Euler Angle Sequences Research Articles

Three-dimensional in vivo scapular kinematics and scapulohumeral rhythm: a comparison between active and passive motion

The aimof this study was to compare the scapular kinematics and scapulohumeral rhythm of healthy participants during arm elevation and loweringand to find the difference between active motion and passive motion of the shoulder. The study examined the shoulders of 10 healthy men (mean age, 23.5 years; age range, 22-28 years). The shoulders of participants were elevated and lowered while fluoroscopic images were taken, and 3-dimensional bone models were created from 2-dimensional to 3-dimensional images using model registration techniques. The Euler angle sequences of the models' scapular kinematics and scapulohumeral rhythm were compared during active and passive shoulder motion. There was a significant statistical difference of upward rotation during arm elevation between active and passive shoulder movements (P = .027). In particular, the upward rotation between 45° and 90° of elevation showed a statistically significant difference (P < .001). When the scapulawas tilted posteriorly by active motion, it resulted in a statistically significant difference as there was more tilting in the high-degree range of motions than when it was tilted by passive motion (P < .001). There was no statistically significant difference between the 2 groups in scapular external rotation. However, during arm lowering, scapular kinematics did not show statistically significant difference between active and passive motion. The scapular kinematics showed statistically significant differences between active and passive motion of upward rotation and posterior tilting of the scapuladuring arm elevation, but there were none during lowering. In terms of upward rotation, active shoulders rotated more upward during arm elevation.

Design optimization of hull size for spar-based floating offshore wind turbines

A newly evolving concept in utility-scale floating wind turbines is investigated through design optimization. The ideal hull length is selected from seven new designs, based on optimizing the trade-off between minimizing structural weight and maximizing electricity harvest. The seven new spar-buoy designs have drafts ranging from 62 to 120 m. Each floater hull has been developed in conformance with industry-standard structural guide API Bulletin 2U. Performance is assessed with the Loose software using time-domain analysis and irregular winds and waves. The simulation method is based on multi-body theory in Euler space, which does not rely on small-angle assumptions. Nonlinear hydrostatic restoring forces and moments are derived for large rotational angles in the pitch-roll-yaw Euler angle sequence. Environmental forcing by wind is computed using aero-elastic theory. A new individual pitch control (IPC) method based on DISCON control routine (Jonkman) is investigated as a possible means to improve generating efficiency. The pitch angle of each blade is individually controlled relative to a mean angle computed by DISCON to maintain the ideal angle of attack by removing the angle change caused by inclining tower. A comparison of the generating efficiency between IPC and traditional collective pitch control shows that IPC is not an effective way to increase output power.

New fundamental parameters for attitude representation

A new attitude parameter set is developed to clarify the geometry of combining finite rotations in a rotational sequence and in combining infinitesimal angular increments generated by angular rate. The resulting parameter set of six Pivot Parameters represents a rotation as a great circle arc on a unit sphere that can be located at any clocking location in the rotation plane. Two rotations are combined by linking their arcs at either of the two intersection points of the respective rotation planes. In a similar fashion, linking rotational increments produced by angular rate is used to derive the associated kinematical equations, which are linear and have no singularities. Included in this paper is the derivation of twelve Pivot Parameter elements that represent all twelve Euler Angle sequences, which enables efficient conversions between Pivot Parameters and any Euler Angle sequence. Applications of this new parameter set include the derivation of quaternions and the quaternion composition rule, as well as, the derivation of the analytical solution to time dependent coning motion. The relationships between Pivot Parameters and traditional parameter sets are included in this work. Pivot Parameters are well suited for a variety of aerospace applications due to their effective composition rule, singularity free kinematic equations, efficient conversion to and from Euler Angle sequences and clarity of their geometrical foundation.

THREE-DIMENSIONAL IN-VIVO SCAPULAR KINEMATICS AND SCAPULOHUMERAL RHYTHM: A COMPARISON BETWEEN ACTIVE AND PASSIVE MOTION

BackgroundThis study set out to offer a three-dimensional description of scapular kinematics and scapulohumeral rhythm (SHR) of healthy subjects during arm elevation and lowering, as well as to compare and...

