Assessment of the accuracy of a human arm model with seven degrees of freedom

We are proposing a human arm model that consists of three rigid segments with seven degrees of freedom. The shoulder joint was modeled as a ball-and-socket joint and the elbow and wrist joints were modelled as skew-oblique joints. Optimal parameters for this model were calculated on the base of in vivo recordings with a spatial tracking system. The criterion of optimality was defined as the minimum of the mean-square deviation between the experimentally obtained sensor positions and orientations and their positions and orientations calculated by solving the direct kinematics problem. The minimal value of the direct kinematics error was found to be 0.5-0.6cm for sensor positions and 5-7 degrees for sensor orientations. We are proposing that these values serve as the assessment for the accuracy of the arm model.     

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.     

Sensitivity of the knee joint kinematics calculation to selection of flexion axes

Various flexion axes have been used in the literature to describe knee joint kinematics. This study measured the passive knee kinematics of six cadaveric human knee specimens using two widely accepted flexion axes; transepicondylar axis and the geometric center axis. These two axes were found to form an angle of 4.0 degrees +/- 0.8 degrees. The tibial rotation calculated using the transepicondylar axis was significantly different than the rotation obtained using the geometric center axis for the same knee motion. At 90 degrees of flexion, the tibial rotation obtained using the transepicondylar axis was 4.8 degrees +/- 9.4 degrees whereas the rotation recorded using the geometric center axis at the same flexion angle was 13.8 degrees +/- 10.2 degrees. At 150 degrees of knee flexion, the rotations obtained from the transepicondylar and the geometric center axes were 7.2 degrees +/- 5.7 degrees and 19.9 degrees +/- 6.9 degrees, respectively. The data suggest that a clear definition of the flexion axis is necessary when reporting knee joint kinematics.     

Kinematics of primate midfoot flexibility

This study describes a unique assessment of primate intrinsic foot joint kinematics based upon bone pin rigid cluster tracking. It challenges the assumption that human evolution resulted in a reduction of midfoot flexibility, which has been identified in other primates as the “midtarsal break.” Rigid cluster pins were inserted into the foot bones of human, chimpanzee, baboon, and macaque cadavers. The positions of these bone pins were monitored during a plantarflexion‐dorsiflexion movement cycle. Analysis resolved flexion‐extension movement patterns and the associated orientation of rotational axes for the talonavicular, calcaneocuboid, and lateral cubometatarsal joints. Results show that midfoot flexibility occurs primarily at the talonavicular and cubometatarsal joints. The rotational magnitudes are roughly similar between humans and chimps. There is also a similarity among evaluated primates in the observed rotations of the lateral cubometatarsal joint, but there was much greater rotation observed for the talonavicular joint, which may serve to differentiate monkeys from the hominines. It appears that the capability for a midtarsal break is present within the human foot. A consideration of the joint axes shows that the medial and lateral joints have opposing orientations, which has been associated with a rigid locking mechanism in the human foot. However, the potential for this same mechanism also appears in the chimpanzee foot. These findings demonstrate a functional similarity within the midfoot of the hominines. Therefore, the kinematic capabilities and restrictions for the skeletal linkages of the human foot may not be as unique as has been previously suggested. Am J Phys Anthropol 155:610–620, 2014. © 2014 Wiley Periodicals, Inc.     

Determination of 3D spinal kinematics without defining a local vertebral coordinate system

In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7° in a range of misalignments up to 10° between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.     

A three-dimensional kinematic and dynamic model of the lower limb

A model describing the kinematics and dynamics of the lower limb is presented. The lower limb is modeled as a sequence of four rigid links connected by three universal rotary joints representing the hip, knee and ankle joints. Each joint is modeled as a sequence of three single axis rotational joints thus ascribing to the lower limb a total of 12 degrees of freedom. A method is described to measure the gait variables so that all nine angles can be computed based on the positions of nine markers placed on the subject during a gait study. The gait variables are then used in an iterative Newton-Euler formulation to compute the moments exerted about the axes of each joint during gait.     

