Determining dual Euler angles of the ankle complex in vivo using "flock of birds" electromagnetic tracking device

The dual Euler angles method has been proposed as an alternative approach to describe the general spatial human joint motion. In this study, the dual Euler angles method was applied to study the three-dimensional motion of the ankle complex. The methodology for obtaining dual Euler angles of the ankle complex was developed by using a "Flock of Birds" electromagnetic tracking device. The repeatability of the methodology was studied based on the intertester and intratester variability analysis. Finally kinematic coupling characteristics of the ankle complex during dorsiflexion-plantarflexion, eversion-inversion, and abduction-adduction were analyzed according to the parameters of the dual Euler angles.     

An optimisation-based model for full-body upright reaching movements

An optimal simulation 3D model for full-body upright reaching movements was developed using graphic-based modelling tools (SimMechanics) to generate an inverse dynamics model of the skeleton and using parameterisation methods for a sensory motor controller. The adaptive weight coefficient of the cost function based on the final motor task error (i.e. distance between end-effector and target at the end of movement) was used to correct motor task error and physiological measurements (e.g. joint power, centre of mass displacement, etc.). The output of the simulation models using various cost functions were compared to experimental data from 15 healthy participants performing full-body upright reaching movements. The proposed method can reasonably predict full-body voluntary movements in terms of final posture, joint power, and movement of the centre of mass (COM) using simple algebraic calculations of inverse dynamics and forward kinematics instead of the complicated integrals of the forward dynamics. We found that the combination of several control strategies, i.e. minimising end-effector error, total joint power and body COM produced the best fit of the full-body reaching task.     

Use of dual Euler angles to quantify the three-dimensional joint motion and its application to the ankle joint complex

This paper presents a modified Euler angles method, dual Euler angles approach, to describe general spatial human joint motions. In dual Euler angles approach, the three-dimensional joint motion is considered as three successive screw motions with respect to the axes of the moving segment coordinate system; accordingly, the screw motion displacements are represented by dual Euler angles. The algorithm for calculating dual Euler angles from coordinates of markers on the moving segment is also provided in this study. As an example, the proposed method is applied to describe motions of ankle joint complex during dorsiflexion–plantarflexion. A Flock of Birds electromagnetic tracking device (FOB) was used to measure joint motion in vivo. Preliminary accuracy tests on a gimbal structure demonstrate that the mean errors of dual Euler angles evaluated by using source data from FOB are less than 1° for rotations and 1 mm for translations, respectively. Based on the pilot study, FOB is feasible for quantifying human joint motions using dual Euler angles approach.     

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.     

On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Rationalization of kinematic descriptors for three-dimensional hand and finger motion

Modelling joint motion in three dimensions is often based on techniques taken from classical dynamics, each analysis resulting in a set of six parameters describing the relative motion betwen two body segments. The literature on joint kinematics has been difficult to compare due to use of different anatomical landmarks, axis nomenclature, and analytical methods. It is here shown that with care in sequence definition, the three alignment-based systems (Euler, Cardan, floating axis) give identical results for angular parameters. While the equivalent screw displacement axis system can be related simply to the other methods only if the functional axis of motion is aligned with a coordinate axis, the basic matrix for relating rigid body positions before and after a motion can always be reconstructed. Therefore the changes in alignment angles may be obtained from screw displacement parameters, permitting the results of different analyses to be compared. Translation parameters are most difficult to interpret in any system. Examples of the way in which simple planar motions are characterized by the various analytical methods are given.     

Diffusion-based learning theory for organizing visuo-motor coordination

A diffusion-based learning theory is presented and applied to organize the visuomotor coordination of an eye-hand system which has redundant motion degree of freedom (dof). This theory considers the spatial optimality of the coordination: to minimize the end-effector position error of the eye-hand system as well as the differentiation of the joint angles with respect to the end-effector positions over all the bounded work space. By introducing variational methods with respect to the space, we derive a partial differential equation (PDE) of the joint angles with respect to the work space. The equation includes a diffusion term. For the given boundary conditions and the initial conditions, it can be solved uniquely, and the solution is a well organized map. From the motor learning point of view, our approach contains both the aspects of supervised learning as well as self-organization. Firstly, we assume that the forward relation from the hand system's joint angles to its end-effector positions can be obtained using supervised learning, and at the boundary of the work space, the supervisor can provide correct joint information. Then, by evolving the diffusion equation, we organize the visuomotor coordination. We show the effectiveness of this approach using a 3-dof scale manipulator. The problems of how to realize the visuomotor map; how to utilize the resultant map in several motions; and what are the influences of the initial conditions on the map formation and the relation to the boundary conditions are also discussed using computer simulations. Our approach has three advantages: (1) it does not require too many trial motions for the eye-hand system; (2) during the map formation process, it requires only the local interactions between each node; and (3) it guarantees the final map's spatial optimality over all the bounded work space. Received: 8 May 1997 / Accepted in revised form: 12 June 1998     

A behavior-based inverse kinematics algorithm to predict arm prehension postures for computer-aided ergonomic evaluation.

