 = 0.98, μError = −0.3 deg), and internal/external rotation (R2 = 0.90, μError = 0.4 deg). When combined across movements, MOCAP/IMU elevation were equal (R2 = 0.98, μError = 1.4 deg). Following validation, the IMU-based system was deployed prospectively capturing continuous shoulder elevation in 10 healthy individuals (4 M, 69 ± 20 years) without shoulder pathology for seven consecutive days (13.5 ± 2.9 h/day). Elevation was calculated continuously daily and outcome metrics included percent spent in discrete ROM (e.g., 0–5 deg and 5–10 deg), repeated maximum elevation (i.e., >10 occurrences), and maximum/average elevation. Average elevation was 40 ± 6 deg. Maximum with >10 occurrences and maximum were on average 145–150 deg and 169 ± 8 deg, respectively. Subjects spent the vast majority of the day (97%) below 90 deg of elevation, with the most time spent in the 25–30 deg range (9.7%). This study demonstrates that individuals have the ability to achieve large ROMs but do not frequently do so. These results are consistent with the previously established lab-based measures. Moreover, they further inform how healthy individuals utilize their shoulders and may provide clinicians a reference for postsurgical ROM.

A Sliding Mode Controller of Quadrotor Based on Unit Quaternion

2014 ◽  
Vol 536-537 ◽  
pp. 1087-1092
Author(s):  
Yue Yue Lv ◽  
Wei Huang ◽  
Juan Liu ◽  
Zheng Fu Peng
Keyword(s):  
Flight Control ◽  
Control Algorithm ◽  
Sliding Mode ◽  
Variable Structure ◽  
Sliding Mode Controller ◽  
Euler Angles ◽  
Unit Quaternion ◽  
Structure Control ◽  
Sliding Mode Variable Structure ◽  
Gimbal Lock

In this paper, quaternionbased mathematical model of Quadrotor without singularity is established to avoid Gimbal Lock problem in Euler angles. Flight control algorithm based on sliding mode variable structure control (SMVSC) is introduced to control the attitude and position to approach the challenge of underactuation, nonlinearity and strong coupling. Numerical simulation is conducted to prove the effectiveness of the proposed method.

scholarly journals Model of Soft Tissue Artifact Propagation to Joint Angles in Human Movement Analysis

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Álvaro Page ◽  
Helios de Rosario ◽  
Vicente Mata ◽  
Antonio Besa
Keyword(s):  
Soft Tissue ◽  
Movement Analysis ◽  
Euler Angle ◽  
Human Movement ◽  
Rotation Vector ◽  
Joint Angles ◽  
Human Movements ◽  
Free Gold ◽  
Marker Cluster ◽  
Soft Tissue Artifact

This work describes the kinematic laws that govern the transmission of soft tissue artifact errors to kinematic variables in the analysis of human movements. Artifacts are described as relative translations and rotations of the marker cluster over the bone, and a set of explicit expressions is defined to account for the effect of that relative motion on different representations of rotations: the rotation around the screw axis, or rotation vector, and three Euler angle sequences (XY′Z, YX′Y″, ZX′Y″). Although the error transmission is nonlinear in all cases, the effect of artifacts is greater on Euler sequences than on the rotation vector. Specifically, there are crosstalk effects in Euler sequences that amplify the errors near singular configurations. This fact is an additional source of variability in studies that describe artifacts by comparing the Euler angles obtained from skin markers, with the angles of an artifact-free gold standard. The transmission of errors to rotation vector coordinates is less variable or dependent on the type of motion. This model has been tested in an experiment with a deformable mechanical model with a spherical joint.