Kinematic performance of a six degree-of-freedom hand model (6DHand) for use in occupational biomechanics

Upper extremity musculoskeletal disorders represent an important health issue across all industry sectors; as such, the need exists to develop models of the hand that provide comprehensive biomechanics during occupational tasks. Previous optical motion capture studies used a single marker on the dorsal aspect of finger joints, allowing calculation of one and two degree-of-freedom (DOF) joint angles; additional algorithms were needed to define joint centers and the palmar surface of fingers. We developed a 6DOF model (6DHand) to obtain unconstrained kinematics of finger segments, modeled as frusta of right circular cones that approximate the palmar surface. To evaluate kinematic performance, twenty subjects gripped a cylindrical handle as a surrogate for a powered hand tool. We hypothesized that accessory motions (metacarpophalangeal pronation/supination; proximal and distal interphalangeal radial/ulnar deviation and pronation/supination; all joint translations) would be small (less than 5° rotations, less than 2mm translations) if segment anatomical reference frames were aligned correctly, and skin movement artifacts were negligible. For the gripping task, 93 of 112 accessory motions were small by our definition, suggesting this 6DOF approach appropriately models joints of the fingers. Metacarpophalangeal supination was larger than expected (approximately 10°), and may be adjusted through local reference frame optimization procedures previously developed for knee kinematics in gait analysis. Proximal translations at the metacarpophalangeal joints (approximately 10mm) were explained by skin movement across the metacarpals, but would not corrupt inverse dynamics calculated for the phalanges. We assessed performance in this study; a more rigorous validation would likely require medical imaging.     

Quantification of the segmental kinematics of spontaneous infant movements

This article introduces a method to capture the movements of the upper and the lower limb of infants using an electromagnetic tracking system and to reliably calculate the segmental kinematics. Analysis of the spontaneous movements of infants is important e.g. in the context of the "General Movement Analysis", which aims at the early diagnosis of motor dysfunctions. Due to special constraints regarding infant anatomy, previous approaches based on optical tracking could only gather position data of the infant' segments, whereas with this method in addition relative segment angles can be calculated. The spontaneous movements of the infant and simple calibration movements of the hand and the foot are used to calculate the joint centers and the joint axes of a multi-segmental chain model. The quality of the calibration movements is assessed at calibration time by calculating the root mean square deviation from the total least squares regression plane. The general accuracy of the recording is evaluated by the difference between recorded and estimated sensor positions and the difference between recorded and estimated sensor orientations. Movements of 20 infants between term and 3 months post term age were recorded and processed. A first application illustrates how abnormal movement patterns are manifested in the segmental kinematics. The results show that the presented method is a practicable and reliable way to record spontaneous infant movements and to calculate the segmental kinematics.     

In situ comparison of A-mode ultrasound tracking system and skin-mounted markers for measuring kinematics of the lower extremity

Skin-mounted marker based motion capture systems are widely used in measuring the movement of human joints. Kinematic measurements associated with skin-mounted markers are subject to soft tissue artifacts (STA), since the markers follow skin movement, thus generating errors when used to represent motions of underlying bone segments. We present a novel ultrasound tracking system that is capable of directly measuring tibial and femoral bone surfaces during dynamic motions, and subsequently measuring six-degree-of-freedom (6-DOF) tibiofemoral kinematics. The aim of this study is to quantitatively compare the accuracy of tibiofemoral kinematics estimated by the ultrasound tracking system and by a conventional skin-mounted marker based motion capture system in a cadaveric experimental scenario. Two typical tibiofemoral joint models (spherical and hinge models) were used to derive relevant kinematic outcomes. Intra-cortical bone pins equipped with optical markers were inserted in the tibial and femoral bones to serve as a reference to provide ground truth kinematics. The ultrasound tracking system resulted in lower kinematic errors than the skin-mounted markers (the ultrasound tracking system: maximum root-mean-square (RMS) error 3.44° for rotations and 4.88 mm for translations, skin-mounted markers with the spherical joint model: 6.32° and 6.26 mm, the hinge model: 6.38° and 6.52 mm). Our proposed ultrasound tracking system has the potential of measuring direct bone kinematics, thereby mitigating the influence and propagation of STA. Consequently, this technique could be considered as an alternative method for measuring 6-DOF tibiofemoral kinematics, which may be adopted in gait analysis and clinical practice.     