The reliability of humerothoracic angles during arm elevation depends on the representation of rotations

The reliability of joint rotation measurements is an issue of major interest, especially in clinical applications. The effect of instrumental errors and soft tissue artifacts on the variability of human motion measures is well known, but the influence of the representation of joint motion has not yet been studied. The aim of the study was to compare the within-subject reliability of three rotation formalisms for the calculation of the shoulder elevation joint angles.Five repetitions of humeral elevation in the scapular plane of 27 healthy subjects were recorded using a stereophotogrammetry system. The humerothoracic joint angles were calculated using the YX′Y″ and XZ′Y″ Euler angle sequences and the attitude vector. A within-subject repeatability study was performed for the three representations. ICC, SEM and CV were the indices used to estimate the error in the calculation of the angle amplitudes and the angular waveforms with each method.Excellent results were obtained in all representations for the main angle (elevation), but there were remarkable differences for axial rotation and plane of elevation. The YX′Y″ sequence generally had the poorest reliability in the secondary angles. The XZ′Y′ sequence proved to be the most reliable representation of axial rotation, whereas the attitude vector had the highest reliability in the plane of elevation.These results highlight the importance of selecting the method used to describe the joint motion when within-subjects reliability is an important issue of the experiment. This may be of particular importance when the secondary angles of motions are being studied.

Increased horizontal shoulder abduction is associated with an increase in shoulder joint load in baseball pitching

Soft tissues of the shoulder undergoes substantial stresses due to humeral head movement, and this may contribute to throwing shoulder injuries in baseball pitchers. Prevention and management of throwing shoulder injuries critically rely on reduction of shear force at the shoulder joint. However, the amount and direction of the force applied to the shoulder during the throwing motion have not been clarified. The purpose of this study was to analyze forces applied to the shoulder during a baseball pitch. We performed biomechanical analysis of 213 baseball pitchers of various ages and skilllevels. Throwing motion was analyzed with a 3-dimensional motion capture system. The Eulerangle sequence was adopted to describe angular values of the upper arm relative to the trunk for shoulder rotation, and inverse dynamics was used to estimate the resultant joint forces at the shoulder. There was a significant relation between horizontal abduction/adduction angle and resultant anterior/posterior force at the point of maximum external rotation (MER) (r=-0.63, P<.01), whereby increased horizontal abduction was associated with increased resultant anterior force. There was a significant but weak correlation between abduction/adduction angle and superior/inferior force at MER (r=0.24, P<.01). Comparison among the groups with variable ages and skill levels showed larger horizontal abduction and smaller external rotation angles at MER in the adult amateur player group, whereas normalized compression force and internal rotation torque values at MER were smaller in the junior high school- and elementary school-aged groups. These results suggest that excessive horizontal abduction at MER increases anterior shear force in the shoulder and may lead to shoulder injuries. Focusing on reducing horizontal abduction at MER in the throwing motion may be key to preventing and managing shoulder injuries in baseball pitchers.

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

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.

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

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.

Orbital mechanics for engineering students

Orbital mechanics is a cornerstone subject for aerospace engineering students. Maintaining the focus of the first edition, the author provides the foundation needed to understand the subject and proceed to advanced topics. Starting with the solution of the two-body problem and formulas for the different kinds of orbits, the text moves on to Kepler's equations, orbits in three dimensions, orbital elements from observations, orbital maneuvers, orbital rendezvous and interplanetary missions. This is followed by an introduction to spacecraft dynamics and a final chapter on basic rocket dynamics. The author's teach-by-example approach emphasizes the analytical procedures and computer-implemented algorithms required by today's students. There are a large number of worked examples, illustrations, end of chapter exercises (with answers) as well as many MATLAB[registered] programs for use in homework and projects. The text can be used for one and two semester courses in space mechanics. Features: a new section on numerical integration methods applicable to space mechanics problems; a more centralized and improved discussion of coordinate systems and Euler angle sequences; an expanded development of relative motion in orbit; a new section on quaternions; new worked-out examples, illustrations and homework problems; new algorithms, MATLAB[registered] scripts and simulations; instructor's manual and lecture slides available online; and included online testing and assessment component helps students assess their knowledge of the topics.