Denavit-Hartenberg Parameterization of Euler Angles

2012 ◽  
Vol 7 (2) ◽  
Author(s):  
S. V. Shah ◽  
S. K. Saha ◽  
J. K. Dutt
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Three Dimensional ◽  
Euler Angle ◽  
Euler Angles ◽  
Spherical Joint ◽  
Multiple Degrees Of Freedom ◽  
Cartesian Space ◽  
Revolute Joints

Euler angles describe rotations of a rigid body in three-dimensional Cartesian space, as can be obtained by, say, a spherical joint. The rotation carried out by a spherical joint can also be expressed by using three intersecting revolute joints that can be described using the popular Denavit-Hartenberg (DH) parameters. However, the motions of these revolute joints do not necessarily correspond to any set of the Euler angles. This paper attempts to correlate the Euler angles and DH parameters by introducing a concept of DH parameterization of Euler angels. A systematic approach is presented in order to obtain the DH parameters for any Euler angles set. This gives rise to the concept of Euler-angle-joints (EAJs), which provide rotations equivalent to a particular set of Euler angles. Such EAJs can be conveniently used for the modeling of multibody systems having multiple-degrees-of-freedom joints.

A Novel Method to Integrate IMU and Magnetometers in Attitude and Heading Reference Systems

2011 ◽  
Vol 64 (4) ◽  
pp. 727-738 ◽  
Author(s):  
Songlai Han ◽  
Jinling Wang
Keyword(s):  
Local Level ◽  
Nonlinear Problems ◽  
Euler Angle ◽  
Model System ◽  
The Body ◽  
Euler Angles ◽  
Reference Systems ◽  
Body Frame ◽  
Promising Alternative ◽  
Stable Orientation

Modern attitude and heading reference systems (AHRS) generally use Kalman filters to integrate gyros with some other augmenting sensors, such as accelerometers and magnetometers, to provide a long term stable orientation solution. The construction of the Kalman filter for the AHRS is flexible, while the general options are the methods based on quaternion, Euler angles, or Euler angle errors. But the quaternion and Euler angle based methods need to model system angular motions, and, meanwhile, all these three methods suffer from nonlinear problems which will increase the system complexities and the computational difficulties. This paper proposes a novel implementation method for the AHRS integrating IMU and magnetometer sensors. In the proposed method, the Kalman filtering is implemented to use the Euler angle errors to express the local level frame (lframe) errors, rather than express the body frame (bframe) errors as the customary methods do. A linear system error model based on the Euler angles errors expressing thelframe errors for the AHRS has been developed and the corresponding system observation model has been derived. This proposed method for AHRS does not need to model system angular motions and also avoids the nonlinear problem which is inherent in the commonly used methods. The experimental results show that the proposed method is a promising alternative for the AHRS.

Noncommutativity of Finite Rotations and Definitions of Curvature and Torsion

2019 ◽  
Vol 14 (9) ◽  
Author(s):  
Ahmed A. Shabana ◽  
Hao Ling
Keyword(s):  
Euler Angle ◽  
Rigid Body Dynamics ◽  
Space Curve ◽  
Euler Angles ◽  
Arc Length ◽  
Important Conclusion ◽  
Finite Rotations ◽  
Definition Of ◽  
Curvature And Torsion ◽  
Curve Geometry

The geometry of a space curve, including its curvature and torsion, can be uniquely defined in terms of only one parameter which can be the arc length parameter. Using the differential geometry equations, the Frenet frame of the space curve is completely defined using the curve equation and the arc length parameter only. Therefore, when Euler angles are used to describe the curve geometry, these angles are no longer independent and can be expressed in terms of one parameter as field variables. The relationships between Euler angles used in the definition of the curve geometry are developed in a closed-differential form expressed in terms of the curve curvature and torsion. While the curvature and torsion of a space curve are unique, the Euler-angle representation of the space curve is not unique because of the noncommutative nature of the finite rotations. Depending on the sequence of Euler angles used, different expressions for the curvature and torsion can be obtained in terms of Euler angles, despite the fact that only one Euler angle can be treated as an independent variable, and such an independent angle can be used as the curve parameter instead of its arc length, as discussed in this paper. The curve differential equations developed in this paper demonstrate that the curvature and torsion expressed in terms of Euler angles do not depend on the sequence of rotations only in the case of infinitesimal rotations. This important conclusion is consistent with the definition of Euler angles as generalized coordinates in rigid body dynamics. This paper generalizes this definition by demonstrating that finite rotations cannot be directly associated with physical geometric properties or deformation modes except in the cases when infinitesimal-rotation assumptions are used.