Comparison of three local frame definitions for the kinematic analysis of the fingers and the wrist

Because the hand is a complex poly-articular limb, numerous methods have been proposed to investigate its kinematics therefore complicating the comparison between studies and the methodological choices. With the objective of overcoming such issues, the present study compared the effect of three local frame definitions on local axis orientations and joint angles of the fingers and the wrist. Three local frames were implemented for each segment. The “Reference” frames were aligned with global axes during a static neutral posture. The “Landmark” frames were computed using palpated bony landmarks. The “Functional” frames included a flexion–extension axis estimated during functional movements. These definitions were compared with regard to the deviations between obtained local segment axes and the evolution of joint (Cardan) angles during two test motions. Each definition resulted in specific local frame orientations with deviations of 15° in average for a given local axis. Interestingly, these deviations produced only slight differences (below 7°) regarding flexion–extension Cardan angles indicating that there is no preferred method when only interested in finger flexion–extension movements. In this case, the Reference method was the easiest to implement, but did not provide physiological results for the thumb. Using the Functional frames reduced the kinematic cross-talk on the secondary and tertiary Cardan angles by up to 20° indicating that the Functional definition is useful when investigating complex three-dimensional movements. Globally, the Landmark definition provides valuable results and, contrary to the other definitions, is applicable for finger deformities or compromised joint rotations.     

A measure for the angle between projections based on the extent of correlation between corresponding central sections

A pre-condition for the ab initio assignment of Euler angles to a set of projections from an asymmetric object is that at least three of the available projections correspond to rotations about different axes. For symmetric objects this condition may be relaxed. There are some applications of single-particle electron microscopy, such as the reconstruction of filamentous macromolecular assemblies, where all available projections more-or-less correspond to rotations about a common rotation axis making it difficult to satisfy this condition. Here, a method has been developed to overcome this problem, based on the fact that the correlation between two central sections of the Fourier transform of a compact object will not be limited to an infinitesimal central line but will have a finite extent, which is related to the angle between the corresponding projections. Projections from model filaments, with different degrees of rotational symmetry about the long axis, have been used to test the methodology. The results show that angle determination is robust down to signal-to-noise ratios as low as 2 and that, in general, the error decreases as the degree of symmetry increases. The method has been used to assign angles to a set of negatively stained muscle thick filament projections to obtain an initial 3D reconstruction. The main features of the projections are seen to be faithfully reproduced in the reprojections from the reconstruction. A real-space adaptation of this method is also discussed.     

Imaging knee position using MRI, RSA/CT and 3D digitisation

The purpose of this study was to compare 3 methods of imaging knee position. Three fresh cadaver knees were imaged at 6 flexion angles between 0 degrees and 120 degrees by MRI, a combination of RSA and CT and 3D digitisation (in two knees). Virtual models of all 42 positions were created using suitable computer software. Each virtual model was aligned to a newly defined anatomically based Cartesian coordinate system. The angular rotations around the 3 coordinate system axes were calculated directly from the aligned virtual models using rigid body kinematics and found to be equally accurate for the 3 methods. The 3 rotations in each knee could be depicted using anatomy-based diagrams for all 3 methods. We conclude that the 3 methods of data acquisition are equally and adequately accurate in vitro. MRI may be the most useful in vivo.     

Scapular taping alters kinematics in asymptomatic subjects

BackgroundScapular taping is frequently used in the management of shoulder pain and as a part of injury prevention strategies in sports. It is believed to alter scapular kinematics and restore normal motion. However, there is little evidence to support its use. The aim of the study was to investigate the effect of shoulder taping on the scapular kinematics of asymptomatic subjects.MethodThirteen asymptomatic subjects performed elevations in the sagittal and scapular planes with no tape and after the application of tape. A motion tracking system and a scapula locator method were used to measure the shoulder movement. Co-ordinate frames were defined for the thorax, humerus and scapula and Euler angles were used to calculate joints rotations.ResultsScapular taping increased the scapular external and upward rotations and posterior tilt in elevations in the sagittal plane (p < 0.001). In the scapular plane, taping increased scapular external rotation (p < 0.05).ConclusionsTaping affects scapulothoracic kinematics in asymptomatic subjects. The effect may be different for different planes of movement. The findings have implications on the use of taping as a preventive measure in high-risk groups. Further work is needed to assess the effect of taping on symptomatic populations.     

