Kinematic Degrees Of Freedom Research Articles

Towards quantum gravity with neural networks: solving the quantum Hamilton constraint of U(1) BF theory

Abstract In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in principle applicable to this problem. We consider U(1) BF theory in three dimensions, quantised with loop quantum gravity methods. In particular, we formulate a master constraint corresponding to Hamilton and Gauß constraints using loop quantum gravity methods. To make the problem amenable for numerical simulation we fix a graph and introduce a cutoff on the kinematical degrees of freedom, effectively considering U q ( 1 ) BF theory at a root of unity. We show that the neural network quantum state ansatz can be used to numerically solve the constraints efficiently and accurately. We compute expectation values and fluctuations of certain observables and compare them with exact results or exact numerical methods where possible. We also study the dependence on the cutoff.

Towards quantum gravity with neural networks: solving quantum Hamilton constraints of 3d Euclidean gravity in the weak coupling limit

Abstract The aim of the present work is to demonstrate the applicability of machine learning techniques and in particular neural network quantum states in the context of loop quantum gravity, albeit for a simplified theory. We consider 3-dimensional Euclidean gravity in a gauge theoretical formulation in a certain weak coupling limit due to Smolin, and show that the gauge group becomes Abelian, resulting in U(1)3 BF- theory. The theory is quantised using loop quantum gravity methods. The kinematical degrees of freedom are truncated, on account of computational feasibility, by fixing a graph and deforming the algebra of the holonomies to impose a cutoff on the charge vectors. This leads to a quantum theory related to Uq(1)3 BF-theory. The effect of imposing the cutoff on the charges is examined. We also implement the quantum volume operator of 3d loop quantum gravity. Most importantly we compare two constraints for the quantum model obtained: a master constraint enforcing curvature and Gauß constraint, as well as a combination of a quantum Hamilton constraint constructed using Thiemann’s strategy and the Gauβ master constraint. The two constraints are solved using the neural network quantum state ansatz, demonstrating its ability to explore models which are out of reach for exact numerical methods. The solutions spaces are quantitatively compared and although the forms of the constraints are radically different, the solutions turn out to have a surprisingly large overlap. We also investigate the behavior of the quantum volume in solutions to the constraints.

Unicompartmental knee arthroplasty approximates healthy knee kinematics more closely than total knee arthroplasty.

Total knee arthroplasty (TKA) and unicompartmental knee arthroplasty (UKA) are effective surgeries to treat end-stage knee osteoarthritis. Clinicians assume that TKA alters knee kinematics while UKA preserves native knee kinematics; however, few studies of in vivo kinematics have evaluated this assumption. This study used biplane radiography to compare side-to-side tibiofemoral kinematics during chair rise, stair ascent, and walking in 16 patients who received either TKA or UKA. We hypothesized that TKA knees would have significant kinematic changes and increased asymmetry with the contralateral knee, while UKA knee kinematics would not change after surgery and preoperative knee symmetry would be maintained. Native bone and implant motion were tracked using a volumetric model-based tracking technique. Six degrees of freedom kinematics were calculated throughout each motion. Kinematics were compared between the operated and contralateral knees pre- and post-surgery using a linear mixed-effects model. TKA knees became less varus with the tibia more medial, posterior, and distal relative to the femur. UKA knees became less varus with the tibia less lateral on average. Postoperative TKA knees were in less varus than UKA knees on average and at low flexion angles, with an internally rotated tibia during chair rise and stair ascent. At high flexion angles, the tibia was more medial and posterior after TKA than UKA. Side-to-side kinematic symmetry worsened after TKA but was maintained or improved after UKA. Greater understanding of kinematic differences between operated and contralateral knees after surgery may help surgeons understand why some patients remain unsatisfied with their new knees.

QUANTIFICATION OF THE ACCURACY OF IN VIVO TIBIOFEMORAL KINEMATICS CALCULATED USING MAGNETIC RESONANCE IMAGING AND BIPLANE VIDEO X-RAY

