Definition Of Reference Frame Research Articles

A reproducible representation of healthy tibiofemoral kinematics during stair descent using REFRAME – Part II: Exploring optimisation criteria and inter-subject differences

Kinematic analysis is a central component of movement biomechanics, describing the relative motion of joint segments during different activities, in different subject cohorts, and at different timepoints. Establishing whether two sets of kinematic signals represent fundamentally similar or different underlying motion patterns is especially challenging, given 1) the lack of consensus around reference frame and joint axis definition, and 2) the substantial effect that minimal variations in frame position and orientation are known to have on signal magnitude and characteristics. As such, enormous variability in the reporting of tibiofemoral kinematics has resulted in joint movement patterns that remain controversially discussed. Previously, we demonstrated the ability of the REference FRame Alignment MEthod (REFRAME) to reorientate and reposition differently aligned local segment frames to achieve convergence in signals representing the same underlying motion, thereby offering a novel approach to consistently report joint motion. In this study, for the first time, we apply REFRAME to assess the rotational and translational in vivo tibiofemoral motion of ten healthy subjects during stair descent based on kinematic signals collected using a moving videofluoroscope. Kinematics were analysed before and after different REFRAME implementations, revealing generally neutral ab/adduction behaviour, accompanied by varying degrees of a sinusoidal int/external tibial rotation pattern over the activity cycle. Our data demonstrate that different selected implementations of REFRAME are able to highlight different characteristics of the motion patterns: Minimisation of the translational root-mean-square revealed proximodistal translation patterns with overall neutral progression, while anteroposterior translation showed seemingly different levels of correlation with flexion/extension in different subjects. On the other hand, REFRAME minimisation of translational variances exposed differences in the relative mean displacement between the femoral and tibial origins between subjects, highlighting differences in mean centre of rotation positions. This early application of REFRAME for providing an understanding of tibiofemoral kinematics demonstrates the potential of this novel approach to bring clarity to an otherwise complex representation of highly variable time-series signals, while highlighting the philosophical challenges of clinically interpretating kinematic signals in the first place.

Particle and light motion in Lyra–Schwarzschild spacetime

Abstract In this paper we recall the static and spherically symmetric solution derived within LyST gravity. LyST stands for “Lyra Scalar-Tensor” and is a scalar-tensor proposal for the gravitational interaction modifying general relativity by adopting Lyra manifold as the spacetime substrate. Lyra manifold is characterized both by the metric tensor gµν(x) and the scale φ(x); the latter being an integral part of the definition of reference frame. In a previous work, we have launched the formal geometrical basis of LyST, we have proposed an associated action integral for the gravitational interaction, we have derived the field equations generalizing Einstein field equation, and we have solved these equation to obtain the generalized version of Schwarzschild line element in Lyra manifold. This lead us to Lyra-Schwarzschild spacetime, which is further explored in the present paper. Herein, the trajectories of test particles is thoroughly studied. This is done for both massive particles and massless particles. The geodesic equations are built and solved. The effective potential associated to the motion of these particles around the source is determined and characterized. The possible trajectories include gravitational capture, scattering, bounded orbits, stable and unstable circular orbits, near-horizon motion. The innermost circular orbit allowed for massive particles is determined and compared to the one predicted by GR. The last photon orbit is also calculated for Lyra-Schwarzschild metric. The equation for the periastron shift in the context of Lyra-Schwarzschild solution is constructed; its application to observational data could be useful to constrain the parameters typical of LyST, telling it apart from GR.

PERFORMANCE OF BURSA-WOLF MODEL FOR DEFORMING REGION: CASE STUDY IN MALAYSIA

Abstract. Bursa-Wolf model is a common mathematical approach for coordinate transformation practice between two reference frames. For the case of deforming region, the existing reference frame has been experiencing a non-linear shifting over the time due to co-seismic and post seismic occurrences. Imprecise coordinate in the reference frame definition could degrading critical positioning, surveying, and navigation activities. This require a new realization of reference frame and the coordinate transformation linkage is suggested to be developed in relating the new and existing reference frame. This study provides performance of Bursa-Wolf model as coordinate transformation approach for a deforming region that is experiencing non-linear shifting due to the co-seismic and post-seismic events. The Bursa-Wolf were generated from 32 dependent Global Positioning System (GPS) Continuously Operating Reference Stations (CORS) in Malaysia meanwhile another 20 independent neighbouring stations were utilized for assessment purposes. Seven parameters (7p) of Bursa-Wolf were estimated with RMS at ±4.5mm, ±9.2mm and ±2.1mm respectively. The independent stations were classified as internal and external assessment station and the root mean square (RMS) were found at less than 10mm. The internal station has depicted a better RMS in each component which are ±5.1mm, ±6.5mm and ±1.5mm respectively. Meanwhile for external stations RMS in each component are ±6.1mm, ±8.7mm and ±3.5mm respectively. The result shows that Bursa-Wolf model is sufficient to be used as coordinate transformation approach for deforming region.

