instantaneous helical axis estimation from 3 d video data in neck kinematics for whiplash diagnostics to date the diagnosis of whiplash injuries has been very difficult and largely based on subjective clinical assessment the work by winters and peles multiple muscle systems biomechanics and movement organization springer new york 1990 suggests that the use of finite helical axes fhas in the neck may provide an objective assessment tool for neck mobility thus the position of the fha describing head trunk motion may allow discrimination between normal and pathological cases such as decreased mobility in particular cervical joints for noisy unsmoothed data the fhas must be taken over rather large angular intervals if the fhas are to be reconstructed with sufficient accuracy in the winters and peles study these intervals were approximately 10 in order to study the movements microstructure the present investigation uses instantaneous helical axes ihas estimated from low pass smoothed video data here the small step noise sensitivity of the fha no longer applies and proper low pass filtering allows estimation of the iha even for small rotation velocity of the moving neck for marker clusters mounted on the head and trunk technical system validation showed that the ihas direction dispersions were on the order of one degree while their position dispersions were on the order of 1 mm for low pass cut off frequencies of a few hz the dispersions were calculated from weighted errors in order to account for the adverse effects of vanishing various simple planar models relating the instantaneous 2 d centre of rotation with the geometry and kinematics of a multi joint neck model are derived in order to gauge the utility of the fha and iha approaches some preliminary results on asymptomatic and pathological subjects are provided in terms of the ruled surface formed by sampled ihas and of their piercing points through the mid sagittal plane during a prescribed flexion extension movement of the neck

orbit automata as a new tool to attack the order problem in automaton groups abstract we introduce a new tool called the orbit automaton that describes the action of an automaton group g on the subtrees corresponding to the orbits of g on levels of the tree the connection between g and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work

orbit decidability and the conjugacy problem for some extensions of groups given a short exact sequence of groups with certain conditions 1 f g h 1 we prove that g has solvable conjugacy problem if and only if the corresponding action subgroup a 6 aut f is orbit decidable from this we deduce that the conjugacy problem is solvable among others for all groups of the form z2 fm f2 fm fn z and zn a fm with virtually solvable action group a 6 gln z also we give an easy way of constructing groups of the form z4 fn and f3 fn with unsolvable conjugacy problem on the way we solve the twisted conjugacy problem for virtually surface and virtually polycyclic groups and give an example of a group with solvable conjugacy problem but unsolvable twisted conjugacy problem as an application an alternative solution to the conjugacy problem in aut f2 is given

3 d attitude representation of human joints a standardization proposal abstract in view of the singularities asymmetries and other adverse properties of existing three dimensional definitions for joint and segment angles the present paper proposes a new convention for unambiguous and easily interpretable 3 d joint angles based on the concept of the attitude vector as derived from euler s theorem the suggested standard can be easily explained to non mathematically trained clinicians is readily implemented in software and can be simply related to classical cardanic eulerian angles for planar rotations about a coordinate system s axes the proposed convention coincides with the cardanic convention the attitude vector dispenses with the gimbal lock and non orthogonality disadvantages of cardanic eulerian conventions therefore its components have better metrical properties and they are less sensitive to measurement errors and to coordinate system uncertainties than cardanic eulerian angles a sensitivity analysis and a physical interpretation of the proposed standard are given and some experimental results that demonstrate its advantages

comparison of different calculations of three dimensional joint kinematics from video based system data when skin fixed marker trajectories are used to calculate 3d joint kinematics the measurement errors i e the difference between the trajectories of the external markers and those of the skeleton influence to some extent the accuracy of the results depending both on the calculation method and on the axes about which the rotations are expressed the purpose of this paper is to compare several expressions of joint angular variations two kinematic concepts are used to calculate the changes in the orientation of the distal segment versus the proximal one the first method consists of computing the components of the spatial attitude vector the second one deals with the determination of elementary rotations about successive axes for each of these methods two sets of three axes are tested to express the results the axes forming the reference frame affixed to the body segment adjacent to the joint named fixed axes and a set consisting of a first axis belonging to the proximal segment a third axis belonging to the distal segment and a second floating axis defined as the cross product between the two other ones named mobile axes to compare these four distinct expressions on the knee joint numerical simulations of perturbed skin marker trajectories are performed based on experimental data recorded by a motion analysis system during a normal gait cycle a significant difference is pointed out only for the internal external rotation angle for which the best expression from the viewpoint of sensitivity to experimental errors is obtained using the components of the attitude vector in a segment embedded reference frame