AbstractObjectivesInvestigate Magnetic Resonance Imaging (MRI) as an alternative to Computerised Tomography (CT) when calculating kinematics using Biplane Video X-ray (BVX) by quantifying the accuracy of a combined MRI-BVX methodology by comparing with results from a gold-standard bead-based method.MethodsWritten informed consent was given by one participant who had four tantalum beads implanted into their distal femur and proximal tibia from a previous study. Three-dimensional (3D) models of the femur and tibia were segmented (Simpleware Scan IP, Synopsis) from an MRI scan (Magnetom 3T Prisma, Siemens). Anatomical Coordinate Systems (ACS) were applied to the bone models using automated algorithms1. The beads were segmented from a previous CT and co-registered with the MRI bone models to calculate their positions. BVX (60 FPS, 1.25 ms pulse width) was recorded whilst the participant performed a lunge. The beads were tracked, and the ACS position of the femur and tibia were calculated at each frame (DSX Suite, C-Motion Inc.). The beads were digitally removed from the X-rays (MATLAB, MathWorks) allowing for blinded image-registration of the MRI models to the radiographs. The mean difference and standard deviation (STD) between bead-generated and image-registered bone poses were calculated for all degrees of freedom (DOF) for both bones. Using the principles defined by Grood and Suntay2, 6 DOF kinematics of the tibiofemoral joint were calculated (MATLAB, MathWorks). The mean difference and STD between these two sets of kinematics were calculated.ResultsThe absolute mean femur and tibia ACS position differences (Table 1) between the bead and image-registered poses were found to be within 0.75mm for XYZ, with all STD within ±0.5mm. Mean rotation differences for both bones were found to be within 0.2º for XYZ (Table 1). The absolute mean tibiofemoral joint translations (Table 1) were found to be within ±0.7mm for all DOF, with the smallest absolute mean in compression-distraction. The absolute mean tibiofemoral rotations were found to be within 0.25º for all DOF (Table 1), with the smallest mean was found in abduction-adduction. The largest mean and STD were found in internal-external rotation due to the angle of the X-rays relative to the joint movement, increasing the difficulty of manual image registration in that plane.ConclusionThe combined MRI-BVX method produced bone pose and tibiofemoral kinematics accuracy similar to previous CT results3. This allows for confidence in future results, especially in clinical applications where high accuracy is needed to understand the effects of disease and the efficacy of surgical interventions. Acknowledgements: This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) doctoral training grant (EP/T517951/1).Declaration of Interest(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.

Identification of deformed configurations of segmental tunnel rings based on measured convergences

If convergences grow so large that the serviceability of a tubbing ring is lost, remedial measures must be taken. In this context, it is useful to reconstruct the displacement history of the tunnel ring in order to gain insight into the evolution of the structural behavior that has led to the current configuration. This challenge is tackled with the help of measured convergences and rigid body kinematics. The latter are sufficient, because the deformations of tubbings, resulting from normal forces and bending moments, do not contribute significantly to the displacements of segmental rings. The analysis is focused on convergences measured during a real-scale test of a symmetric tunnel ring. It consists of six tubbings and has three kinematic degrees of freedom. Deformed configurations are reproduced by optimizing the three scalar components of one symmetric and two antisymmetric modes of rigid body displacements. This problem is under-determined, because convergences are routinely measured in two directions only. Its solution is obtained in two steps. At first, the component of the symmetric mode of rigid body displacements is identified such that the measured convergences are reproduced in the best-possible fashion. Thereafter, the remaining differences between measured and modeled convergences are reduced to zero by optimizing the components of the two antisymmetric modes. This kind of structural analysis starts with the most recent set of measured convergences. It proceeds, in a step-by-step manner backwards in time to older sets of monitored data. It is shown that the developed method allows for a satisfactory reproduction of the displacement history of the tested tubbing ring, making use of measured vertical and horizontal convergences. The obtained visualization of the displacement history of the entire tunnel ring provides more insight into the structural behavior than diagrams showing only the evolution of single convergences.

Head injury criteria assessment using head kinematics from crash tests and accident reconstructions