Scapular kinematics: effects of altering the Euler angle sequence of rotations

An analysis of Euler angle sequences is presented for the scapula. In vivo kinematics were collected with a magnetic tracking device on eight healthy volunteers. To ensure accurate representation of scapular motion, pins were rigidly drilled into the scapular spine. Three rotations of the scapula with respect to the thorax were recorded during humeral elevation in the scapular plane: posterior (or backward) tilting, upward (or lateral) rotation and external rotation (or retraction). Rotations using all six possible Euler angle sequences were calculated for which each angle was represented only once. The sequence proposed by an International Society of Biomechanics subcommittee on shoulder motion (external rotation, upward rotation, posterior tilting) is consistent with both research- and clinical-based two-dimensional representations of scapular motion. Results from the present study indicate that changing sequence results in significant alterations in the description of motion, with differences up to 50° noted for some angles. Therefore, in order to compare results across different laboratories, it is recommended that the proposed standard sequence be adopted.

Error Analysis of Euler Angle Transformations

Error analyses of Euler angle transformations arise in the design of precision pointing systems, guidance systems and other systems containing gimbals. The generalized problem, including nonorthogonality of nominally orthogonal coordinate axes as well as errors in the Euler angles, is treated. The usual approach by tedious matrix techniques is simplified to yield a vector solution by application of a similarity transformation to the skew- symmetric error matrices. A vector solution is obtained directly by invoking the vector property of infinitesimal rotations. Piograms, symbolic representations of Euler angle transformations, are used to formulate the problem and to develop the vector solution. EQUENCES of angular rotations are universally used in the analysis of rigid-body dynamics. Examples can be widely found in analysis of precision pointing systems and aircraft, missiles, and space vehicles. As shown by Euler, a minimum of three rotations are required to specify the relative orientation of two orthogonal coordinate systems with arbitrary attitudes. Any physical realization of coordinate transformations, as with gimbals, for example, will introduce angular errors so that each coordinate axis is perturbed from its idealized position. The most general error analysis of an Euler angle sequence must include the effects of nonorthogonal ity of the nominally orthogonal coordinate axes as well as errors in the angles of rotation. An example problem is presented to illustrate the various approaches available for error analysis of an Euler angle sequence. The usual but tedious solution by matrix techniques is given, A vector solution is obtained by applying a similarity transformation to the matrix solution. In a second approach a vector solution to the problem is obtained directly by invoking the vector property of infinitesimal rotations. Piograms, symbolic representations of rotational coordinate transformations,1'2 are used to define the problem and are shown to give the vector solution in a particularly compact way. Three different Euler angle sequences are commonly used in the literature. One of these three is used as the example problem in this paper. The method of solution presented in the paper is applicable to any of the twelve possible three-angle Euler sequences. The method is applicable to rotational sequences of any length by an obvious extension of the technique.

The Integrated Mission Simulator

Space mission simulator programs may be divided into two broad categories: (1) training tools (quali tative devices often simulating a continuous mission), and (2) laboratory tools (quantitative devices treating the mission in phases, each phase being programmed separately to obtain optimum scaling). This paper describes the development of an analog program capable of continuously simulating an entire lunar mission in six degrees of freedom with high resolu tion throughout. The reported work logically traces the program development through the equations of motion, the guidance and control equations, and the analog mechanization. The translation equations are de veloped using a modified form of Encke's method; two reference origins are utilized at the two points of primary interest—the landing site and the target vehicle—such that the displacements are approach ing a minimum in the regions where the highest reso lution is required. The variables are rescaled as this region is approached to obtain maximum accuracy. Relays, stepping switches and diode gates are used for rescaling and to re-reference origins. A particular Euler angle sequence is selected based on matrix validity criteria applied to the mission. A previously reported guidance technique is shown to be appli cable to all phases of the mission. It is concluded that the method demonstrated in this paper leads to minimum computer loading for simulating a manned space mission without program discontinuities. Supporting data include an analog- computed trajectory representative of a long-dura tion mission, which is compared in detail with a digital solution.