estimation of the centre of rotation a methodological contribution the location of the centre of rotation of human joints that can be modelled as a spherical hinge can be estimated using kinematics information about the two adjacent bony segments involved recorded while the subject makes them move one relative to the other functional method in order to solve the relevant analytical problem several algorithms have been proposed most recently two methods one based on a spherical best fit approach and another based on the reuleaux construction have been presented as being different and submitted to comparative evaluation this paper modifies the second method taking all information in the data set into account and shows that having done this the two methods coincide analytically

the conjugacy problem in automaton groups is not solvable abstract free abelian by free self similar groups generated by finite self similar sets of tree automorphisms and having unsolvable conjugacy problem are constructed along the way finitely generated orbit undecidable free subgroups of gl d z for d 6 and aut f d for d 5 are constructed as well

a comparison of two non invasive methods for measuring scapular orientation in functional positions identification of scapular dyskinesis and evaluation of interventions depend on the ability to properly measure scapulothoracic st motion the most widely used measurement approach is the acromion marker cluster amc which can yield large errors in extreme humeral elevation and can be inaccurate in children and patient populations recently an individualized regression approach has been proposed as an alternative to the amc this technique utilizes the relationship between st orientation humerothoracic orientation and acromion process position derived from calibration positions to predict dynamic st orientations from humerothoracic and acromion process measures during motion these individualized regressions demonstrated promising results for healthy adults however this method had not yet been compared to the more conventional amc this study compared st orientation estimates by the amc and regression approaches to static st angles determined by surface markers placed on palpated landmarks in typically developing adolescents performing functional tasks both approaches produced errors within the range reported in the literature for skin based scapular measurement techniques the performance of the regression approach suffered when applied to positions outside of the range of motion in the set of calibration positions the amc significantly underestimated st internal rotation across all positions and overestimated posterior tilt in some positions overall root mean square errors for the regression approach were smaller than the amc for every position across all axes of st motion accordingly we recommend the regression approach as a suitable technique for measuring st kinematics in functional motion

point of optimal kinematic error improvement of the instantaneous helical pivot method for locating centers of rotation this paper proposes a variation of the instantaneous helical pivot technique for locating centers of rotation the point of optimal kinematic error poke which minimizes the velocity at the center of rotation may be obtained by just adding a weighting factor equal to the square of angular velocity in woltring s equation of the pivot of instantaneous helical axes piha calculations are simplified with respect to the original method since it is not necessary to make explicit calculations of the helical axis and the effect of accidental errors is reduced the improved performance of this method was validated by simulations based on a functional calibration task for the gleno humeral joint center noisy data caused a systematic dislocation of the calculated center of rotation towards the center of the arm marker cluster this error in piha could even exceed the effect of soft tissue artifacts associated to small and medium deformations but it was successfully reduced by the poke estimation

estimation of the axis of a screw motion from noisy data a new method based on plucker lines the problems of estimating the motion and orientation parameters of a body segment from two n point set patterns are analyzed using the plucker coordinates of a line plucker 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 plucker line the plucker 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 plucker lines plucker 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

instantaneous moment arm determination of the cat knee the moment arm is an important parameter for calculating forces and pressures at a joint present techniques described in the literature are limited for joint studies in animals because of the invasive procedures required which destroy the joint integrity this paper describes a new application of the instantaneous helical axis iha for determination of the moment arm of the knee joint without compromising its integrity measurements based on the iha technique are compared to an established technique using six cadaveric cat hind limbs one experiment using the iha technique was performed to demonstrate its application in situ it was found that the moment arm determined by both techniques resulted in continuous estimations of similar magnitudes over the expected range of motion of the knee joint although the iha technique is sensitive to smoothing a trend toward increasing moment arm as a function of increasing knee angle was observed in four of six specimens the in situ experiment demonstrated the ability to use the iha technique without compromising the integrity of the knee joint so that further histological morphological or topological information could be investigated