Objective The aim of this study was to assess head injury criteria based on their correlation to brain strain in a Finite Element (FE) head model (the KTH Royal Institute of Technology model), by simulation of head kinematics data from frontal and side crash tests with Anthropomorphic Test Devices (ATDs), and from Human Body Model (HBM) accident reconstructions. Methods Six Degrees of Freedom (DoF) head kinematic data was extracted from 221 crash tests, consisting of frontal impacts with the THOR-50M ATD, near-side and far-side impacts with the WorldSID-50M ATD, and from 19 FE HBM accident reconstructions. The head injury criteria HIC15, HIP, BrIC, UBrIC, DAMAGE and CIBIC were calculated, and FE head model simulations were conducted using the six DoF kinematics data. The 100th, 99th, and 95th percentile Maximum Principal Strains (MPS) of the brain were extracted and linear regression models with respect to the injury criteria were created. The injury criteria were then evaluated based on the coefficient of determination, R2, and the Normalized Root Mean Square Error (NRMSE) of each regression model. Results For all the data sets combined and for the WorldSID far-side data, CIBIC had the best goodness of fit, with R2 of 0.76 and 0.85. For frontal impacts with THOR and the combined ATD data set, DAMAGE had highest R2, 0.83 and 0.78, respectively. Injury criteria including translational accelerations were ranked lower, and BrIC were among the three lowest ranked for most data sets evaluated. UBrIC generally ranked after DAMAGE and CIBIC with respect to the goodness of fit but had the lowest NRMSE for all data sets. Conclusions The two mass-spring-damper brain surrogate model criteria, DAMAGE and CIBIC, were best in capturing the head model MPS response for both the THOR and WorldSID data sets. BrIC had lower correlation to the head model MPS and performed marginally better than the linear acceleration only criteria for all the data sets combined. This study supports the suitability of DAMAGE and CIBIC as brain injury criteria to be used with THOR-50M and WorldSID-50M in vehicle crash test conditions, as they outperform BrIC.

Kirigami tiled surfaces with multiple configurations

This paper presents new kirigami patterns consisting oftilesconnected bysub-foldsthat can approximate multiple specified target surfaces. The curvature of the surfaces approximated by the tiles varies as the patterns are folded, allowing access to a wide range of curvatures. A numerical framework is developed for the synthesis of the fold patterns that approximate a given set of target surfaces. The pattern synthesis process is framed as a tile placement problem, where compatible tile arrangements associated with each target surface are computed by solving a constrained optimization problem. After computing a set of tile arrangements, sub-folds are added to connect adjacent tiles. The resulting patterns are rigid foldable with many kinematic degrees of freedom, allowing them to achieve configurations that approximate the specified target surfaces. Kinematic simulations verify the existence of continuous paths between the target surfaces. A prototype pattern with six target surfaces is fabricated using three-dimensional printed components.

A higher-order plate theory for the analysis of vibrations of thick orthotropic laminates

In this contribution, flexural vibrations of linear elastic laminates composed of thick orthotropic layers, such as cross-laminated timber, are addressed. For efficient computation, an equivalent single-layer plate theory with eight kinematic degrees of freedom is derived, both in terms of equations of motion at the continuum level and in terms of a finite element representation. The validity of the plate theory is demonstrated by comparing natural frequencies of a simply supported plate over a wide frequency range for which an analytical solution is available. Furthermore, the influence of individual material properties on the accuracy of the plate theory is investigated, demonstrating its broad applicability. The influence of material orientation on the accuracy of the plate theory is examined by comparative finite element simulations. It is shown that, for cross-ply laminates, the plate theory is valid for elements oriented at any angle to the material principal axes.

Estimation of Joint Moments During Turning Maneuvers in Alpine Skiing Using a Three Dimensional Musculoskeletal Skier Model and a Forward Dynamics Optimization Framework.

In alpine skiing, estimation of the joint moments acting onto the skier is essential to quantify the loading of the skier during turning maneuvers. In the present study, a novel forward dynamics optimization framework is presented to estimate the joint moments acting onto the skier incorporating a three dimensional musculoskeletal model (53 kinematic degrees of freedom, 94 muscles). Kinematic data of a professional skier performing a turning maneuver were captured and used as input data to the optimization framework. In the optimization framework, the musculoskeletal model of the skier was applied to track the experimental data of a skier and to estimate the underlying joint moments of the skier at the hip, knee and ankle joints of the outside and inside leg as well as the lumbar joint. During the turning maneuver the speed of the skier was about 14 m/s with a minimum turn radius of about 16 m. The highest joint moments were observed at the lumbar joint with a maximum of 1.88 Nm/kg for lumbar extension. At the outside leg, the highest joint moments corresponded to the hip extension moment with 1.27 Nm/kg, the knee extension moment with 1.02 Nm/kg and the ankle plantarflexion moment with 0.85 Nm/kg. Compared to the classical inverse dynamics analysis, the present framework has four major advantages. First, using a forward dynamic optimization framework the underlying kinematics of the skier as well as the corresponding ground reaction forces are dynamically consistent. Second, the present framework can cope with incomplete data (i.e., without ground reaction force data). Third, the computation of the joint moments is less sensitive to errors in the measurement data. Fourth, the computed joint moments are constrained to stay within the physiological limits defined by the musculoskeletal model.

Particle and Continuum Rotations of Granular Materials: Discrete-Element Method Simulations and Experiment

AbstractFor granular materials, the kinematic degrees of freedom at the microscale of particles are the particles’ displacements and rotations. In classical continuum mechanics, the kinematic degre...

