Estimation of the axis of a screw motion from noisy data--a new method based on Plücker lines

The problems of estimating the motion and orientation parameters of a body segment from two n point-set patterns are analyzed using the Plücker coordinates of a line (Plücker lines). The aim is to find algorithms less complex than those in conventional use, and thus facilitating more accurate computation of the unknown parameters. All conventional techniques use point transformation to calculate the screw axis. In this paper, we present a novel technique that directly estimates the axis of a screw motion as a Plücker line. The Plücker line can be transformed via the dual-number coordinate transformation matrix. This method is compared with Schwartz and Rozumalski [2005. A new method for estimating joint parameters from motion data. Journal of Biomechanics 38, 107-116] in simulations of random measurement errors and systematic skin movements. Simulation results indicate that the methods based on Plücker lines (Plücker line method) are superior in terms of extremely good results in the determination of the screw axis direction and position as well as a concise derivation of mathematical statements. This investigation yielded practical results, which can be used to locate the axis of a screw motion in a noisy environment. Developing the dual transformation matrix (DTM) from noisy data and determining the screw axis from a given DTM is done in a manner analogous to that for handling simple rotations. A more robust approach to solve for the dual vector associated with DTM is also addressed by using the eigenvector and the singular value decomposition.     

A new method for estimating the axis of rotation and the center of rotation.

A new method is presented for estimating the parameters of two different models of a joint. The two models are: (1) A rotational joint with a fixed axis of rotation, also referred to as a hinge joint and (2) a ball and socket model, corresponding to a spherical joint. Given the motion of a set of markers, it is shown how the parameters can be estimated, utilizing the whole data set. The parameters are estimated from motion data by minimizing two objective functions. The method does not assume a rigid body motion, but only that each marker rotates around the same fixed axis of rotation or center of rotation. Simulation results indicate that in situations where the rigid body assumption is valid and when measurement noise is present, the proposed method is inferior to methods that utilize the rigid body assumption. However, when there are large skin movement artefacts, simulation results show the proposed method to be more robust.     

The finite displacements vector's method: an application to the scoliotic spine

This paper presents a vectorial method to directly obtain the components of the screw displacement between two positions of a body in a three-dimensional space (position of the helical axis of motion, rotation around this axis and translation along it). This method can be applied either to the case of a bone, moving with respect to the reference frame, or to the case of the relative motion of a joint; it gives exact formulae even if the displacements are finite; it generalizes the results (already published) obtained for finite displacements in the plane. The involved computation is easy, and the use of this method deals with only a small magnification of experimental errors. The technique of a screw displacement is applied to the vertebral segments of a scoliolic spine. The necessary data is taken from a couple of in-vivo X-rays. The goals of this study are: first, to describe the shape of the spine at each step of its evolution and second, to quantify the evolution in time of any segment of the spine between two states.     

Effects of data smoothing on the reconstruction of helical axis parameters in human joint kinematics

In biomechanical joint-motion analyses, the continuous motion to be studied is often approximated by a sequence of finite displacements, and the Finite Helical Axis (FHA) or "screw axis" for each displacement is estimated from position measurements on a number of anatomical or artificial landmarks. When FHA parameters are directly determined from raw (noisy) displacement data, both the position and the direction of the FHA are ill-determined, in particular when the sequential displacement steps are small. This implies, that under certain conditions, the continuous pathways of joint motions cannot be adequately described. The purpose of the present experimental study is to investigate the applicability of smoothing (or filtering) techniques, in those cases where FHA parameters are ill-determined. Two different quintic-spline smoothing methods were used to analyze the motion data obtained with Roentgenstereophotogrammetry in two experiments. One concerning carpal motions in a wrist-joint specimen, and one relative to a kinematic laboratory model, in which the axis positions are a priori known. The smoothed and non-smoothed FHA parameter errors were compared. The influences of the number of samples and the size of the sampling interval (displacement step) were investigated, as were the effects of equidistant and nonequidistant sampling conditions and noise invariance.     

Factors influencing accuracy of screw displacement axis detection with a D.C.-based electromagnetic tracking system.