A Simple Method to Obtain Consistent and Clinically Meaningful Pelvic Angles from Euler Angles during Gait Analysis

2007 ◽  
Vol 23 (3) ◽  
pp. 218-223 ◽  
Author(s):  
Tishya A.L. Wren ◽  
Paul C. Mitiguy
Keyword(s):  
Gait Analysis ◽  
Elevation Angle ◽  
Euler Angle ◽  
Technical Note ◽  
Euler Angles ◽  
Simple Method ◽  
Lean Angle ◽  
Angle Rotation ◽  
Clinical Gait Analysis ◽  
Rotation Sequence

Clinical gait analysis usually describes joint kinematics using Euler angles, which depend on the sequence of rotation. Studies have shown that pelvic obliquity angles from the traditional tilt-obliquity-rotation (TOR) Euler angle sequence can deviate considerably from clinical expectations and have suggested that a rotation-obliquity-tilt (ROT) Euler angle sequence be used instead. We propose a simple alternate approach in which clinical joint angles are defined and exactly calculated in terms of Euler angles from any rotation sequence. Equations were derived to calculate clinical pelvic elevation, progression, and lean angles from TOR and ROT Euler angles. For the ROT Euler angles, obliquity was exactly the same as the clinical elevation angle, rotation was similar to the clinical progression angle, and tilt was similar to the clinical lean angle. Greater differences were observed for TOR. These results support previous findings that ROT is preferable to TOR for calculating pelvic Euler angles for clinical interpretation. However, we suggest that exact clinical angles can and should be obtained through a few extra calculations as demonstrated in this technical note.

scholarly journals Patterns of enhancement in paretic shoulder kinematics after stroke with musical cueing

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Shinil Kang ◽  
Joon-Ho Shin ◽  
In Young Kim ◽  
Jongshill Lee ◽  
Ji-Yeoung Lee ◽  
...  
Keyword(s):  
Euler Angle ◽  
The Other ◽  
Shoulder Abduction ◽  
Specific Effects ◽  
Angle Measurements ◽  
Upper Limb Movements ◽  
Measurement Units ◽  
Hemiparetic Stroke ◽  
Auditory Cueing ◽  
Shoulder Kinematics

Abstract Musical cueing has been widely utilised in post-stroke motor rehabilitation; however, the kinematic evidence on the effects of musical cueing is sparse. Further, the element-specific effects of musical cueing on upper-limb movements have rarely been investigated. This study aimed to kinematically quantify the effects of no auditory, rhythmic auditory, and melodic auditory cueing on shoulder abduction, holding, and adduction in patients who had experienced hemiparetic stroke. Kinematic data were obtained using inertial measurement units embedded in wearable bands. During the holding phase, melodic auditory cueing significantly increased the minimum Euler angle and decreased the range of motion compared with the other types of cueing. Further, the root mean square error in the angle measurements was significantly smaller and the duration of movement execution was significantly shorter during the holding phase when melodic auditory cueing was provided than when the other types of cueing were used. These findings indicated the important role of melodic auditory cueing for enhancing movement positioning, variability, and endurance. This study provides the first kinematic evidence on the effects of melodic auditory cueing on kinematic enhancement, thus suggesting the potential use of pitch-related elements in psychomotor rehabilitation.

Quaternion Parameters in the Simulation of a Spinning Rigid Body

SIMULATION ◽  
1965 ◽  
Vol 4 (6) ◽  
pp. 390-396 ◽  
Author(s):  
E.E.L. Mitchell ◽  
A.E. Rogers
Keyword(s):  
Rigid Body ◽  
Euler Angles ◽  
Analog Implementation ◽  
Gimbal Lock

The use of quaternions in describing the orientation of a rigid body allows all possible attitudes to be sim ulated. The problem of gimbal lock encountered when using the more commonly understood Euler angles is avoided. The analog implementation of the quaternion description is given together with the transformations between quaternion parameters and Euler angles in order that the latter may be available for display.

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