Practical Algorithms on Lunar Reference Frame Transformations for Korea Pathfinder Lunar Orbiter Flight Operation

This technical paper deals the practical transformation algorithms between several lunar reference frames which will be used for Korea pathfinder lunar orbiter (KPLO) flight operation. Despite of various lunar reference frame definitions already exist, use of a common transformation algorithm while establishing lunar reference frame is very important for all members related to KPLO mission. This is because use of slight different parameters during frame transformation may result significant misleading while reprocessing data based on KPLO flight dynamics. Therefore, details of practical transformation algorithms for the KPLO mission specific lunar reference frames is presented with step by step implementation procedures. Examples of transformation results are also presented to support KPLO flight dynamics data user community which is expected to give practical guidelines while post processing the data as their needs. With this technical paper, common understandings of reference frames that will be used throughout not only the KPLO flight operation but also science data reprocessing can be established. It is expected to eliminate, or at least minimize, unnecessary confusion among all of the KPLO mission members including: Korea Aerospace Research Institute (KARI), National Aeronautics and Space Administration (NASA) as well as other organizations participating in KPLO payload development and operation, or further lunar science community world-wide who are interested in KPLO science data post processing.

Evaluating the Stability and Adequacy of NIGNET for the Definition of Nigerian Geodetic Reference Frame

A set of Continuously Operating Reference Stations (CORS) distributed all over Nigeria constitutes the Nigerian GNSS Reference Network referred to as NIGNET. Global Navigation Satellite System (GNSS) is a system tha uses satellites for autonomous position determination, and is a critical component of the modern-day geodetic infrastructure and services. Using CORS provide geodetic controls of comparable accuracy and a better alternative to the classical geodetic network. As the NIGNET infrastructure is utilised for different geodetic applications, it has become necessary to evaluate the suitability of the network data for the definition of a geodetic reference frame (GRF). This study utilised the technique of Precise Point Positioning (PPP) in position estimation, and time series analysis for temporal monitoring of the network. The sufficiency and adequacy of the NIGNET data archive was also evaluated against that of an International GNSS Service (IGS) Station. The temporal stability of the station coordinates measured in terms of standard deviations varied between 10 mm and 22 mm. This analysis suggests a relative stability required for Tiers 1 and 2 CORS in line with the IGS standards. Based on this reported stability, it is concluded that NIGNET is fit for purpose in defining the Nigerian Geodetic Reference Frame. However, despite the good data quality observed, the adequacy of the network has been compromised by infrastructural failures and lack of continuity in data transmission. Accordingly, it is recommended that both practical and policy measures required to ensure the realisation of the goal of the network should be implemented.
 Keywords: Geodetic reference frame, NIGNET, CORS, precise point positioning, temporal stability and adequacy.

Contemporary deformation and seismicity analysis in Southwest Japan during 2010–2018 based on GNSS measurements

A significant amount of work has been conducted in the Japanese islands on high-precision positioning, surveying, natural disaster mitigation, reference frame, and datum definitions; however, there is substantial scope for exploring the current seismotectonic activity of Japan, which would provide further awareness of disaster management. The short recurrence time of great inter-plate earthquakes and well-recorded geodetic observations provide one of the best examples to analyze the combination of contemporary deformation and seismic intensity in Southwest (SW) Japan. In the current study, we analyzed three districts of SW Japan which include mainly Kyushu district and parts of Chugoku and Shikoku districts. We predicted Global Navigation Satellite System (GNSS) measurements based on Amurian-fixed reference frame (AREF) velocities with the help of singular spectrum analysis (SSA) method and examined the regional deformation from April 01, 2010 to December 31, 2018. In addition, we analyzed the earthquakes clustered calculated by the nearest neighborhood distance method, which showed prominently bimodal seismicity of SW Japan and revealed the existence of two statistically distinct earthquake populations. The events inside a cluster were normally close to their nearest neighbors, whereas events from distinct clusters were comparatively aloof from each other. Finally, the paper provides the spatial strain and rotational rate variation for selected seismotectonic districts that are in relatively good agreement with the seismic deformation inferred from earthquake focal mechanisms. We believe that our integrated approaches would provide a better insight into the active deformation of SW Japan.