In this paper, the computational problem of inverse kinematics of arm prehension movements was investigated. How motions of each joint involved in arm movements can be used to control the end-effector (hand) position and orientation was first examined. It is shown that the inverse kinematics problem due to the kinematic redundancy in joint space is ill-posed only at the control of hand orientation but not at the control of hand position. Based upon this analysis, a previously proposed inverse kinematics algorithm (Wang et Verriest, 1998a) to predict arm reach postures was extended to a seven-DOF arm model to predict arm prehension postures using a separate control of hand position and orientation. The algorithm can be either in rule-based form or by optimization through appropriate choice of weight coefficients. Compared to the algebraic inverse kinematics algorithm, the proposed algorithm can handle the non-linearity of joint limits in a straightforward way. In addition, no matrix inverse calculation is needed, thus avoiding the stability and convergence problems often occurring near a singularity of the Jacobian. Since an end-effector motion-oriented method is used to describe joint movements, observed behaviors of arm movements can be easily implemented in the algorithm. The proposed algorithm provides a general frame for arm postural control and can be used as an efficient postural manipulation tool for computer-aided ergonomic evaluation.     

Influence of kinematic analysis methods on detecting ankle and subtalar joint instability

Patients with subtalar joint instability may be misdiagnosed with ankle instability, which may lead to chronic instability at the subtalar joint. Therefore, it is important to understand the difference in kinematics after ligament sectioning and differentiate the changes in kinematics between ankle and subtalar instability. Three methods may be used to determine the joint kinematics; the Euler angles, the Joint Coordinate System (JCS) and the helical axis (HA). The purpose of this study was to investigate the influence of using either method to detect subtalar and ankle joints instability. 3D kinematics at the ankle and subtalar joint were analyzed on 8 cadaveric specimens while the foot was intact and after sequentially sectioning the anterior talofibular ligament (ATFL), the calcaneofibular ligament (CFL), the cervical ligament and the interosseous talocalcaneal ligament (ITCL). Comparison in kinematics calculated from sensor and anatomical landmarks was conducted as well as the influence of Euler angles and JCS rotation sequence (between ISB recommendation and previous research) on the subtalar joint. All data showed a significant increase in inversion when the ITCL was sectioned. There were differences in the data calculated using sensors coordinate systems vs. anatomic coordinate systems. Anatomic coordinate systems were recommended for these calculations. The Euler angle and JCS gave similar results. Differences in Euler angles and JCS sequence lead to the same conclusion in detecting instability at the ankle and subtalar joint. As expected, the HA detected instability in plantarflexion at the ankle joint and in inversion at the subtalar joint.     

A Biomechanical Model of the Scapulothoracic Joint to Accurately Capture Scapular Kinematics during Shoulder Movements

The complexity of shoulder mechanics combined with the movement of skin relative to the scapula makes it difficult to measure shoulder kinematics with sufficient accuracy to distinguish between symptomatic and asymptomatic individuals. Multibody skeletal models can improve motion capture accuracy by reducing the space of possible joint movements, and models are used widely to improve measurement of lower limb kinematics. In this study, we developed a rigid-body model of a scapulothoracic joint to describe the kinematics of the scapula relative to the thorax. This model describes scapular kinematics with four degrees of freedom: 1) elevation and 2) abduction of the scapula on an ellipsoidal thoracic surface, 3) upward rotation of the scapula normal to the thoracic surface, and 4) internal rotation of the scapula to lift the medial border of the scapula off the surface of the thorax. The surface dimensions and joint axes can be customized to match an individual’s anthropometry. We compared the model to “gold standard” bone-pin kinematics collected during three shoulder tasks and found modeled scapular kinematics to be accurate to within 2mm root-mean-squared error for individual bone-pin markers across all markers and movement tasks. As an additional test, we added random and systematic noise to the bone-pin marker data and found that the model reduced kinematic variability due to noise by 65% compared to Euler angles computed without the model. Our scapulothoracic joint model can be used for inverse and forward dynamics analyses and to compute joint reaction loads. The computational performance of the scapulothoracic joint model is well suited for real-time applications; it is freely available for use with OpenSim 3.2, and is customizable and usable with other OpenSim models.     

Interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting tasks

Video-based field methods that estimate L5/S1 net joint moments from kinematics based on interpolation in the sagittal plane of joint angles alone can introduce a significant error on the interpolated joint angular trajectory when applied to asymmetric dynamic lifts. Our goal was to evaluate interpolation of segment Euler angles for a wide range of dynamic asymmetric lifting tasks using cubic spline methods by comparing the interpolated values with the continuous measured ones. For most body segments, the estimated trajectories of segment Euler angles have less than 5° RMSE (in each dimension) with 5-point cubic spline interpolation when there is no measurement error of interpolation points. Sensitivity analysis indicates that when the measurement error exists, the root mean square error (RMSE) of estimated trajectories increases. Comparison among different lifting conditions showed that lifting a load from a high initial position yielded a smaller RMSE than lifting from a low initial position. In conclusion, interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting when measurement error of interpolation points can be controlled at a low level.     

Validation of a model-based inverse kinematics approach based on wearable inertial sensors

Abstract

Wearable inertial measurement units (IMUs) are a promising solution to human motion estimation. Using IMUs 3D orientations, a model-driven inverse kinematics methodology to estimate joint angles is presented. Estimated joint angles were validated against encoder-measured kinematics (robot) and against marker-based kinematics (passive mechanism). Results are promising, with RMS angular errors respectively lower than 3 and 6?deg over a minimum range of motion of 50?deg (robot) and 160?deg (passive mechanism). Moreover, a noise robustness analysis revealed that the model-driven approach reduces the effects of experimental noises, making the proposed technique particularly suitable for application in human motion analysis.     

Knee kinematics and kinetics during shuttle run cutting: comparison of the assessments performed with and without the point cluster technique

The differences between the assessments performed with and without the point cluster technique (PCT) for knee joint motions during the high-risk movements associated with non-contact anterior cruciate ligament (ACL) injuries have not been reported. This study aims to examine the differences between PCT and non-PCT assessments for knee joint angles and moments during shuttle run cutting. Fourteen high school athletes performed a maximal effort shuttle run cutting task. Motion data were collected by an 8-camera motion analysis system at 200 Hz, and ground reaction force data were recorded using a force plate at 1000 Hz. In both PCT and non-PCT approaches, the knee joint angles were calculated using Euler angle rotations, and the knee joint moments were obtained by solving the Newton-Euler equations using an inverse dynamics technique. For the extension/flexion angle, good agreement was measured between PCT and non-PCT assessments. The abduction angle obtained in the non-PCT assessment was smaller than that obtained with the PCT. An internal rotation angle was obtained in the PCT assessment, whereas a small external rotation angle was obtained in the non-PCT assessment. For the knee joint moments, good agreement between PCT and non-PCT assessments was observed for all the components. The differences in the knee joint angles were attributed in part to the differences in the position of the medial femoral epicondyle. The results suggest that the ACL injury risk during shuttle run cutting is estimated lower in the non-PCT assessment than in the PCT assessment.     

Prediction of fingers posture using artificial neural networks

Predicting the hand and fingers posture during grasping tasks is an important issue in the frame of biomechanics. In this paper, a technique based on neural networks is proposed to learn the inverse kinematics mapping between the fingertip 3D position and the corresponding joint angles. Finger movements are obtained by an instrumented glove and are mapped to a multichain model of the hand. From the fingertip desired position, the neural networks allow predicting the corresponding finger joint angles keeping the specific subject coordination patterns. Two sets of movements are considered in this study. The first one, the training set, consisting of free fingers movements is used to construct the mapping between fingertip position and joint angles. The second one, constructed for testing purposes, is composed of a sequence of grasping tasks of everyday-life objects. The maximal mean error between fingertip measured position and fingertip position obtained from simulated joint angles and forward kinematics is 0.99+/-0.76mm for the training set and 1.49+/-1.62mm for the test set. Also, the maximal RMS error of joint angles prediction is 2.85 degrees and 5.10 degrees for the training and test sets respectively, while the maximal mean joint angles prediction error is -0.11+/-4.34 degrees and -2.52+/-6.71 degrees for the training and test sets, respectively. Results relative to the learning and generalization capabilities of this architecture are also presented and discussed.     

Knee joint kinematics and kinetics during the hop and cut after soft tissue artifact suppression: Time to reconsider ACL injury mechanisms?

The recent development of a soft tissue artifact (STA) suppression method allows us to re-evaluate the tibiofemoral kinematics currently linked to non-contact knee injuries. The purpose of this study was therefore to evaluate knee joint kinematics and kinetics in six degrees of freedom (DoF) during the loading phases of a jump lunge and side cut using this in silico method. Thirty-five healthy adults completed these movements and their surface marker trajectories were then scaled and processed with OpenSim’s inverse kinematics (IK) and inverse dynamics tools. Knee flexion angle-dependent kinematic constraints defined based on previous bone pin (BP) marker trajectories were then applied to the OpenSim model during IK and these constrained results were then processed with the standard inverse dynamics tool. Significant differences for all hip, knee, and ankle DoF were observed after STA suppression for both the jump lunge and side cut. Using clinically relevant effect size estimates, we conclude that STA contamination had led to misclassifications in hip transverse plane angles, knee frontal and transverse plane angles, medial/lateral and distractive/compressive knee translations, and knee frontal plane moments between the NoBP and the BP IK solutions. Our results have substantial clinical implications since past research has used joint kinematics and kinetics contaminated by STA to identify risk factors for musculoskeletal injuries.     

