Kinematic Curves Research Articles

Kinect-Based Gait Analysis System Design and Concurrent Validity in Persons with Anterolateral Shoulder Pain Syndrome, Results from a Pilot Study

As part of an investigation to detect asymmetries in gait patterns in persons with shoulder injuries, the goal of the present study was to design and validate a Kinect-based motion capture system that would enable the extraction of joint kinematics curves during gait and to compare them with the data obtained through a commercial motion capture system. The study included eight male and two female participants, all diagnosed with anterolateral shoulder pain syndrome in their right upper extremity with a minimum 18 months of disorder evolution. The participants had an average age of 31.8 ± 9.8 years, a height of 173 ± 18 cm, and a weight of 81 ± 15 kg. The gait kinematics were sampled simultaneously with the new system and the Clinical 3DMA system. Shoulder, elbow, hip, and knee kinematics were compared between systems for the pathological and non-pathological sides using repeated measures ANOVA and 1D statistical parametric mapping. For most variables, no significant difference was found between systems. Evidence of a significant difference between the newly developed system and the commercial system was found for knee flexion–extension (p < 0.004, between 60 and 80% of the gait cycle), and for shoulder abduction–adduction. The good concurrent validity of the new Kinect-based motion analysis system found in this study opens promising perspectives for clinical motion tracking using an affordable and simple system.

3-Dimensional Biomechanics of Noncontact Anterior Cruciate Ligament Injuries in Male Professional Soccer Players

Background: The understanding of noncontact anterior cruciate ligament (ACL) injury causation in soccer has improved over the past decades. Bidimensional video analyses have significantly augmented our awareness, representing to date the only practical method to describe injury biomechanics. However, the extent of the problem continues to raise serious concerns. Purpose: To advance our understanding of the causal pathways leading to ACL injury with a large-scale reconstruction of 3-dimensional (3D) whole-body joint kinematics of injuries that occurred to male elite soccer players, as well as to compare the joint angle time course among situational patterns. Study Design: Descriptive laboratory study. Methods: A total of 33 consecutive noncontact and indirect contact ACL injuries that occurred in 6 national and 2 international professional leagues (seasons 2020-2021 to 2022-2023 until December 2022) were analyzed: (1) multiview noncoaxial television images were inspected; (2) multiple camera views were taken from 400 ms before the initial ground contact to 200 ms after the injury frame; (3) a size-matched pitch was modeled and used to calibrate cameras; (4) a 3D skeletal model was adjusted to fit the player's pose in each frame/view; and (5) poses were interpolated, and Euler joint angles were extracted. Results: The authors reconstructed the 3D lower limb joint kinematic curves preceding and during ACL injuries in 33 cases; notably, a sudden external (up to 5°) and then internal knee rotation was observed after the initial contact and before the injury frame. The overall kinematics at injury were knee moderately flexed (45.9°± 21.7°), abducted (4.3°± 5.1°), and externally rotated (3.0°± 6.4°); trunk shallowly flexed (17.4°± 12.5°) and rotated and tilted toward the injured side; and hip flexed (32.0°± 18.7°), abducted (31.1°± 12.0°), and slightly internally rotated (6.6°± 12.2°). Variable behaviors were observed at the ankle level. Conclusion: Via reconstruction of the sequence of whole-body joint motion leading to injury, we confirmed the accepted gross biomechanics (dynamic valgus trend). This study significantly enriches the current knowledge on multiplanar kinematic features (transverse and coronal plane rotations). Furthermore, it was shown that ACL injuries in male professional soccer players manifest through distinct biomechanical footprints related to the concurrent game situation. Clinical Relevance: Interventions aimed at reducing ACL injuries in soccer should consider that environmental features (ie, situational patterns) affect injury mechanics.