Impedance Aggregation Method of Multiple Wind Turbines and Accuracy Analysis

The sequence domain impedance modeling of wind turbines (WTs) has been widely used in the stability analysis between WTs and weak grids with high line impedance. An aggregated impedance model of the wind farm is required in the system-level analysis. However, directly aggregating WT small-signal impedance models will lead to an inaccurate aggregated impedance model due to the mismatch of reference frame definitions among different WT subsystems, which may lead to inaccuracy in the stability analysis. In this paper, we analyze the impacts of the reference frame mismatch between a local small-signal impedance model and a global one on the accuracy of aggregated impedance and the accuracy of impedance-based stability analysis. The results revealed that the impact is related to the power distribution of the studied network. It was found that that the influence of mismatch on stability analysis became subtle when subsystems were balanced loaded. Considering that balanced loading is a common configuration of the practical application, direct impedance aggregation by local small-signal models can be applied due to its acceptable accuracy.

Empirical Orthogonal Function analysis and modeling of ionospheric TEC over South Korean region

This paper presents the ionospheric Total Electron Content (TEC) variations over the low-middle latitude South Korean region using dual frequency Global Navigation Satellite System (GNSS) observations from 14 permanent stations with the data spanning approximately eight years (January 2010 to December 2017). Although, significant work has been conducted in the Korean territory on high-precision positioning, surveying, natural disaster mitigation, and reference frame and datum definition; however, there is substantial scope for modeling of the low-middle latitude ionosphere over the region, which would provide further navigational and communicational benefits. Therefore, in this study, we investigated spatial and temporal TEC variations in GNSS observables through Empirical Orthogonal Function (EOF) modeling and substantiate our findings against existing empirical International Reference Ionosphere (IRI-2016) and NeQuick-2 models. In addition, observation and modeling studies conducted during a geomagnetic storm period (3–9 September, 2017), when the vertical TEC (VTEC) value was almost double that of its regular level, confirm the superior performance of the EOF model in the percentage deviation and correlation plots. To ascertain the performance of the EOF model, the geomagnetic coordinates and PCN index were considered in this study along with other solar and geomagnetic indices (F10.7, Ap and Dst). Analysis of results emphasizes the superior performance of the EOF model compared to other regional and global models with respect to its accuracy and quality relating to quick convergence of decomposition modes and discrimination of temporal as well as spatial components.

MODELS AND TECHNIQUES IN GEODETIC MONITORING OF TECTONIC DEFORMATIONS IN GREECE

The assessment and interpretation of the geodetic results regarding the detection of possible spatial displacements and the deformation parameters have to be combined with a realistic geophysical model for the area. Usually, this study is carried out by fitting the geodetic data to a polynomial function, which is considered sufficient to describe adequately the deformation pattern. In terms of the computational steps needed, this polynomial fitting can be accomplished simultaneously by the analysis of the geodetic observations in a dynamic adjustment or non simultaneously in a sequential approach. The main goal of this article is to give a short description of the related methods and to present rigorous processing strategies for the analysis of GNSS observations from continuously permanent stations in order to create a modern and improved geodetic velocity field for Greece. Emphasis is given on the reference frame definition problem.

Investigating Alignment Effect on Inspection Accuracy of AM Part Using 3D Scanner

Presently, parts having intricate custom-made profiles are mostly fabricated using additive manufacturing (AM) processes. It becomes an essential task to verify the accuracy of AM parts so that they meet customer’s need and requirement. In product quality control, quick error comparison of manufactured part and an original CAD model is usually laborious but still a critical issue. Noncontact inspections using 3D scanners were preferred over conventional coordinate measurements, due to the significant amount of point data capturing in very short span of time. One of the important step of the noncontact inspection procedure using the 3D scanner is the correct localization of the datum reference frame. This step would help in the effective alignment of the digitized point data. This paper takes into consideration various 3-2-1 alignment approaches and investigates their influence on the inspection results. The result provides an evidence that an incorrect description of the product reference frame can lead to erroneous estimation of actual part deviations. The results show higher distance distribution for most of the point data of third alignment as the distance distribution is influenced by the worst description of the part reference frame. On the contrary, second alignment shows least distance distribution among point data due to correct reference frame definition.