Simulation of Codman's paradox reveals a general law of motion

Codman's paradox refers to a specific pattern of motion at the shoulder joint. It asked how a mysterious axial rotation about the longitudinal axis of the arm occurred during two or three sequential arm rotations that did not involve rotation about the long-axis. The objective of this paper was to find how the mysterious axial rotation occurred in the Codman's paradox. First, Codman's paradox and Codman's rotation were defined in general situations that involved arm rotations about orthogonal axes starting from the neutral attitude as well as rotations about non-orthogonal axes and starting from non-neutral attitudes. Then a general law of motion was proposed to answer the question of the Codman's paradox, which is stated as when the long-axis of the arm performs a closed-loop motion by three sequential rotations defined as Codman's rotation, it produces an equivalent axial rotation angle about the long-axis. The equivalent axial rotation angle equals the angle of swing-the second rotation in the three sequential long-axis rotations. Validity of the proposed law of motion is demonstrated by computer simulation of various Codman's rotations. Clinical relevance of the proposed law of motion is also discussed in the paper.     

Carpal bone kinematics and ligament lengthening studied for the full range of joint movement

Present data on carpal kinematics and carpal ligament behaviour are limited to flexion and deviation movements of the hand. These motions do not represent all the wrist-joint motions which are important for the activities of daily living. The goal of this project was to obtain insight into carpal kinematics and carpal ligament behaviour during motions of the hand covering the full range of motion of the wrist joint.

The carpals and the ligaments of four wrist-joint specimens were provided with radiopaque markers. These joints were subjected to Röntgenstereophotogrammetric experimentation in a large number of hand positions to determine carpal positions and ligament lengths. The movements of the carpal bones were described by means of finite helical axes (FHA).

It was found that the movements of the carpals in the distal row closely resemble those of the hand. Conversely, the motions of the carpals of the proximal row appeared not to be directly proportional to the hand motions and exhibited clear out-of-plane movements. Furthermore, it could be shown that movements of the hand into the ulnodorsal quadrant of the full range of hand motion corresponds to larger helical rotations and translations for most of the carpals than when the hand was moved into any other quadrant. The maximal ligament length changes determined did not exceed the length changes reported for pure flexion and pure deviation movements of the hand.     

A kinematic model of the human hand to evaluate its prehensile capabilities.

A kinematic model has been developed for simulation and prediction of the prehensile capabilities of the human hand. The kinematic skeleton of the hand is characterized by ideal joints and simple segments. Finger-joint angulation is characterized by yaw (abduction-adduction), pitch (flexion-extension) and roll (axial rotation) angles. The model is based on an algorithm that determines contact between two ellipsoids, which are used to approximate the geometry of the cutaneous surface of the hand segments. The model predicts the hand posture (joint angles) for power grasp of ellipsoidal objects by 'wrapping' the fingers around the object. Algorithms for two grip types are included: (1) a transverse volar grasp, which has the thumb abducted for added power; and (2) a diagonal volar grasp, which has the thumb adducted for an element of precision. Coefficients for estimating anthropometric parameters from hand length and breadth are incorporated in the model. Graphics procedures are included for visual display of the model. In an effort to validate the predictive capabilities of the model, joint angles were measured on six subjects grasping circular cylinders of various diameters and these measured joint angles were compared with angles predicted by the model. Sensitivity of the model to the various input parameters was also determined. On an average, the model predicted joint flexion angles that were 5.3% or 2.8 degrees +/- 12.2 degrees larger than the measured angles. Good agreement was found for the MCP and PIP joints, but results for DIP were more variable because of its dependence on the predictions for the proximal joints.     