Full-body kinematics and head stabilisation strategies during walking in patients with chronic unilateral and bilateral vestibulopathy

Chronic imbalance is a frequent and limiting symptom of patients with chronic unilateral and bilateral vestibulopathy. A full-body kinematic analysis of the movement of patients with vestibulopathy would provide a better understanding of the impact of the pathology on dynamic tasks such as walking. Therefore, this study aimed to investigate the global body movement during walking, its variability (assessed with the GaitSD), and the strategies to stabilise the head (assessed with the head Anchoring Index). The full-body motion capture data of 10 patients with bilateral vestibulopathy (BV), 10 patients with unilateral vestibulopathy (UV), and 10 healthy subjects (HS) walking at several speeds (slow, comfortable, and fast) were analysed in this prospective cohort study. We observed only a few significant differences between groups in parts of the gait cycle (shoulder abduction–adduction, pelvis rotation, and hip flexion–extension) during the analysis of kinematic curves. Only BV patients had significantly higher gait variability (GaitSD) for all three walking speeds. Head stabilisation strategies depended on the plan of motion and walking speed condition, but BV and UV patients tended to stabilise their head in relation to the trunk and HS tended to stabilise their head in space. These results suggest that GaitSD could be a relevant biomarker of chronic instability in BV and that the head Anchoring Index tends to confirm clinical observations of abnormal head-trunk dynamics in patients with vestibulopathy while walking.

Improved markerless gait kinematics measurement using a biomechanically-aware algorithm with subject-specific geometric modeling

Despite the advancements in developing markerless gait analysis systems, they still demonstrate lower accuracy compared to gold-standard systems. Hence, in this research, a novel approach is presented to improve the lower limb kinematics accuracy in markerless gait analysis. This approach refines the 3D lower-limb skeletons obtained by AI-based pose estimation algorithms in a subject-specific geometric manner, preserves skeleton links’ length, benefits from gait phases information that adds biomechanical awareness to the algorithm, and utilizes an embedded trajectory smoothing. Validation of the proposed method shows that it reduces 12.6–43.5 % of root mean square error (RMSE) and significantly improves kinematic curves’ similarity to the gold-standard ones. Results also prove the feasibility of more accurate lower limb kinematics calculation using a single (2.02–7.57° RMSE) or dual RGB-D camera (1.66–7.25° RMSE). Development of such algorithms could result in requirement of fewer cameras that deliver comparable or even superior measurement accuracy compared to multi-camera approaches.

SIMULATION OF A WELL JET PUMP WORKING PROCESS

A mathematical model of the movement of the working flow in the flow part of the jet pump was developed based on the use of a radial function of a complex variable with a shifted leakage center. According to the accepted model, the working fluid radially asymmetrically exits from the displaced leakage center in all directions. The distance to the center of the leak has an inverse effect on the rate of spread of the working fluid. The offset turn of the radial function allows you to take into account the misalignment of the working nozzle and the mixing chamber due to poor manufacturing of jet pump parts. The vector of the complex potential with a shifted origin is defined as the difference of vectors whose origin is at the center of coordinates, and the endpoints characterize the initial and final positions of the shifted function. Using the equation of the potential of velocities and the stream function, the relationship for the complex potential of the plane-radial and spatial working flow with one-way and two-way displacement of the leakage center is obtained. The kinematic picture of the movement of the working medium is determined by a spatial hydrodynamic grid formed by equipotential surfaces and flow surfaces of leakage functions, which has the form of orthogonally placed coaxial spheres and radial meridional planes. The leakage displacement determines the deviation of the axis of the working nozzle from the axis of the displacement chamber of the jet pump. It is established that the velocity profiles of the radial flow with a displaced leak lose their similarity and the series of kinematic curves cannot be replaced by a single dimensionless dependence that would determine the flow kinematics regardless of the distance between the leak point and the inlet cross- section of the mixing chamber of the jet pump. The displacement of the leakage center has an inverse effect on the radial flow rate and decreases with increasing distance to the mixing chamber. As the value of the leakage displacement increases, the asymmetry of the velocity profile increases and its unevenness increases. Superimposition of the obtained characteristic function of the asymmetric radial flow and the vortex function of the complex variable allows to determine the structure of the mixed flow equation when simulating the rotation process of the jet pump in the well.

Exploring Teslasuit's Potential in Detecting Sequential Slip-Induced Kinematic Changes among Healthy Young Adults.