a survey of formal methods for determining the centre of rotation of ball joints abstract the determination of an accurate centre of rotation cor from segment marker positions is of interest across a wide range of applications but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee for limb alignment purposes for the first time in this survey of formal methods we classify analyse and compare different methods geometric algebraic bias compensated algebraic and pratt sphere fit methods as well as the centre transformation technique the holzreiter approach the helical pivot technique the schwartz transformation techniques the minimal amplitude point method and the stoddart approach for the determination of spherical joint centres from marker position data in addition we propose a new method the symmetrical cor estimation or score in which the coordinates of the joint centre must only remain constant relative to each segment thus not requiring the assumption that one segment should remain at rest for each method 1000 cor estimations were analysed with the application of isotropic independent and identically distributed gaussian noise standard deviation 0 1 cm to each of the marker positions to all markers on the segment simultaneously and the two in combination for the test conditions used here most techniques were capable of determining the cor to within 0 3 cm as long as the spherical range of motion rom of the joint was 45 or more under the most stringent conditions tested however the score was capable of best determining the cor to within approximately 1 2 mm with a rom of 20 the correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement

relevance of mandibular helical axis analysis in functional and dysfunctional tmjs the helical axis ha or motion screw yields a comprehensive description of joint motion the perspective representation of this axis clearly visualizes the regularity of mandibular functional movements yatabe et al 1997 journal of dentist research 76 714 719 and gallo et al 2000 journal of dental research 79 1566 1572 in this study the sensitivity of the ha representation was investigated relative to a irregularities in pathologic motion of clicking temporomandibular joints tmjs for jaw opening closing and b differences in food bolus size and consistency for unilateral mastication in subjects with normal tmjs mandibular motion relative to the head was acquired using a jaw tracker with six degrees of freedom with a sampling frequency of 70 hz the ha was calculated according to an eigenvalue method spoor and veldpaus 1980 journal of biomechanics 13 391 393 and parameters were defined describing its position and orientation relative to the anatomy we analyzed 39 subjects with unilateral or bilateral reciprocal tmj clicking during jaw opening closing and seven asymptomatic subjects during unilateral mastication of five different types of soft and hard food in two different bolus sizes the results showed a greater variability of the ha parameters in the group of clicking joints than in the asymptomatic group in particular the area in which the ha moved was wider in clicking joints than in normal ones and the ha in clicking tmjs had a much greater fluctuation than in normal ones during unilateral mastication for more consistent food or a bigger bolus the ha showed a significantly greater excursion of the orientation parameters furthermore a significantly greater excursion of the dorsoventral and of the craniocaudal component of the distance vector from the ha to the condyle were found the helical axis analysis of mandibular movements was sensitive to kinematic irregularities of the mandible due to an internal joint derangement as well as to differences in food bolus size and consistency

optimal average path of the instantaneous helical axis in planar motions with one functional degree of freedom this paper presents a model for determining the path of the instantaneous helical axis iha that optimally represents human planar motions with one functional degree of freedom fdof a human movement is said to have one fdof when all degrees of freedom dofs are coordinated such that all the kinematic variables can be expressed across movement repetitions as functions of only one independent dof except for a small natural intercycle variability quantified as lower than a prespecified value the concept of fdof allows taking into account that due to motor coordination human movements are executed in a repeatable manner our method uses the measurement of several repetitions of a given movement to obtain the optimal average iha path the starting point is a change of variables from time to a joint position magnitude generally an angle in this way instead of operating with the time dependent single valued trajectory of the successive cycles our model permits the representation of any motion variable e g positions and their time derivatives as a cloud of points dependent on the joint angle this allows the averaging to be performed over the displacements and their derivatives before determining the mean iha path we thus avoid the nonlinear magnification of errors and variability inherent in the iha computation moreover the iha path can be considered as a geometric attribute of the joint and the type of motion rather than of each single movement execution an experiment was performed that show the accuracy and usefulness of the method

robust estimation of dominant axis of rotation a simple method is developed for robustly estimating a fixed dominant axis of rotation aor of anatomical joints from surface marker data previous approaches which assume a model of circular marker trajectories use plane fitting to estimate the direction of the aor however when there is limited joint range of motion and rotation due to a second degree of freedom minimizing only the planar error can give poor estimates of the aor direction optimizing a cost function which includes the error component within a plane instead of only the component orthogonal to a plane leads to improved estimates of the aor direction for joints which exhibit additional rotational motion from a second degree of freedom results from synthetic data validation show the ranges of motion where the new method has lower estimation error compared to plane fitting techniques estimates of the flexion extension aor from empirical motion capture data of the knee and index finger joints were also more anatomically plausible