Simple and efficient improvement of spin image for three-dimensional object recognition

This paper presents a highly distinctive and robust local three-dimensional (3-D) feature descriptor named longitude and latitude spin image (LLSI). The whole procedure has two modules: local reference frame (LRF) definition and LLSI feature description. We employ the same technique as Tombari to define the LRF. The LLSI feature descriptor is obtained by stitching the longitude and latitude (LL) image to the original spin image vertically, where the LL image was generated similarly with the spin image by mapping a two-tuple ( θ,φ ) into a discrete two-dimensional histogram. The performance of the proposed LLSI descriptor was rigorously tested on a number of popular and publicly available datasets. The results showed that our method is more robust with respect to noise and varying mesh resolution than existing techniques. Finally, we tested our LLSI-based algorithm for 3-D object recognition on two popular datasets. Our LLSI-based algorithm achieved recognition rates of 100%, 98.2%, and 96.2%, respectively, when tested on the Bologna, University of Western Australia (UWA) (up to 84% occlusion), UWA datasets (all). Moreover, our LLSI-based algorithm achieved 100% recognition rate on the whole UWA dataset when generating the LLSI descriptor with the LRF proposed by Guo.

National Datum Uncertainty due to Reference Frame Transformation: Case Study for the Geodetic Datum of Taiwan

AbstractWith the advent of global navigation satellite systems (GNSSs), many national geodetic datums have been established with modern technology and referenced to a specific epoch of the international terrestrial reference frame (ITRF) definition. Following the static datum concept, the datum remains unchanged after its publication, which consequently creates problems in datum maintenance. In the recent update of TWD97, the national datum presently used in Taiwan, the resurvey coordinates are transformed back to the original frame but expressed in a recent epoch. In this study, the uncertainties resulting from the transformation between ITRF definitions in the region of Taiwan were investigated. Based on error propagation, a standard error of ±7 cm was estimated due to the transformation of the TWD97 coordinates between ITRF2005(2010.0) and ITRF94(2010.0). The uncertainties propagated from transformation parameters are more significant than those from station coordinates and velocities, and the uncertai...

A new velocity field from the analysis of the Egyptian Permanent GPS Network (EPGN)

For studying recent crustal movements and their relation to earthquake occurrence in large scales, the National Research Institute of Astronomy and Geophysics (NRIAG), Helwan, Cairo, Egypt started in 2006 the establishment of the Egyptian Permanent GPS Network (EPGN). Beginning with 4 stations in 2007, 15 stations were operational at the end of 2011. In addition, a station in Alexandria of the French “Centre d'Etudes Alexandrines” (CEALX) was added as station to the EPGN. Nowadays, 16 stations are operational and an extension to 20 in the near future is expected. The collected EPGN data of the last 6 years are used in this work to throw light upon the present state of recent crustal movement of the whole of Egypt. Bernese software V. 5.0 was used for processing the collected data according to the IGS standards. In addition, selected IGS, AFREF, and EPN sites are processed for reference frame definition. In this first comprehensive analysis of the permanent network, a complete and consistent evaluation resulted in the first estimates of present day horizontal velocities and coordinate time series.

A decade of horizontal deformation from great earthquakes

The 21st Century has seen the occurrence of 17 great earthquakes (Mw >8), including some of the largest earthquakes ever recorded. Numerical modeling of the earthquakes shows that nearly half of the Earth's surface has undergone horizontal coseismic deformation >1 mm, with the 2004 Sumatra‐Andaman earthquake dominating the global deformation field. This has important implications for both the realization of a terrestrial reference frame and in the interpretation of regional tectonic studies based on GPS velocities. We show that far‐field coseismic deformations from great earthquakes will, if unaccounted for, introduce errors in estimates of linear site velocities of at least 0.1‐0.3 mm/yr across most of the surface of the Earth. The accumulated global deformation field shows that two regions, Australia and the north Atlantic/Arctic Ocean, have been largely undeformed by these great earthquakes, with accumulated deformations generally <0.5 mm. Using GPS estimates of surface deformation, we show that the majority of the Australian continent is deforming at <0.2 mm/yr, the northern part of New Zealand is rotating clockwise relative to the Australian Plate with relative horizontal velocities of ∼2 mm/yr, while the southeastern coast of Australia is undergoing post‐seismic relaxation caused by the 2004 Mw = 8.1 Macquarie Ridge earthquake. The presence of ongoing post‐seismic relaxation thousands of kilometers from plate margins violates the secular/linear assumption made in current terrestrial reference frame definitions. These effects have significant ramifications for regional tectonic interpretations and global studies such as sea level rise that require reference frame accuracy greater than this level.