This study aimed to assess whether the Teslasuit, a wearable motion-sensing technology, could detect subtle changes in gait following slip perturbations comparable to an infrared motion capture system. A total of 12 participants wore Teslasuits equipped with inertial measurement units (IMUs) and reflective markers. The experiments were conducted using the Motek GRAIL system, which allowed for accurate timing of slip perturbations during heel strikes. The data from Teslasuit and camera systems were analyzed using statistical parameter mapping (SPM) to compare gait patterns from the two systems and before and after slip. We found significant changes in ankle angles and moments before and after slip perturbations. We also found that step width significantly increased after slip perturbations (p = 0.03) and total double support time significantly decreased after slip (p = 0.01). However, we found that initial double support time significantly increased after slip (p = 0.01). However, there were no significant differences observed between the Teslasuit and motion capture systems in terms of kinematic curves for ankle, knee, and hip movements. The Teslasuit showed promise as an alternative to camera-based motion capture systems for assessing ankle, knee, and hip kinematics during slips. However, some limitations were noted, including kinematics magnitude differences between the two systems. The findings of this study contribute to the understanding of gait adaptations due to sequential slips and potential use of Teslasuit for fall prevention strategies, such as perturbation training.

Navigated functional alignment total knee arthroplasty achieves reliable, reproducible and accurate results with high patient satisfaction

PurposeThe decision on which technique to perform a total knee arthroplasty (TKA) has become more complicated over the last decade. Perceived limitations of mechanical alignment (MA) and kinematic alignment (KA) have led to the development of the functional alignment (FA) philosophy. This study aims to report the 2-year results of an initial patient cohort in terms of revision rate, PROMs and complications for Computer Aided Surgery (CAS) Navigated FA TKA.MethodsThis paper reports a single surgeon’s outcomes of 165 consecutive CAS FA TKAs. The final follow-up was 24 months. Pre-operative and post-operative patient-reported outcome measures, WOMAC and KSS, and intra-operative CAS data, including alignment, kinematic curves, and gaps, are reported. Stress kinematic curves were analysed for correlation with CAS final alignment and CAS final alignment with radiographic long-leg alignment. Pre- and post-operative CPAK and knee phenotypes were recorded. Three different types of prostheses from two manufacturers were used, and outcomes were compared. Soft tissue releases, revision and complication data are also reported.ResultsMean pre-operative WOMAC was 48.8 and 1.2 at the time of the final follow-up. KSS was 48.8 and 93.7, respectively. Pre- and post-operative range of motion was 118.6° and 120.1°, respectively. Pre-operative and final kinematic curve prediction had an accuracy of 91.8%. CAS data pre-operative stress alignment and final alignment strongly correlate in extension and flexion, r = 0.926 and 0.856, p < 0.001. No statistical outcome difference was detected between the types of prostheses. 14.5% of patients required soft tissue release, with the lateral release (50%) and posterior capsule (29%) being the most common.ConclusionCAS FA TKA in this cohort proved to be a predictable, reliable, and reproducible technique with acceptable short-term revision rates and high PROMs. FA can account for extremes in individual patient bony morphology and achieve desired gap and kinematic targets with soft tissue releases required in only 14.5% of patients.Level of evidenceIV (retrospective case series review).

An analytical model to quantify the impact of the propagation of uncertainty in knee joint angle computation

ABSTRACT Joint kinematics are typically described using Cardan angles or the attitude vector and its projection on the joint axes. Whichever the notation used, the uncertainties present in gait measurements affect the computed kinematics, especially for the knee joint. One notation – the attitude vector – enables the derivation of an analytical model of the propagation of uncertainty. Thus, the objective of this study was to derive this analytical model and assess the propagation of uncertainty in knee joint angle computation. Multi-session gait data acquired from one asymptomatic adult participant was used as reference data (experimental mean curve and standard deviations). Findings showed that an input uncertainty of 5° in the attitude vector and joint axes parameters matched experimental standard deviations. Taking each uncertainty independently, the cross-talk effect could result from uncertainty in the orientation of either the attitude vector (intrinsic variability) or the first joint axis (extrinsic variability). We concluded that the model successfully estimated the propagation of input uncertainties on joint angles and enabled an investigation of how that propagation occurred. The analytical model could be used to a priori estimate the standard deviations of experimental kinematics curves based on expected intrinsic and extrinsic uncertainties.