A kinematic model of the shoulder complex to evaluate the arm-reachable workspace

Upper-arm evaluation including shoulder motion in physiotherapy has no three-dimensional tool for an arm-functioning evaluation, which hampers an uniform, objective comparison. Human shoulder complex models suffer from lack of shoulder girdle kinematic data. A kinematic shoulder-complex model with six degrees of freedom is proposed as the composition of the inner joint representing the shoulder-girdle joints and outer joint representing the glenohumeral joint. The outer shoulder joint has three perpendicular rotations: adduction/abduction, retroflexion/flexion and internal/external rotation of the humerus. The inner shoulder joint has two rotations, depression/elevation and retraction/protraction, and one translation, which are all dependent on the elevation angle of the humerus. The human arm-reachable workspace that represents the area within reach of the wrist is calculated on the basis of the shoulder-complex model and the additional elbow-joint direct kinematics. It was demonstrated that cross-sections of the calculated workspace are in agreement with the measured arm-reachable workspace in all three anatomical planes. The arm-reachable workspace volume and graphics were calculated and a comparison of the arm's workspaces during a patient's shoulder treatment was made. The obtained numerical and graphical arm-reachable workspaces can be used for arm-functioning evaluations in rehabilitation and ergonomics.     

Toward a realistic optoelectronic-based kinematic model of the hand: representing the transverse metacarpal arch reduces accessory rotations of the metacarpophalangeal joints

A kinematic model representing the versatility of the human hand is needed to evaluate biomechanical function and predict injury risk in the workplace. We improved upon an existing optoelectronic-based kinematic hand model with grouped metacarpals by defining segmented metacarpals and adding the trapeziometacarpal joint of the thumb. Eight participants performed three static postures (neutral pose, cylinder grip, cap grip) to evaluate kinematic performance of three different models, with one, two, and four metacarpal segment(s). Mean distal transverse metacarpal arch angles in the four-segment metacarpal model were between 22.0° ± 3.3° (neutral pose) and 32.1° ± 3.7° (cap grip). Representation of the metacarpals greatly influenced metacarpophalangeal joint rotations. Both the two- and four-segment metacarpal models displayed significantly lower metacarpophalangeal joint ‘supination’ angles (than the one-segment model) for the fourth and fifth fingers. However, the largest reductions were for the four- versus one-segment models, with mean differences ranging from 9.3° (neutral pose) to 17.0° (cap grip) for the fourth finger and 16.3° (neutral pose) to 33.0° (cylinder grip) for the fifth finger. MCP joint abduction/adduction angles of the fourth and fifth fingers also decreased with segmentation of the metacarpals, although the lowest magnitudes generally occurred in the four-segment model. Overall, the four-segment metacarpal model produced the lowest accessory rotations in non-dominant axes, and best matched previous radiological studies that found MCP joint pronation/supination angles were typically less than 10°. The four-segment metacarpal model, with improved anatomic fidelity, will better serve future studies of detailed actions of the hand in clinical or work applications.     

Computer-assisted evaluation of kinematics of the two bundles of the anterior cruciate ligament.

The aim of this cadaveric study was to describe the kinematics of the anterior cruciate ligament (ACL)-intact, posterolateral (PL) bundle-deficient and ACL-deficient knee by applying a protocol for computer-assisted evaluation of knee kinematics. The hypothesis that the PL bundle functions mainly at low knee flexion angles was tested. An optical tracking system was used to acquire knee joint motion on 10 knees during clinical evaluations by tracking markers rigidly attached to the bones. The protocol included acquisition of anterior-posterior (AP) translations and internal-external (IE) rotations, and evaluation of three clinical knee laxity tests (anterior drawer, manual and instrumented Lachman). The data demonstrated no significant contribution to AP translation and IE laxity from the PL bundle over the entire range of motion. The clinical knee laxity tests showed no significant differences between the ACL-intact and PL bundle-deficient states. The hypothesis could not be proven. Current clinical knee laxity measurements may not be suited for detecting subtle changes such as PL bundle deficiency in the ACL anatomy. The computation of knee laxity might be a step towards a more precise kinematic test of knee stability not only in the native and torn ACL state of the knee but also in the reconstructed knee.