Turning circle based trajectory planning method of an underactuated AUV for the mobile docking mission

In this paper, a turning circle based trajectory planning method (TCBTPM) is proposed to conduct trajectory planning of an underactuated autonomous underwater vehicle (AUV) for mobile docking mission. Firstly, the six degrees of freedom kinematics and dynamics model of underactuated AUV is acquired. Following this, the simulation of horizontal turning circle trial is studied and the overview of mobile docking mission is introduced. Furthermore, TCBTPM is used to predict the relative position of AUV and the mobile docking station (MDS) in advance and generate a feasible trajectory for the mobile docking mission. Finally, a mobile docking guidance system containing TCBTPM, pure pursuit (PP) guidance law and line-of-sight (LOS) guidance law is employed to obtain desired guidance commands and guides the underactuated AUV to dock efficiently and reliably.

Investigation of normal knees kinematics in walking and running at different speeds using a portable motion analysis system

ABSTRACT Walking and running at different speeds are common in daily life. This study investigated 6 degrees of freedom (DOF) kinematics of normal knees of Chinese during walking and running. Forty healthy participants were investigated in 4 conditions: comfortable walking, normal walking, slow running and ordinary running. The range of motion (ROM) and peak values in 6 DOF kinematics were analysed. As the speed increased, a general increase in flexion, lateral and proximal translations occurred. Significant increases of ROM in flexion/extension, axial rotation and medial/lateral translations were observed. The ROM of adduction/abduction, anterior/posterior and proximal/distal translations were greatest during normal walking. The maximum and minimum flexion/extension, maximum internal rotation and tibial lateral translations increased with the increase of speed. The maximum and minimum tibial proximal translations in running were found being greater than walking. A phenomenon between walking and running was observed: both tibial proximal/distal and medial/lateral translations increased when changed from walking to running. Non-linear transition exists in 6 DOF kinematics during walking to running. Discoveries in this study may have potential clinical values to serve as references of normal walking and running in the management of knee injury and knee rehabilitation.

A robust and efficient iterative strategy for nonlinear analysis of structures subjected to buckling

A robust and efficient iterative strategy for nonlinear analysis of structures subjected to buckling

The effect of patellofemoral pain syndrome on patellofemoral joint kinematics under upright weight-bearing conditions.

Patellofemoral pain (PFP) is commonly caused by abnormal pressure on the knee due to excessive load while standing, squatting, or going up or down stairs. To better understand the pathophysiology of PFP, we conducted a noninvasive patellar tracking study using a C-arm computed tomography (CT) scanner to assess the non-weight-bearing condition at 0° knee flexion (NWB0°) in supine, weight-bearing at 0° (WB0°) when upright, and at 30° (WB30°) in a squat. Three-dimensional (3D) CT images were obtained from patients with PFP (12 women, 6 men; mean age, 31 ± 9 years; mean weight, 68 ± 9 kg) and control subjects (8 women, 10 men; mean age, 39 ± 15 years; mean weight, 71 ± 13 kg). Six 3D-landmarks on the patella and femur were used to establish a joint coordinate system (JCS) and kinematic degrees of freedom (DoF) values on the JCS were obtained: patellar tilt (PT, °), patellar flexion (PF, °), patellar rotation (PR, °), patellar lateral-medial shift (PTx, mm), patellar proximal-distal shift (PTy, mm), and patellar anterior-posterior shift (PTz, mm). Tests for statistical significance (p < 0.05) showed that the PF during WB30°, the PTy during NWB0°, and the PTz during NWB0°, WB0°, and WB30° showed clear differences between the patients with PFP and healthy controls. In particular, the PF during WB30° (17.62°, extension) and the PTz during WB0° (72.5‬0 mm, posterior) had the largest rotational and translational differences (JCS Δ = patients with PFP—controls), respectively. The JCS coordinates with statistically significant difference can serve as key biomarkers of patellar motion when evaluating a patient suspected of having PFP. The proposed method could reveal diagnostic biomarkers for accurately identifying PFP patients and be an effective addition to clinical diagnosis before surgery and to help plan rehabilitation strategies.