Recent technical improvements and cost reductions in electromagnetic motion tracking systems invite their application to motion axis determination in the surgical setting. After evaluation of the accuracy of a state-of-the-art D.C. electromagnetic tracking system, which generates complete three-dimensional kinematic outputs from just a single receiver, we calculated screw displacement axes (SDA's) from its source data. The accuracy of SDA determination from such source data was evaluated for various rotational increment sizes around a revolute joint. A novel smoothing procedure, customized for this type of source data, was developed, enabling SDA detection from incremental rotations of less than 1 deg, at an accuracy appropriate for intra-operative measurement of human joint motion. Examples of SDA determination are given for motion tracking of a ball joint and of the elbow articulation.     

The analysis of golf swing as a kinematic chain using dual Euler angle algorithm

The manner in which anatomical rotation from an individual segment contributes to the position and velocity of the endpoint can be informative in the arena of many athletic events whose goals are to attain the maximal velocity of the most distal segment. This study presents a new method of velocity analysis using dual Euler angles and its application in studying rotational contribution from upper extremity segments to club head speed during a golf swing. Dual Euler angle describes 3D movement as a series of ordered screw motions about each orthogonal axis in a streamlined matrix form-the dual transformation matrix- and allows the translation and rotation component to be described in the same moving frame. Applying this method in biomechanics is a novel idea and the authors have previously applied the methodology to clinical studies on its use in displacement analysis. The focus of this paper is velocity analysis and applications in sports biomechanics. In this study, electrogoniometers (Biometrics, UK) with a frequency of 1000 Hz were attached to a subject during the execution of the swing to obtain the joint angles throughout the motion. The velocity of the club head was then analyzed using the dual velocity which specifies the velocity distribution of a rigid body in screw motion at any point in time as the dual vector. The contributions of each segment to the club-head velocity were also compared. In order to evaluate this method, the calculated position and velocity of the club head were compared to the values obtained from video image analysis. The results indicated that there is good agreement between calculated values and video data, suggesting the suitability of using the Dual Euler method in analyzing a kinematic chain motion.     

Globographic visualisation of three dimensional joint angles

Three different methods for describing three dimensional joint angles are commonly used in biomechanics. The joint coordinate system and Cardan/Euler angles are conceptually quite different but are known to represent the same underlying mathematics. More recently the globographic method has been suggested as an alternative and this has proved particularly attractive for the shoulder joint. All three methods can be implemented in a number of ways leading to a choice of angle definitions. Very recently Rab has demonstrated that the globographic method is equivalent to one implementation of the joint coordinate system. This paper presents a rigorous analysis of the three different methods and proves their mathematical equivalence. The well known sequence dependence of Cardan/Euler is presented as equivalent to configuration dependence of the joint coordinate system and orientation dependence of globographic angles. The precise definition of different angle sets can be easily visualised using the globographic method using analogues of longitude, latitude and surface bearings with which most users will already be familiar. The method implicitly requires one axis of the moving segment to be identified as its principal axis and this can be extremely useful in helping define the most appropriate angle set to describe the orientation of any particular joint. Using this technique different angle sets are considered to be most appropriate for different joints and examples of this for the hip, knee, ankle, pelvis and axial skeleton are outlined.     

In vivo tests of an improved method for functional location of the subtalar joint axis

The subtalar joint is important in frontal plane movement and posture of the hindfoot. Abnormal subtalar joint moments caused by muscle forces and the ground reaction force acting on the foot are thought to play a role in various foot deformities. Calculating joint moments typically requires knowledge of the location of the joint axis; however, location of the subtalar axis from measured movement is difficult because the talus cannot be tracked using skin-mounted markers. The accuracy of a novel technique for locating the subtalar axis was assessed in vivo using magnetic resonance imaging. The method was also tested with skin-mounted markers and video motion analysis. The technique involves applying forces to the foot that cause pure subtalar joint motion (with negligible talocrural joint motion), and then using helical axis decomposition of the resulting tibiocalcaneal motion. The resulting subtalar axis estimates differed by 6° on average from the true best-fit subtalar axes in the MRI tests. Motion was found to have been applied primarily about the subtalar joint with an average of only 3° of talocrural joint motion. The proposed method provides a potential means for obtaining subject-specific subtalar axis estimates which can then be used in inverse dynamic analyses and subject-specific musculoskeletal models.     

Finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics

Recent work on joint kinematics indicates that the finite centroid (centre of rotation) and the finite helical axis (axis of rotation, screw axis, twist axis) are highly susceptible to measurement errors when they are experimentally determined from landmark position data. This paper presents an analytical model to describe these effects, under isotropic conditions for the measurement errors and for the spatial landmark distribution. It appears that the position and direction errors are inversely proportional to the rotation magnitude, and that they are much more error-prone than the relatively well-determined rotation and translation magnitudes. Furthermore, the direction and rotation magnitude errors are inversely proportional to the landmark distribution radius, and the position and translation magnitude errors are minimal if the mean position of the landmarks coincides with the centroid or helical axis. For the planar centroid, the use of rigid-body constraints results in considerable precision improvement relative to the classical, finite Reuleaux method for centroid reconstruction. These analytical results can be used to define suitable measurement configurations, and they are used in this paper to explain experimental results on R?ntgenphotogrammetrically acquired in vitro wrist joint movement.     

Mobile platform for motion capture of locomotion over long distances

Motion capture is usually performed on only a few steps of over-ground locomotion, limited by the finite sensing volume of most capture systems. This makes it difficult to evaluate walking over longer distances, or in a natural environment outside the laboratory. Here we show that motion capture may be performed relative to a mobile platform, such as a wheeled cart that is moved with the walking subject. To determine the person’s absolute displacement in space, the cart’s own motion must be localized. We present three localization methods and evaluate their performance. The first detects cart motion solely from the relative motion of the subject’s feet during walking. The others use sensed motion of the cart’s wheels to perform odometry, with and without an additional gyroscope to enhance sensitivity to turning about the vertical axis. We show that such methods are practical to implement, and with present-day sensors can yield accuracy of better than 1% over arbitrary distances.     

Analysis of human mandibular mechanics based on screw theory and in vivo data

In this paper the mechanics of human mandibular function is described in terms of the associated screws. The two distinct, yet related features of jaw mechanics, involving the motion itself as well as the forces, are both functions of the anatomical constraints, namely the contact areas that exist within the temporomandibular joint, and the forces of the muscles and tendons that allow motion to occur. The relationships that exist between these two aspects of jaw-motion are identified in this paper showing that muscle forces can be uniquely represented in terms of the action screw. This new approach to analyzing the mechanics of jaw-motion also incorporates the previously studied motion screw or helical axis. A consistent dynamic model is formulated where the action screw is used to represent the action of the closing muscle forces while the moment arms of the muscle forces are determined about the motion screw representing mandibular kinematics. The action screw formulation is verified using in vivo motion data and MR image information for a single asymptomatic subject. The results confirm the feasibility of the method and its application in dental research. A general increase in the mechanical advantage of most muscles, in the distance between action and motion screws as well as in the expended energy towards the end of the jaw-closing phase was observed. Asymmetries in the distribution of muscle force magnitudes appeared to influence the resultant force and moment of the action screw but had little effect on its spatial location. The method presented is intended to facilitate understanding of mandibular function and dysfunction.     

Analysis of the Stress and Displacement Distribution of Inferior Tibiofibular Syndesmosis Injuries Repaired with Screw Fixation: A Finite Element Study

Background

Studies of syndesmosis injuries have concentrated on cadaver models. However, they are unable to obtain exact data regarding the stress and displacement distribution of various tissues, and it is difficult to compare models. We investigated the biomechanical effects of inferior tibiofibular syndesmosis injuries (ITSIs) and screw fixation on the ankle using the finite element (FE) method.

Methodology/Principal Findings

A three-dimensional model of a healthy ankle complex was developed using computed tomography (CT) images. We established models of an ITSI and of screw fixation at the plane 2.5 cm above and parallel to the tibiotalar joint surface of the injured syndesmosis. Simulated loads were applied under three conditions: neutral position with single-foot standing and internal and external rotation of the ankle. ITSI reduced contact forces between the talus and fibula, helped periarticular ankle ligaments withstand more load-resisting movement, and increased the magnitude of displacement at the lower extreme of the tibia and fibula. ITSI fixation with a syndesmotic screw reduced contact forces in all joints, decreased the magnitude of displacement at the lower extreme of the tibia and fibula, and increased crural interosseous membrane stress.

Conclusions/significance

Severe syndesmosis injuries cause stress and displacement distribution of the ankle to change multidirectional ankle instability and should be treated by internal fixation. Though the transverse syndesmotic screw effectively stabilizes syndesmotic diastasis, it also changes stress distribution around the ankle and decreases the joint''s range of motion (ROM). Therefore, fixation should not be performed for a long period of time because it is not physiologically suitable for the ankle joint.     