the centre of rotation of the shoulder complex and the effect of normalisation shoulder motions consist of a composite movement of three joints and one pseudo joint which together dictate the humerothoracic motion the purpose of this work was to quantify the location of the centre of rotation cor of the shoulder complex as a whole dynamic motion of 12 participants was recorded using optical motion tracking during coronal scapular and sagittal plane elevation the instantaneous cor was found for each angle of elevation using helical axes projected onto the three planes of motion the location of an average cor for each plane was evaluated using digitised and anthropometric measures for normalisation when conducting motion in the coronal scapular and sagittal planes respectively the coefficients for locating the cors of the shoulder complex are 61 61 and 65 of the anterior posterior dimension the vector between the midpoint of the incisura jugularis and the xiphoid process and the midpoint of the seventh cervical vertebra and the eighth thoracic vertebra 0 1 and 2 of the superior inferior dimension the vector between the midpoint of the acromioclavicular joints and the midpoint of the anterior superior iliac spines and 57 57 and 78 of the medial lateral dimension 0 129 times the height of the participant knowing the location of the cor of the shoulder complex as a whole enables improved participant positioning for evaluation and rehabilitation activities that involve movement of the hand with a fixed radius such as those that employ isokinetic dynamometers

bayesian vs least squares inverse kinematics simulation experiments with models of 3d rigid body motion and 2d models including soft tissue artefacts abstract two simulation experiments are presented to gauge the accuracy of a new inverse kinematics method based on bayesian inference bik pataky et al 2019 j biomech in more realistic models than were considered previously the first application concerns planar kinematics in the presence of soft tissue artefacts and the second application concerns rigid body kinematics in 3d with finite helical axes fha the percentage of simulations in which bik was more accurate than least squares based methods was only high in cases of relatively large noise magnitudes noise sd 5 mm or when the rotation magnitude was very small 5 deg in the 3d fha model correlated parameters are the likely culprit of the low performance of bik also computation time is a major deficit of the bik approach 20 s for the movement between two time frames these results indicate that more research will be necessary to improve the accuracy of bik for complex biomechanical models at realistic noise levels and to reduce computation time

assessment of anatomical frame variation effect on joint angles a linear perturbation approach although the interpretability and reliability of joint kinematics depends strongly on the accuracy and precision of determining the anatomical frame af orientation the exact dependency of joint angle error on af misalignment is still not clear to fully understand the behavior this study uses linear perturbations to quantify joint angle error due to known modifications of the afs where the joint angles are calculated according to the cardanic convention the result is a functional representation of joint angle error with dependence on nominal joint angles and on the orientations of the alternative afs relative to the nominal afs the results are validated using numerical analysis on knee joint angle data during walking the derived relationship elucidates results from previous work studying this effect and allows af differences to be inferred by joint angle curves when multiple sets of joint angle curves are collected simultaneously

on precision limits for derivatives numerically calculated from noisy data abstract this paper has three purposes 1 1 to verify an error formula from which the maximal precision in derivatives obtained from noisy measurement data can be calculated the formula is verified by comparison with the resulting noise in derivatives obtained by local least squares polynomial fitting it is also verified that differentiation by fourier series expansion gives noise exceeding the minimum value according to the error formula 2 2 an index called the relative noise amplification rna is introduced for an arbitrary differentiating filter it is defined as the noise transmission of the filter divided by the minimal noise transmission according to the above mentioned error formula when the filter produces unbiased estimates the value of the rna always exceeds one the rna can be used as a quality index for differentiating filters the filter with the smallest value on the rna also has the smallest amount of noise superimposed on the calculated derivatives provided the input noise is white and additive 3 3 the bandwidth and the relative noise amplification of differentiating filters obtained by local least squares polynomial fitting are presented the 0th 1st and 2nd order derivatives have been investigated for polynomials up to 8th order these results can be used for the determination of suitable filter parameters in various applications

stable iteration procedures for strong pseudo contractions and nonlinear operator equations of the accretive type it is proved that certain mann and ishikawa iteration procedures arestable with respect to strongly pseudo contractive mappingsin real banach spaces which areq uniformly smooth 1 q a related result deals with stable iteration procedures forsolutions of nonlinear equations of the accretive type