Kinematic Evaluation of the Sagittal Posture during Walking in Healthy Subjects by 3D Motion Analysis Using DB-Total Protocol.

Posture can be evaluated by clinical and instrumental methods. Three-dimensional motion analysis is the gold standard for the static and dynamic postural assessment. Conventional stereophotogrammetric protocols are used to assess the posture of pelvis, hip, knee, ankle, trunk (considered as a single segment) and rarely head and upper limbs during walking. A few studies also analyzed the multi-segmental trunk and whole-body kinematics. Aim of our study was to evaluate the sagittal spine and the whole-body during walking in healthy subjects by 3D motion analysis using a new marker set. Fourteen healthy subjects were assessed by 3D-Stereophotogrammetry using the DB-Total protocol. Excursion Range, Absolute Excursion Range, Average, intra-subject Coefficient of Variation (CV) and inter-subject Standard Deviation Average (SD Average) of eighteen new kinematic parameters related to sagittal spine and whole-body posture were calculated. The analysis of the DB-Total parameters showed a high intra-subject (CV < 50%) and a high inter-subject (SD Average < 1) repeatability for the most of them. Kinematic curves and new additional values were reported. The present study introduced new postural values characterizing the sagittal spinal and whole-body alignment of healthy subjects during walking. DB-Total parameters may be useful for understanding multi-segmental body biomechanics and as a benchmark for pathological patterns.

A Structural Design of a Child Seat Based on Morphological Elements and Ergonomics.

In order to improve the safety and comfort of child seat structural design, this paper combines ergonomics and morphological elements to analyze the structural design of child seat and establish a crash model. Moreover, the obtained kinematic response and injury curves are compared with the corresponding actual tested kinematic response and injury parameters to analyze the biomechanics of child occupant injury, the injury characteristics of child occupants in frontal and side collisions, and the evaluation criteria for head, neck, and chest injuries. In addition, this paper combines the intelligent design method to design a safety seat that meets the needs of children. The results show that the structural design method of child seat based on morphological elements and ergonomics proposed in this paper can play an important role in the design of child seat.

Altered Multisegment Ankle and Foot Kinematics During Gait in Patients With Hypermobile Ehlers-Danlos Syndrome/Hypermobility Spectrum Disorder: A Case-Control Study.

Ankle-foot problems have a considerable impact on daily functioning in patients with hypermobile Ehlers-Danlos syndrome and hypermobility spectrum disorder (hEDS/HSD). Therefore, the objective of this study was to identify alterations in multisegment ankle and foot kinematics during gait and to assess foot function and pain in these patients. Twenty-three women with hEDS/HSD and 23 healthy controls participated in this 3-dimensional gait analysis. Multisegment ankle and foot kinematics were collected using the Ghent Foot Model and analyzed with Statistical Parametric Mapping. Foot function and pain were assessed using visual analog scale scores, the Margolis Pain Diagram, and the Foot Function Index. Levels of pain and foot dysfunction were significantly higher in subjects with hEDS/HSD (P < 0.001). Kinematic curve analyses provide evidence for a hypermobile first ray, represented by a significantly increased eversion position of the medial forefoot during stance phase (P < 0.001) in subjects with hEDS/HSD compared to controls. In addition, significantly more dorsiflexion was found in the medial and lateral forefoot and the rearfoot (P < 0.001). At the midfoot, an increased plantar flexion (P < 0.001) and at the level of the hallux a decreased dorsiflexion (P = 0.037) and increased inversion (P < 0.001) and abduction (P = 0.016) were found in subjects with hEDS/HSD. This study is the first to apply a multisegment foot model during gait in hEDS/HSD, which confirms the characteristic hypermobility throughout the foot, especially the hypermobile first ray.

The Influence of the Shoe over the Medial Foot Arch and the Lower Limbs Kinematics in Toddlers.