A motion-decomposition approach to address gimbal lock in the 3-cylinder open chain mechanism description of a joint coordinate system at the glenohumeral joint

In this study, the standard-sequence properties of a joint coordinate system were implemented for the glenohumeral joint by the use of a set of instantaneous geometrical planes. These are: a plane that is bound by the humeral long axis and an orthogonal axis that is the cross product of the scapular anterior axis and this long axis, and a plane that is bounded by the long axis of the humerus and the cross product of the scapular lateral axis and this long axis. The relevant axes are updated after every decomposition of a motion component of a humeral position. Flexion, abduction and rotation are then implemented upon three of these axes and are applied in a step-wise uncoupling of an acquired humeral motion to extract the joint coordinate system angles. This technique was numerically applied to physiological kinematics data from the literature to convert them to the joint coordinate system and to visually reconstruct the motion on a set of glenohumeral bones for validation.     

Reproducibility of kinematic motion coupling parameters during manual upper cervical axial rotation mobilization: A 3-dimensional in vitro study of the atlanto-axial joint

IntroductionThe reproducibility of the 3-dimensional (3D) kinematic aspects of motion coupling patterns of segmental manual mobilizing techniques is not yet known. This study analyzes the segmental 3D aspects of manual mobilization of the atlanto-axial joint in vitro.Methods and materialsTwenty fresh human cervical specimens were studied in a test–retest situation with two examiners. The specimens were manually mobilized using three different techniques: a regional mobilization technique, a segmental mobilization technique on the atlas with manual fixation of the axis and a segmental mobilization applying a locking technique. Segmental kinematics were registered with a Zebris CMS20 ultrasound-based tracking system. The 3D aspects of motion coupling between main axial rotation and coupled lateral bending were analyzed by six parameters: the range of motion the three motion components, the cross-correlation, the ratio and the shift.ResultsThe results indicate stronger intra- than inter-examiner reproducibility. The range of motion of the axial rotation component shows a substantial level of intra- and inter-examiner reproducibility (ICC’s 0.67–0.76). The parameters describing the coupling patterns show only moderate to substantial intra-examiner reproducibility for the more experienced of the two examiners (ICC’s 0.55–0.68). All other correlations were not significant and no differences could be observed between regional versus segmental techniques.ConclusionReproducibility of segmental 3D-aspects of manual mobilization of the atlanto-axial joint in an in vitro situation can differ between examiners. The results of the present study may indicate a possible tendency to higher reproducibility if mobilizations are performed by an examiner with high expertise and experience in applying the specific techniques. Continued investigation including more examiners with different levels of experience and different techniques is necessary to confirm these observations.     

Kinematical models to reduce the effect of skin artifacts on marker-based human motion estimation

The estimation of the skeletal motion obtained from marker-based motion capture systems is known to be affected by significant bias caused by skin movement artifacts, which affects joint center and rotation axis estimation. Among different techniques proposed in the literature, that based on rigid body model, still the most used by commercial motion capture systems, can smooth only part of the above effects without eliminating their main components. In order to sensibly improve the accuracy of the motion estimation, a novel technique, named local motion estimation (LME), is proposed. This rests on a recently described approach that, using virtual humans and extended Kalman filters, estimates the kinematical variables directly from 2D measurements without requiring the 3D marker reconstruction. In this paper, we show how such method can be extended to include the computation of the local marker displacement due to skin artifacts. The 3D marker coordinates, expressed in the corresponding local reference coordinate frames, are inserted into the state vector of the filter and their dynamics is automatically estimated, with adequate accuracy, without assuming any particular deformation function. Simulated experiments of lower limb motion, involving systematic mislocations (5, 10, 20 mm) and random errors of the marker coordinates and joint center locations (+/-5, +/-10, +/-15 mm), have shown that artifact motion can be substantially decoupled from the global skeletal motion with an effective increase of the accuracy wrt standard techniques. In particular, the comparison between the nominal kinematical variables and the one recovered from markers attached to the skin surface proved LME to be sensibly superior (50% in the worse condition) to the methods imposing marker-bone rigidity. In conclusion, while requiring further validation on real movement data, we argue that the proposed method can constitute an appropriate approach toward the improvement of the human motion estimation.