Refined Zigzag Theory: an appropriate tool for the analysis of CLT-plates and other shear-elastic timber structures

Cross laminated timber (CLT), as a structural plate-like timber product, has been established as a load bearing product for walls, floor and roof elements. In a bending situation due to the transverse shear flexibility of the crossing layers, the warping of the cross section follows a zigzag pattern which should be considered in the calculation model. The Refined Zigzag Theory (RZT) can fulfill this requirement in a very simple and efficient way. The RZT, founded in 2007 by A. Tessler (NASA Langley Research Center), M. Di Sciuva and M. Gherlone (Politecnico Torino) is a very robust and accurate analysis tool, which can handle the typical zigag warping of the cross section by introducing only one additional kinematic degree of freedom in case of plane beams and two more in case of biaxial bending of plates. Thus, the RZT-kinematics is able to reflect the specific and local stress behaviour near concentrated loads in combination with a warping constraint, while most other theories do not. A comparison is made with different methods of calculation, as the modified Gamma-method, the Shear Analogy method (SA) and the First Order Shear Deformation Theory (FSDT). For a test example of a two-span continuous beam, an error estimation concerning the maximum bending stress is presented depending on the slenderness L/h and the width of contact area at the intermediate support. A stability investigation shows that FSDT provides sufficiently accurate results if the ratio of bending and shear stiffness is in a range as stated in the test example. It is shown that by a simple modification in the determination of the zigzag function, the scope can be extended to beams with arbitrary non-rectangular cross section. This generalization step considerably improves the possibilities for the application of RZT. Furthermore, beam structures with interlayer slip can easily be treated. So the RZT is very well suited to analyze all kinds, of shear-elastic structural element like CLT-plate, timber-concrete composite structure or doweled beam in an accurate and unified way.

Biomechanics of Cervical Disc Arthroplasty-A Review of Concepts and Current Technology.

Activities of daily living require the subaxial cervical spine (C2-C7) to have substantial mobility. Cervical degenerative changes can cause abnormal motions and altered load distribution, leading to pain and limiting the ability of individuals to perform activities of daily living. Anterior cervical discectomy and fusion (ACDF) has been widely used to treat symptomatic cervical spondylosis. Clinical studies have shown cervical disc arthroplasty (CDA) to be a viable alternative to ACDF for the treatment of radiculopathy and myelopathy. The benefits of CDA are based on the premise that preservation of physiologic motions and load-sharing at the treated level would lead to longevity of the index-level facet joints and mitigate the risk of adjacent segment degeneration.This review article classifies cervical disc prostheses according to their kinematic degrees of freedom and device constraints. Discussion on how these design features may affect cervical motion after implantation will provide the reader with valuable information on how disc prostheses may function clinically.The ability of a disc prosthesis to work in concert with remaining bony and soft tissue structures to restore physiologic motion and load-sharing is a function of the following design features and surgical factors: Kinematic degrees of freedom-Prostheses that allow translation independent of rotation allow, in theory, the spinal anatomy to dictate segmental motion after CDA potentially restoring physiologic motion and load-sharing. A 6-degrees-of-freedom disc prosthesis may be best equipped to achieve the intended function of CDA.Built-in stiffness-A disc prosthesis with built-in resistance to angular and translational motion may have an advantage in restoring stability to a hypermobile segment without eliminating motion.Surgical factors related to prosthesis implantation may influence cervical segments after CDA. These factors include the amount of disc space distraction caused by the prosthesis, prosthesis placement in the sagittal and coronal planes, and integrity of the soft tissue envelope.

Backstepping active disturbance rejection control for trajectory tracking of underactuated autonomous underwater vehicles with position error constraint

In this article, the three-dimensional trajectory tracking control of an autonomous underwater vehicle is addressed. The vehicle is assumed to be underactuated and the system parameters and the external disturbances are unknown. First, the five degrees of freedom kinematics and dynamics model of underactuated autonomous underwater vehicle are acquired. Following this, reduced-order linear extended state observers are designed to estimate and compensate for the uncertainties that exist in the model and the external disturbances. A backstepping active disturbance rejection control method is designed with the help of a time-varying barrier Lyapunov function to constrain the position tracking error. Furthermore, the controller system can be proved to be stable by employing the Lyapunov stability theory. Finally, the simulation and comparative analyses demonstrate the usefulness and robustness of the proposed controller in the presence of internal parameter uncertainties and external time-varying disturbances.