Objective To evaluate the biomechanical behavior of the medial longitudinal arch (MLA) of the foot and the kinematic parameters of the lower limbs with biomimetic footwear (BF) and non-biomimetic (NB1, NB2, NB3 and NB4) footwear in children at the beginning of the gait acquisition phase. Methods Four toddlers were evaluated at the beginning of the gait acquisition phase under the following conditions: walking barefoot, ambulation with BF and NB1, NB2, NB3 and NB4 footwear in hard floor. BF is described as biomimetic because of its property of emulating natural and irregular floors through a dynamic internal insole. The MLA and kinematics of the hip, knee, and ankle during gait were evaluated by three-dimensional motion analysis system. The similarity between the kinematic curves of barefoot and footwear conditions was analyzed by root mean square error (RMSE). Results The use of BF presented the highest magnitude of MLA and the greatest difference in relation to barefoot condition (higher RMSE). The BF showed less difference in the kinematics of the knee and ankle joints during gait when compared to barefoot condition (lower RMSE). NB2 footwear presented hip kinematics more similar to barefoot condition (lower RMSE). Conclusion Biomimetics footwear and NB2 shoes (both with wider forefoot region) generated smaller differences in lower limbs compared to barefoot. In addition, the MLA was higher in the BF, probably because different design from other shoes.

Healthy Knee Kinematic Phenotypes Identification Based on a Clustering Data Analysis

The purpose of this study is to identify healthy phenotypes in knee kinematics based on clustering data analysis. Our analysis uses the 3D knee kinematics curves, namely, flexion/extension, abduction/adduction, and tibial internal/external rotation, measured via a KneeKG™ system during a gait task. We investigated two data representation approaches that are based on the joint analysis of the three dimensions. The first is a global approach that is considered a concatenation of the kinematic data without any dimensionality reduction. The second is a local approach that is considered a set of 69 biomechanical parameters of interest extracted from the 3D kinematic curves. The data representations are followed by a clustering process, based on the BIRCH (balanced iterative reducing and clustering using hierarchies) discriminant model, to separate 3D knee kinematics into homogeneous groups or clusters. Phenotypes were obtained by averaging those groups. We validated the clusters using inter-cluster correlation and statistical hypothesis tests. The simulation results showed that the global approach is more efficient, and it allows the identification of three descriptive 3D kinematic phenotypes within a healthy knee population.

Obstacle Capability of an Air-Ground Amphibious Reconnaissance Robot with a Planetary Wheel-Leg Type Structure.

According to the requirements of the reconnaissance robot for the ability to adapt to a complex environment and the in-depth study of the obstacle climbing mechanisms, a planetary wheel-leg-combined mechanism capable of adapting to complex terrains is proposed. According to the proposed planetary wheel-leg-combined mechanism, the land part of the air-ground amphibious reconnaissance robot is designed. Considering the obstacle and fast marching performance, four groups of combined wheel-leg mechanisms are adopted in the land bank. Under the action of three kinds of obstacles, the stability and the movement ability of the robot are analyzed by using the static method. The parameter model of the reconnaissance robot is built by a virtual prototype dynamics software MSC.ADMAS. The kinematic characteristic curves of each component and the whole prototype are obtained, which provides a theoretical basis for the design and numerical calculation of the robot structure. Finally, the climbing ability tests of the reconnaissance robot prototype verify the reliability and practicability of the body structure of the reconnaissance robot.

Experimental visualization of two-phase flow inside a real-size piston of a crosshead-type marine engine

ABSTRACT The oscillating cooling method is one of the most effective cooling solutions to improve the piston cooling ability for diesel engines. Most of the experimental studies were focused on the simplified model, and few were based on the actual complex piston cooling cavities. To give a better insight into the flow mechanism inside the actual cavities, a flow visualization test rig was built based on a real-size piston model with a stroke of 1550 mm and a cylinder diameter of 350 mm. The model replicates the piston and cooling cavities of a typical low-speed two-stroke crosshead marine engine MAN B&W 6S35ME. The test rig ensures that the coolant supply mode, the coolant flow path, and the kinematic curve of the piston head are consistent with the real machine. The piston model is an exact replica of the original scale made of PC material. A high-speed camera was used to capture the transient flow patterns of the gas-liquid two-phase flow inside the cooling cavities during the reciprocating motion of the whole stroke. More accurate boundary conditions are thus provided for the numerical simulation method, which significantly improves the accuracy of previous simulations under the same research topic. Analysis of the piston’s oscillatory cooling method is beneficial to optimizing the thermal management of engines in the future.