Rotational Projection Statistics for 3D Local Surface Description and Object Recognition

Recognizing 3D objects in the presence of noise, varying mesh resolution, occlusion and clutter is a very challenging task. This paper presents a novel method named Rotational Projection Statistics (RoPS). It has three major modules: local reference frame (LRF) definition, RoPS feature description and 3D object recognition. We propose a novel technique to define the LRF by calculating the scatter matrix of all points lying on the local surface. RoPS feature descriptors are obtained by rotationally projecting the neighboring points of a feature point onto 2D planes and calculating a set of statistics (including low-order central moments and entropy) of the distribution of these projected points. Using the proposed LRF and RoPS descriptor, we present a hierarchical 3D object recognition algorithm. The performance of the proposed LRF, RoPS descriptor and object recognition algorithm was rigorously tested on a number of popular and publicly available datasets. Our proposed techniques exhibited superior performance compared to existing techniques. We also showed that our method is robust with respect to noise and varying mesh resolution. Our RoPS based algorithm achieved recognition rates of 100, 98.9, 95.4 and 96.0 % respectively when tested on the Bologna, UWA, Queen’s and Ca’ Foscari Venezia Datasets.

Does medio-lateral motion occur in the normal knee? An in-vitro study in passive motion

Medio-lateral translation during knee flexion continues to raise controversy. Small population sizes, small joint flexion ranges, less-reliable measurement techniques and disparate experimental conditions led to inconsistent reports in the past. To study this subject with more accurate and reliable measurements, we carried out femur and tibia tracking in 22 intact cadaver knees during passive joint motion using a state-of-the-art surgical navigation system. Trackers with active light-emitting diodes were fixed onto the femur and tibia, and an instrumented pointer was used to digitize a number of anatomical landmarks. International recommendations were adopted for anatomical-based reference frame definitions and joint kinematic analysis. For the first time, knee joint translations were reported in both the femoral and tibial reference frames, and over a flexion/extension arc as large as 140°. During flexion, in the femoral reference frame, the center of the tibial plateau moved 4.8±2.8mm medially when averaged over the specimens. In the tibial frame, the knee center moved 13.3±5.7mm laterally. The relative femoral-to-tibial medio-lateral translation was, on average over the specimens, nearly 20% of the width of the tibial plateau, and can be as large as 35%. Medio-lateral translation occurs in the natural normal knee joint.

Active tectonics in northern Victoria Land (Antarctica) inferred from the integration of GPS data and geologic setting

A semipermanent Global Positioning System (GPS) network of 30 vertices known as the Victoria Land Network for Deformation Control (VLNDEF) was set up in the Austral summer of 1998 in northern Victoria Land (NVL), including Terra Nova Bay (TNB), Antarctica. The locations were selected according to the known Cenozoic fault framework, which is characterized by a system of NW‐SE regional faults with right‐lateral, strike‐slip kinematics. The TNB1 permanent GPS station is within the VLNDEF, and following its installation on a bedrock monument in October 1998, it has been recording almost continuously. The GPS network has been surveyed routinely every two summers, using high‐quality, dual‐frequency GPS receivers. In this study we present the results of a distributed session approach applied to the processing of the GPS data of the VLNDEF. An improved reference frame definition was implemented, including a new Euler pole, to compute the Antarctic intraplate residual velocities. The projection of the residual velocities on the main faults in NVL show present‐day activities for some faults, including the Tucker, Leap Year, Lanterman, Aviator, and David faults, with right‐lateral strike‐slip kinematics and local extensional and compressional components. This active fault pattern divides NVL into eight rigid blocks, each characterized by its relative movements and rigid rotations. These show velocities of up to several millimeters per year, which are comparable to those predicted by plate tectonic theory at active plate margins.