A constraint-based approach to modelling the mobility of the human knee joint

A model of knee mobility able to predict the range and pattern of movement in the unloaded joint was proposed by Wilson et al. (J. Biomech. 31 (1998) 1127-1136). The articular surfaces in the lateral and medial compartments and isometric fascicles in three of the knee ligaments were represented as five constraints on motion between the femur and tibia in a single degree-of-freedom parallel spatial mechanism. The path of movement of the bones during passive flexion was found by solving the forward kinematics of the mechanism using an iterative method. The present paper shows that such a mechanism-based solution approach can lead to an underestimation of the flexion range. This is due to the mechanism reaching a 'stationary configuration' and 'locking'. A new, constraint-based approach to the solution of the model joint displacement is proposed. It avoids the representation of ligaments and articular surfaces by kinematically equivalent chains of one degree-of-freedom pairs which are prone to singularities. It relies instead on a numerical solution of five non-linear constraint equations to find the relative positions of the bones at a series of flexion angles. The method is successful both in its ability to predict motion through a physiological range and in its efficiency with a solution rate forty times faster than the original algorithm. The new approach may be extended to include more complex joint surface geometry, allowing a study of the effects of articular surface shape and ligament arrangement on joint kinematics.     

Optimization-based prediction of asymmetric human gait

An optimization-based formulation and solution method are presented to predict asymmetric human gait for a large-scale skeletal model. Predictive dynamics approach is used in which both the joint angles and joint torques are treated as unknowns in the equations of motion. For the optimization formulation, the joint angle profiles are treated as the primary unknowns, and velocities and accelerations are calculated using them. In numerical implementation, the joint angle profiles are discretized using the B-spline interpolation. An algorithm is presented to inversely calculate the joint torques and the ground reaction forces. The sum of the joint-torques squared, called the dynamic effort, is minimized as the human performance measure. Constraints are imposed on the joint strengths (torques) and joint ranges of motion along with other physical constraints. The formulation is validated by simulating a symmetric gait and comparing the results with the experimental data. Then asymmetric gait motion is simulated, where the left and right step lengths are different. The kinematics and kinetics results from the simulation are presented and discussed. Predicted ground reaction forces are explained by using the inverted pendulum model. Predicted kinematics and kinetics have trends that are similar to those reported in the literature. Potential practical applications of the formulation and the solution approach are discussed.     

Physical sensor difference-based method and virtual sensor difference-based method for visual and quantitative estimation of lower limb 3D gait posture using accelerometers and magnetometers

An approach using a physical sensor difference-based algorithm and a virtual sensor difference-based algorithm to visually and quantitatively confirm lower limb posture was proposed. Three accelerometers and two MAG(3)s (inertial sensor module) were used to measure the accelerations and magnetic field data for the calculation of flexion/extension (FE) and abduction/adduction (AA) angles of hip joint and FE, AA and internal/external rotation (IE) angles of knee joint; then, the trajectories of knee and ankle joints were obtained with the joint angles and segment lengths. There was no integration of acceleration or angular velocity for the joint rotations and positions, which is an improvement on the previous method in recent literature. Compared with the camera motion capture system, the correlation coefficients in five trials were above 0.91 and 0.92 for the hip FE and AA, respectively, and higher than 0.94, 0.93 and 0.93 for the knee joint FE, AA and IE, respectively.     

A computer vision based method for 3D posture estimation of symmetrical lifting

Work-related musculoskeletal disorders (WMSD) are commonly observed among the workers involved in material handling tasks such as lifting. To improve work place safety, it is necessary to assess musculoskeletal and biomechanical risk exposures associated with these tasks. Such an assessment has been mainly conducted using surface marker-based methods, which is time consuming and tedious. During the past decade, computer vision based pose estimation techniques have gained an increasing interest and may be a viable alternative for surface marker-based human movement analysis. The aim of this study is to develop and validate a computer vision based marker-less motion capture method to assess 3D joint kinematics of lifting tasks. Twelve subjects performing three types of symmetrical lifting tasks were filmed from two views using optical cameras. The joints kinematics were calculated by the proposed computer vision based motion capture method as well as a surface marker-based motion capture method. The joint kinematics estimated from the computer vision based method were practically comparable to the joint kinematics obtained by the surface marker-based method. The mean and standard deviation of the difference between the joint angles estimated by the computer vision based method and these obtained by the surface marker-based method was 2.31 ± 4.00°. One potential application of the proposed computer vision based marker-less method is to noninvasively assess 3D joint kinematics of industrial tasks such as lifting.