Analysis Choices Impact Movement Evaluation: A Multi-Aspect Inferential Method Applied to Kinematic Curves of Vertical Hops in Knee-Injured and Asymptomatic Persons.

Three-dimensional human motion analysis provides in-depth understanding in order to optimize sports performance or rehabilitation following disease or injury. Recent developments of statistical methods for functional data allow for novel ways to analyze often complex biomechanical data. Even so, for such methods as well as for traditional well-established statistical methods, the interpretations of the results may be influenced by analysis choices made prior to the analysis. We evaluated the consequences of three such choices when comparing one-leg vertical hop (OLVH) performance in individuals who had ruptured their anterior cruciate ligament (ACL), to that of asymptomatic controls, and also athletes. Kinematic data were analyzed using a statistical approach for functional data, targeting entire curve data. This was done not only for one joint at a time but also for multiple lower limb joints and movement planes simultaneously using a multi-aspect methodology, testing for group differences while also accounting for covariates. We present the results of when an individual representative curve out of three available was either: (1) a mean curve (Mean), (2) a curve from the highest hop (Max), or (3) a curve describing the variability (Var), as a representation of performance stability. We also evaluated choice of sample leg comparison; e.g., ACL-injured leg compared to either the dominant or non-dominant leg of asymptomatic groups. Finally, we explored potential outcome effects of different combinations of included joints. There were slightly more pronounced group differences when using Mean compared to Max, while the specifics of the observed differences depended on the outcome variable. For Var there were less significant group differences. Generally, there were more disparities throughout the hop movement when comparing the injured leg to the dominant leg of controls, resulting in e.g., group differences for trunk and ankle kinematics, for both Mean and Max. When the injured leg was instead compared to the non-dominant leg of controls, there were trunk, hip and knee joint differences. For a more stringent comparison, we suggest considering to compare the injured leg to the non-dominant leg. Finally, the multiple-joint analyses were coherent with the single-joint analyses. The direct effects of analysis choices can be explored interactively by the reader in the Supplementary Material. To summarize, the choices definitively have an impact on the interpretation of a hop test results commonly used in rehabilitation following knee injuries. We therefore strongly recommend well-documented methodological analysis choices with regards to comparisons and representative values of the measures of interests.

Restoration of Joint Inclination in Total Knee Arthroplasty Offers Little Improvement in Joint Kinematics in Neutrally Aligned Extremities.

Kinematically aligned total knee replacements have been shown to better restore physiological kinematics than mechanical alignment and also offer good postoperative satisfaction. The purpose of this study is to evaluate the extent to which an inclined joint line in a kinematically aligned knee can alter the postoperative kinematics. A multi-body dynamic simulation was used to identify kinematic changes in the joint. To accurately compare mechanical alignment, kinematic alignment and a natural knee, a “standard” patient with neutral alignment of the lower extremities was selected for modeling from a joint database. The arthroplasty models in this study were implanted with a single conventional cruciate-retaining prosthesis. Each model was subjected to a flexion movement and the anteroposterior translation of the femoral condyles was collected for kinematic analysis. The results showed that the mechanical alignment model underwent typical paradoxical anterior translation of the femoral condyles. Incorporating an inclined joint line in the model did not prevent the paradoxical anterior translation, but a 3° varus joint line in the kinematic alignment model could reduce the peak value of this motion by about 1 mm. Moreover, the inclined joint line did not restore the motion curve back to within the range of the kinematic curve of the natural knee. The results of this study suggest that an inclined joint line, as in the kinematic alignment model, can slightly suppress paradoxical anterior translation of the femoral condyles, but cannot restore kinematic motions similar to the physiological knee. This finding implies that prostheses intended to be used for kinematic alignment should be designed to optimize knee kinematics with the intention of restoring a physiological motion curve.