registration of 6 dofs electrogoniometry and ct medical imaging for 3d joint modeling the paper describes a method in which two data collecting systems medical imaging and electrogoniometry are combined to allow the accurate and simultaneous modeling of both the spatial kinematics and the morphological surface of a particular joint the joint of interest joi is attached to a plexiglas jig that includes four metallic markers defining a local reference system r gonio for the kinematics data volumetric data of the joi and the r gonio markers are collected from medical imaging the spatial location and orientation of the markers in the global reference system r ct of the medical imaging environment are obtained by applying object recognition and classification methods on the image dataset segmentation and 3d isosurfacing of the joi are performed to produce a 3d model including two anatomical objects the proximal and distal joi segments after imaging one end of a custom made 3d electrogoniometer is attached to the distal segment of the joi and the other end is placed at the r gonio origin the joi is displaced and the spatial kinematics data is recorded by the goniometer after recording data registration from r gonio to r ct occurred prior to simulation data analysis was performed using both joint coordinate system jcs and instantaneous helical axis iha finally the 3d joint model is simulated in real time using the experimental kinematics data the system is integrated into a computer graphics interface allowing free manipulation of the 3d scene the overall accuracy of the method has been validated with two other kinematics data collection methods including a 3d digitizer and interpolation of the kinematics data from discrete positions obtained from medical imaging validation has been performed on both superior and inferior radio ulna joints i e prono supination motion maximal rms error was 1 degrees and 1 2mm on the helical axis rotation and translation respectively prono supination of the forearm showed a total rotation of 132 degrees for 0 8mm of translation the method reproducibility using jcs parameters was in average 1 degrees maximal deviation 2 degrees for rotation and 1mm maximal deviation 2mm for translation in vitro experiments have been performed on both knee joint and ankle joint averaged jcs parameters for the knee were 109 degrees 17 degrees and 4 degrees for flexion internal rotation and abduction respectively averaged maximal translation values for the knee were 12 3 and 4mm posteriorly medially and proximally respectively averaged jcs parameters for the ankle were 43 degrees 9 degrees and 3 degrees for plantarflexion adduction and internal rotation respectively averaged maximal translation values for the ankle were 4 2 and 1mm anteriorly medially and proximally respectively

finite centroid and helical axis estimation from noisy landmark measurements in the study of human joint kinematics abstract 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 rontgenphotogrammetrically acquired in vitro wrist joint movement

accuracy of a ct based bone contour registration method to measure relative bone motions in the hindfoot abstract for measuring the in vivo range of motion of the hindfoot a ct based bone contour registration method ct bcm was developed to determine the three dimensional position and orientation of bones to validate this technique we hypothesized that the range of motion in the hindfoot is equally accurately measured by roentgen stereophotogrammetric analysis rsa as by the ct bcm technique tantalum bone markers were placed in the distal tibia talus and calcaneus of one cadaver specimen with a fixed lower leg the cadaveric foot was held in neutral and subsequently loaded in eight extreme positions immediately after acquiring a ct scan with the foot in a position rsa radiographs were made bone contour registration and rsa was performed helical axis parameters were calculated for talocrural and subtalar joint motion from neutral to extreme positions and between opposite extreme positions differences between ct bcm and rsa were calculated compared with rsa the ct bcm data registered an overall root mean square difference rmsd of 0 21 for rotation about the helical axis and 0 20 mm translation along the helical axis for the talocrural and subtalar joint and for all motions combined the rmsd of the position and direction of the helical axes was 3 3 mm and 2 4 respectively the latter errors were larger with smaller helical rotations the differences are similar to those reported for validated rsa and thus are not clinically relevant concluding ct bcm is an accurate and accessible alternative for studying joint motion as it does not have the risk of infection and overlapping bone markers

calculating the 2d motion of lumbar vertebrae using splines in this study we investigate the use of splines and the icp method besl p mckay n 1992 a method for registration of 3d shapes ieee transactions on pattern analysis and machine intelligence 14 239 256 for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane we demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion extension radiographs of the lumbar spine in an in vitro error study the method displayed an average error of rotation of 0 44 0 45 degrees and an average error in fcr calculation of 7 6 8 5 mm the method was shown to be superior to that of crisco et al two dimensional rigid body kinematics using image contour registration journal of biomechanics 28 1 119 124 and brinckmann et al quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace part i the shape of vertebrae and intervertebral discs study of a yound healthy population and a middle aged control group clinical biomechanics supplement 1 s5 s83 for the tests performed here in general we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons first with appropriate software splines require less effort to define and are a compact representation with most vertebra outlines using less than 30 control points second splines are inherently sub pixel representations of curves even if the control points are limited to pixel resolutions third there is a well defined method the icp algorithm for registering shapes represented as splines finally like digitised curves splines are able to represent a large class of shapes with little effort but reduce potential segmentation errors from two dimensions parallel and perpendicular to the image gradient to just one parallel to the image gradient we have developed an application for performing all the necessary computations which can be downloaded from http www claritysmart com