Kinematics and constitutive relations in the stress-gradient theory: interpretation by homogenization

The stress-gradient theory has a third order tensor as kinematic degree of freedom, which is work-conjugate to the stress gradient. This tensor was called micro-displacements just for dimensional reasons. Consequently, this theory requires a constitutive relation between stress gradient and micro-displacements, in addition to the conventional stress-strain relation. The formulation of such a constitutive relation and identification of the parameters therein is difficult without an interpretation of the micro-displacement tensor.The present contribution presents an homogenization concept from a Cauchy continuum at the micro-scale towards a stress-gradient continuum at the macro-scale. Conventional static boundary conditions at the volume element are interpreted as a Taylor series whose next term involves the stress gradient. A generalized Hill-Mandel lemma shows that the micro-displacements can be identified with the deviatoric part of the first moment of the microscopic strain field. Kinematic and periodic boundary conditions are provided as alternative to the static ones. The homogenization approach is used to compute the stress-gradient properties of an elastic porous material. The predicted negative size effect under uni-axial loading is compared with respective experimental results for foams and direct numerical simulations from literature.

Whole-body kinematics and coordination in a complex dance sequence: Differences across skill levels

This study examined differences across skill levels in the kinematics of a complex, whole-body, asymmetrical, cyclical dance sequence, the ‘Alternate Basic’ in Cha-Cha-Cha, to determine whether observed differences were consistent with Bernstein's (1967) model of development of coordination. Bernstein proposed that with novel motor skills, beginners move their bodies rigidly and spastically, freezing kinematic degrees of freedom (DOF) to constrain the motor system. As the skill becomes practised, the DOF unfreeze and movements become more dynamic, allowing the integration of reactional elements (passive forces, moments, etc.) and organisation of more complex coordinative structures. Twenty-nine dancers - beginners (n = 10), intermediates (n = 10), experts (n = 9) - performed 12 cycles of the dance sequence (total duration ~60 s). Three-dimensional kinematic data from 36 joint angles were collected using a 14-camera infrared motion capture system. Most joints displayed increased amplitude and speed of movement, especially early in skill progression (beginner-intermediate stage), with no evidence of any decreases, showing that unfreezing occurred around the general movement pattern early. Speed of movement continued to increase later (intermediate-expert stage), as well as further unfreezing of the upper limbs. Changes to intra-limb couplings were limited, comprising some early reductions in coupling strength. Principal component analyses (PCA) showed that the structure of movement became more organised with increased skill. There was an early reduction in the number of coordinative structures, while later, movement was integrated more into the first coordinative structure. As predicted by Bernstein's coordination development model, therefore, the kinematic DOF unfroze as skill level progressed, leading to increased organisation of coordinative structures. The results of this study support the importance of a whole-body perspective in studies of coordination, with incorporation of kinetic variables in future research in order to examine the role that reactional elements play in motor skill development.

In vivo gait kinematics of the knee after anatomical and non-anatomical single-bundle anterior cruciate ligament reconstruction-a prospective study.

The factors that influence functions of knees after anterior cruciate ligament reconstruction (ACLR) still remains uncertain. The functional restoration of knees after ACLR can be reflected on gait kinematics restoration. The purpose of this study was to evaluate the gait kinematics and clinical outcomes of knees after anatomical and non-anatomical single-bundle ACLR during level walking. Thirty-four patients with unilateral primary single-bundle ACLR and 18 healthy people were recruited. Patients were divided into anatomical reconstruction group (AR group; n=13) and non-anatomical reconstruction group (Non-AR group; n=21) according to Bernard Quadrant method. The ACL graft orientations on coronal and sagittal planes were measured on 3D models from medical images. The 6 degrees of freedom (DOF) kinematics of knees and range of motion (ROM) of 6 DOF kinematics were measured with a portable optical tracking system. The comparison of 6 DOF kinematics and ROM of 6 DOF kinematics were performed between the ACLR knees and contralateral knees. The following assessments were also performed including clinical examination, KT-2000 arthrometer measurement, International Knee Documentation Committee (IKDC) and Lysholm scores. All patients reached a minimum follow-up of 6 months (10±4 months). For AR group and Non-AR group, no statistically significant differences were observed in gait kinematics between the ACLR knees and contralateral knees. No statistically significant differences between the ACLR knees and contralateral knees were observed in terms of ROM of 6 DOF kinematics in AR group. However, in Non-AR group, the ACLR knees exhibited significant ROM of anterior-posterior translation by approximately 0.5 cm than contralateral knees (P=0.0080). No statistically significant differences between the two groups were observed regarding IKDC subjective score, Lysholm score and KT-2000 arthrometer test. The anatomical ACLR can restore close to normal gait kinematics and ROM of 6 DOF kinematics compared with non-anatomical ACLR. The ACL graft after anatomical ACLR simulated native ACL fibers to function in terms of graft orientation.