The use of Horizon graphs to visualize bilateral biomechanical time-series of multiple joints

Movement analysis provides a vast amount of data, which, frequently, are not used in the clinical decision-making process. For example, traditional gait data visualization is based on a time-based display of joint angles, but part of the information is lost when these time-series are averaged across different gait strides. Horizon graph is a data display method that increases the density of time-series data by horizontally dividing and layering multiple filled line graphs. This higher data density increases the amount of information displayed in the same graph and, consequently, enables visual data comparisons between multiple time series. Horizon graph of kinematic data allows displaying several cycles of different joints and their respective continuous symmetry ratio between sides. The aim of this work is to introduce the Horizon graph as a method to analyze kinematic gait data and help to characterize its symmetry. Examples of Horizon graph application to running is offered. Horizon graph may prove to be a useful clinical tool to visualize kinematic time-series and facilitate their clinical interpretation.•Continuous gait time series is a powerful tool for clinical analysis.•Horizon graph, higher data density graph, increases the information displayed.•Horizon graph is a clinical tool to visualize kinematic curves.

Multi-class classification of biomechanical data: A functional LDA approach based on multi-class penalized functional PLS

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cycle, etc.). Since kinematic curves are measured in the same sample of individuals performing different activities, they are a clear example of functional data with repeated measures. On the other hand, the sample curves are observed with noise. Then, a roughness penalty might be necessary in order to provide a smooth estimation of the discriminant functions, which would make them more interpretable. Moreover, because of the infinite dimension of functional data, a reduction dimension technique should be considered. To solve these problems, we propose a multi-class approach for penalized functional partial least squares (FPLS) regression. Then linear discriminant analysis (LDA) will be performed on the estimated FPLS components. This methodology is motivated by two case studies. The first study considers the linear acceleration recorded every two seconds in 30 subjects, related to three different activities (walking, climbing stairs and down stairs). The second study works with the triaxial angular rotation, for each joint, in 51 children when they completed a cycle walking under three conditions (walking, carrying a backpack and pulling a trolley). A simulation study is also developed for comparing the performance of the proposed functional LDA with respect to the corresponding multivariate and non-penalized approaches.

Research of quality indicators of gears with a complex non-evolvent profile of the teeth flanks

The article substantiates the relevance of the study of gears with a complex non-involute profile of the side surfaces of the teeth, which in some applications have advantages over involute gears and are devoid of some of their drawbacks associated with quality indicators.A technique for obtaining mating surfaces of the teeth of non-invasive gears as envelopes of the specified surfaces of the teeth of tools is described. A scheme for forming pairs of non-involute gears, from which a gearing can be composed, is proposed. It is shown that to obtain the mating surfaces of the teeth of two non-involute gears, two tool rails can be used with the profiles of the side surfaces of the teeth opposite to each other. As a nonlinear profile of the tooth lateral surface of the tool rail, some part of one of the simulated flat kinematic curves is considered. A description of the program is given, which allows you to calculate the geometric characteristics of the shaped profiles of the gear pair wheels, visualize the shaping process, and also determine the quality indicators of the gearing. Thus, the prerequisites were created for choosing from the resulting geometric modeling of the curve field of such tooth profiles of the tools, which would provide the most rational combination of the tooth profiles of the gears processed by them and the required quality parameters of the gear teeth. The results of the study of the pressure ratio between the teeth of a gear and the overlap ratio of gears when choosing the shape of the tooth profiles are presented. A series of numerical experiments for gearing, formed by pairs of tool rails with different profiles of the side surfaces of the teeth - straight, convex and concave, as well as convex-concave were performed. It is shown that non-involute gearing can have large reduced radii of curvature (and consequently smaller pressure coefficients) at the points of tangency of the profiles compared to involute gearing with a slight increase or decrease in the gearing overlap ratio. The most preferable is the variant of the rails with convex and concave tooth profiles, which provides the best values of both quality indicators of the engagement.