a note on the stability of iteration procedures for strong pseudocontractions and strongly accretive type equations abstract we show that recent theorems of hai yun zhou 1999 j math anal appl 230 1 10 concerning stable iteration procedures for strong pseudocontractions and nonlinear equations involving strongly accretive operators without lipschitz assumptions are false

on intrinsic equivalences of the finite helical axis the instantaneous helical axis and the sara approach a mathematical perspective accurate determination of joint axes is essential for understanding musculoskeletal function whilst numerous algorithms to compute such axes exist the conditions under which each of the methods performs best remain largely unknown typically algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance we derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data finite helical axes fha instantaneous helical axes iha and sara symmetrical axis of rotation approach including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the fha and sara approach are equivalent for the analysis of two time frames moreover we show that the position of a helical axis derived from the iha using positional data is affected by a systematic error perpendicular to the true axis direction whereas the axis direction is identical to those computed with either the fha or sara approach true direction finally with an appropriate choice of weighting factors the mean fha mfha method is equivalent to the symmetrical centre of rotation estimation score algorithm for determination of a centre of rotation cor and similarly equivalent to the sara algorithm for determination of an axis of rotation aor the deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient robust methods for determining aors and cors with confidence

comparison of the score and ha methods for locating in vivo the glenohumeral joint centre a recent paper has described a new functional method the symmetrical centre of rotation score for locating joint centre position ehrig r m taylor w r duda g n heller m o 2006 a survey of formal methods for determining the centre of rotation of ball joints journal of biomechanics 39 15 2798 2809 for in vitro analyses the score method showed better precision than helical axis ha or sphere fitting methods despites ha determination is very sensitive to small angular velocity the international society of biomechanics has recommended to use ha for locating the glenohumeral joint centre this paper aims at comparing the score method with the ha method for locating in vivo the glenohumeral joint centre according to the movement characteristics nine subjects performed 10 cycles of three different movements at two different velocities for each test combination of movements the location of the centre of rotation was estimated with both methods score and ha analyses focused on the 3d location of the glenohumeral joint centre and on the repeatability of location standard deviation this study showed that score and ha methods yielded the same gh location nevertheless with score method the location of the glenohumeral joint centre was different according to the test this study evidenced that the score method was more precise than ha method error of 3 mm versus 4 6 mm and that the gh location with the score method was not affected by movements with slow velocities

ishikawa and mann iteration methods with errors for nonlinear equations of the accretive type abstract let e be an arbitrary banach space and t e e a lipschitz strongly accretive operator it is proved that for a given f e the ishikawa and the mann iteration methods with errors introduced by 18 converge strongly to the solution of the equation tx f furthermore if e is a uniformly smooth banach space and t e e is demicontinuous and strongly accretive it is also proved that both the ishikawa and the mann iteration methods with errors converge strongly to the solution of the equation tx f related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators and the solution of the equation x tx f f e when t e e is m accretive

high precision three dimensional photogrammetric calibration and object space reconstruction using a modified dlt approach two modified dlt algorithms are presented that improve the accuracy of three dimensional object space reconstruction by almost an order of magnitude when compared with conventional methods the improvement in the linear modified dlt mdlt algorithm is achieved by satisfying certain orthogonality conditions in the form of a non linear constraint thereby effectively eliminating a redundant dlt parameter in the non linear mdlt algorithm the improvement and computational stability results from the appropriate elimination of implicit variables from one side of the approximating relations and the corresponding reformulation of the objective function to be minimized the highest reconstruction accuracy of 0 733 mm rms mean error was obtained with the non linear mdlt algorithm this corresponds to a spatial resolution of about one part in 2860 or 0 035 overall accuracy the accuracy obtainable with the linear mdlt was found to be slightly less and about 0 041 0 833 mm rms mean error

freeness of automaton groups vs boundary dynamics abstract we prove that the boundary dynamics of the semi group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group we specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to the existence of a finite schreier graph in the boundary of the enriched dual pointed at some essentially non trivial point from these results we derive some consequences from the algebraic algorithmic and dynamical points of view