Adjustment and transformation strategies of ItalPoS Permanent GNSS Network

A private network of 133 Global Navigation Satellite Systems (GNSS) permanent sites, named ItalPoS (Italian Positioning Service) and uniformly covering the entire Italian territory, was established in April 2006 by the Ital- ian Division of Leica Geosystems S.p.A. This network also involves several GPS stations of the INGV (Italian National Institute of Geophysics and Volcanology) RING (Real-time Integrated National Gps) network and GPS stations from other public and private bodies. Indeed Leica Geosystems contributed with its experience and its products to these networks which currently fulfil the national coverage where there are no ItalPoS stations. For instance, the purpose of the ItalPoS network is mainly GNSS data distribution in terms of real time corrections and RINEX files for the post-processing. In order to compute and distribute to private and scientific users a set of adjusted coordinates of the ItalPoS net- work in the IGS05 and ETRF89-2000 reference frames, a dataset of RINEX of about 120 GPS permanent sites was created and processed, using the distributed sessions approach, by means of Gamit/Globk 10.3 GPS data processor, also using some SOPAC (Scripps Orbits and Permanent Array Center) and EUREF (European Per- manent Network) solutions to improve the reference frame definition and the internal constraints. This paper describes all the strategies adopted to estimate coordinates and velocities of the ItalPoS Network in IGS05 and in ETRF89-2000 reference frames in the whole Italian territory.

Impact of regional reference frame definition on geodynamic interpretations

Abstract Ten years (1997–2006) of weekly GNSS solutions of 205 globally distributed stations have been used to investigate the impact of the reference frame definition on the estimated station velocities. For that purpose, weekly regional solutions (covering the European region) and global solutions have been, respectively, stacked to obtain regional and global velocity fields. In both cases, the estimated long-term solutions (station positions and velocities) were tied to the ITRF2005 under minimal constraints using a selected set of reference stations. Several sets of global and regional reference stations were tested to evaluate first the impact of the reference frame definition on the global and regional velocity fields and later the impact on the derived geodynamic interpretations. Results confirm that the regional velocity fields show systematic effects with respect to the global velocity field with differences reaching up to 1.3 mm/year in the horizontal and 2.9 mm/year in the vertical depending on the geographical extent of the network and the chosen set of regional reference stations. In addition, the estimations of the Euler pole for Western Europe differ significantly when considering a global or a regional strategy. After removing the rigid block rotation, the residual velocity fields show differences which can reach up to 0.8 mm/year in horizontal component. In Northern Europe, the vertical ground motion is dominated by the Glacial Isostatic Adjustment (GIA). A proper modeling of this effect requires sub-mm/year precision for the vertical velocities for latitudes below 56°. We demonstrate that a profile of vertical velocities shows significant discrepancies according to the reference frame definition strategy. In the case of regional solutions, the vertical modeling does not predict any subsidence around 52° as predicted by the global solution and previous studies. In summary, we evidence the limitation of regional networks to reconstruct absolute velocity fields and conclude that when geodynamics require the highest precisions for the GNSS-based velocities, a global reference frame definition is more reliable.

Quantitative comparison of current models for trunk motion in human movement analysis

Background A number of different models for human trunk kinematics during locomotion have been proposed, though mainly addressing specific clinical questions rather than general populations. These differ considerably for the skeletal segments considered, marker-set, anatomical axis and frame definitions, and joint conventions. The scope of the present study is to compare quantitatively these models on the basis of the same motion. Methods Ten subjects were analysed, instrumented with a single comprehensive marker-set of 14 markers identified from the union of the corresponding from eight current models for trunk kinematics. Activities of daily living (walking, chair rising/sitting, step-up/down), elementary trunk movements (flexion, bending and axial rotation), and isolated motion of the shoulders, both synchronous and asynchronous were collected. Resulting rotations in the three anatomical planes, both in the laboratory and in the pelvis reference frames, were calculated. Findings In addition to the expected bias between the rotation angle time-histories, very different patterns and range of motion were found between the models. In chair rising/sitting, and in the laboratory global frame, the range of flexion averaged over the subjects was measured by the different models in the full scale from about 28° to 44°. In elementary trunk rotation and in the pelvis anatomical reference frame, three models measured about 10° excursion of the coupled bending motion, other two about 38° and 49° on average. Interpretation In trunk kinematics analysis, it is recommended that all models, both in terms of markers involved and of reference frame definitions, are understood carefully before interpreting the results in clinical decision making.