the glenohumeral joint rotation centre in vivo within the framework of the current call for standardization in upper extremity research three methods to determine the glenohumeral joint rotation centre in vivo were tested therefore subjects performed humeral movements while a 3d electromagnetic tracking device registered the motion of the humerus with respect to the scapula for the first method to estimate the glenohumeral joint rotation centre five scapular bony landmarks served as input to regression equations the second method fitted a sphere through the humeral position data and the third method calculated the rotation centre determining an optimal helical axis the experiment consisted of two parts at first one subject was measured 10 times subsequently one observer measured 10 subjects twice and another observer measured these subjects once the first part of the experiment demonstrated that all methods are capable to reproduce the rotation centre within 4mm but the location of the centre differed significantly between methods p 0 001 the second part showed that inter and intra observer reliability was sufficiently for the sphere fitting method and for the helical axes method the two observations of one observer differed significantly p 0 008 using the regression method the authors prefer the helical axes method it is a reliable and valid method which can be applied in movement registration of healthy subjects and patients with a shoulder endoprosthesis it can be applied in hinge joints to determine a rotation axis instead of a rotation centre which is desirable in standardized upper extremity research and calculation time is short

error propagation from kinematic data to modeled muscle tendon lengths during walking kinematic data from 3d gait analysis together with musculoskeletal modeling techniques allow the derivation of muscle tendon lengths during walking however kinematic data are subject to soft tissue artifacts sta referring to skin marker displacements during movement sta are known to significantly affect the computation of joint kinematics and would therefore also have an effect on muscle tendon lengths which are derived from the segmental positions the present study aimed to introduce an analytical approach to calculate the error propagation from sta to modeled muscle tendon lengths skin marker coordinates were assigned uncorrelated isotropic error functions with given standard deviations accounting for sta two different musculoskeletal models were specified one with the joints moving freely in all directions and one with the joints constrained to rotation but no translation using reference kinematic data from two healthy boys mean age 9 y 5 m the propagation of sta to muscle tendon lengths was quantified for semimembranosus gastrocnemius and soleus the resulting average sd ranged from 6 to 50 of the normalized muscle tendon lengths during gait depending on the muscle the sta magnitudes and the musculoskeletal model these results highlight the potential impact sta has on the biomechanical analysis of modeled muscle tendon lengths during walking and suggest the need for caution in the clinical interpretation of muscle tendon lengths derived from joint kinematics

the use of optimally regularized fourier series for estimating higher order derivatives of noisy biomechanical data abstract optimally regularized filtered fourier series can be used most effectively for estimating higher order derivatives of noisy data sequences such as occur in biomechanical investigations as the optimal filtering process takes place in the derivative domain use being made of the statistical information contained in the periodogram of the data sequence no numerical differentiation as such takes place and all the problems known to be associated with such a procedure are avoided the optimally filtered approximation to the function itself is obtained by the same technique the algorithm is based on known results from time series and approximation theory and offers several advantages when compared with other techniques the optimally filtered approximations of the function and all its required derivatives are obtained in a single run compact analytical fourier representations of the filtered function and the derivatives are available allowing interpolation between data points and further analytical treatment of the function all the desirable properties of fourier approximations such as periodicity end point continuity etc can be utilized if fast fourier transforms are used the algorithm is computationally far more efficient than other techniques

stable iteration procedures for strong pseudocontractions and nonlinear equations involving accretive operators without lipschitz assumption abstract let e be a real uniformly smooth banach space and t e e a strong pseudocontraction with a bounded range we prove that the mann and ishikawa iteration procedures are t stable some related results deal with the stability of these procedures for the iteration approximation of solutions of nonlinear equations involving accretive operators our results improve and or extend those corresponding results announced by osilike

on the burnside problem for periodic groups narain gupta 1 and said sidki 2 1 university of manitoba department of mathematics winnipeg manitoba r3t 2n2 canada 2 university of brasilia department of mathematics brasilia d f brazil introduction the generalized burnside problem refers to the question are finitely generated periodic groups finite this was answered in the negative by golod 1 who proved that for each prime p there exists a finitely generated infinite p group golod s construction in not however direct and is based on his celebrated work with safarevi recently grigor uk 2 has given a direct and elegant construction of an infinite 2 group which is generated by three elements of order 2 in this paper we give for each odd prime p a direct construction of an infinite p group on two generators each of order p our group is a subgroup of the automorphism group of a regular tree of degree p and as might be expected it is residually finite and has infinite exponent preliminaries let p be an odd prime and let t 0 be the infinite regular tree of degree p with vertex 0 so that through each vertex u of t 0 there are p regular subtrees

in vivo estimation of the glenohumeral joint centre by functional methods accuracy and repeatability assessment abstract several algorithms have been proposed for determining the centre of rotation of ball joints these algorithms are used rather to locate the hip joint centre few studies have focused on the determination of the glenohumeral joint centre however no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre this paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre ghrc can be estimated in vivo by functional methods the reference joint centre is the glenohumeral anatomical centre obtained by medical imaging five functional methods were tested the algorithm of gamage and lasenby 2002 bias compensated halvorsen 2003 symmetrical centre of rotation estimation ehrig et al 2006 normalization method chang and pollard 2007 helical axis woltring et al 1985 the glenohumeral anatomical centre ghac was deduced from the fitting of the humeral head four subjects performed three cycles of three different movements flexion extension abduction adduction and circumduction for each test the location of the glenohumeral joint centre was estimated by the five methods analyses focused on the 3d location on the repeatability of location and on the accuracy by computing the euclidian distance between the estimated ghrc and the ghac for all the methods the error repeatability was inferior to 8 25 mm this study showed that there are significant differences between the five functional methods the smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of gamage and lasenby 2002

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

a least squares algorithm for the equiform transformation from spatial marker co ordinates the present paper describes an algorithm for estimating the translation vector and the rotation matrix of a moving body from noisy measurements on the spatial co ordinates of at least three non collinear markers a sensitivity analysis of the estimated parameters and of the helical axis is presented in terms of characteristics of the marker distribution the implementation of the proposed algorithm in a fortran subroutine is appended

stability of the mann and ishikawa iteration procedures for φ strong pseudocontractions and nonlinear equations of the φ strongly accretive type abstract we study the stability of the mann and ishikawa iteration procedures for the class of lipschitz strongly pseudocontractive maps in arbitrary real banach spaces as a consequence we study the stability of these iteration procedures for the iterative approximation of solutions of nonlinear equations of the strongly accretive type furthermore we prove that the t stability of the mann iteration procedure leads to the strong convergence to the fixed point of t of the so called mann iteration method with errors introduced by liu j math anal appl 194 1995 114 125

an automaton group with undecidable order and engel problems abstract for every turing machine we construct an automaton group that simulates it precisely starting from an initial configuration of the turing machine we explicitly construct an element of the group such that the turing machine stops if and only if this element is of finite order if the turing machine is universal the corresponding automaton group has an undecidable order problem this solves a problem raised by grigorchuk the above group also has an undecidable engel problem there is no algorithm that given g h in the group decides whether there exists an integer n such that the n iterated commutator g h h h is the identity or not this solves a problem raised by bartholdi

optimal marker placement for calculating the instantaneous center of rotation abstract a computer simulation with error propagation was performed to determine the optimal placement of marker points for calculating the instantaneous center of rotation cri the authors assume that planar rigid body motion occurs between two positions each defined by marker points noisy marker points were generated by perturbing their coordinates with random values from a normal population of errors the effects of these errors on the range of errors in calculating cri location were investigated parametric analysis determined that marker point placement had important effects on cri error marker placement was optimal when the estimated cri was located at the midpoint between the marker points while increasing the distance between marker points increased accuracy there is a critical distance above which no additional increase in accuracy was noted when using this placement the farther the marker midpoint was from the cri the greater was the error at these placements increasing the distance between the marker points continually decreased cri error the methodologies presented here help to improve the accuracy with which the location of the cri can be calculated however it is emphasized that the cri remains sensitive to noise and investigators should apply this kinematic parameter knowingly

determination of rigid body registration marker error from edge error registration markers affixed to rigid bodies fixed to bone as opposed to skin are commonly used when tracking 3d rigid body motion the measured positions of registration markers are subject to unavoidable errors both systematic and non systematic prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes while others have focused on the error associated with a specific position tracking system under restricted conditions theoretical and simulation based error propagation requires knowledge of the variation due to individual registration markers however the variation in registration marker position measurement has previously been either assumed or determined from static cases the objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers edge lengths which are invariant under rotation and translation simulations were used to validate and characterize the introduced technique demonstrating that the predictions improve with greater edge length and additional markers converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation and that under ideal conditions the confidence interval about the predicted variation is within 7 of the maximum variation associated with that marker set the introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non static measurements of the same registration markers where the non static variation exceeded the static variation by an average factor of 12 7