Hip joint stabilization vs. propulsion and resistance in individuals with transfemoral amputation

Joint moments and joint powers are widely used to determine the effects of rehabilitation programs and prosthetic components (e.g., alignments). A complementary analysis of the 3D angle between joint moment and joint angular velocity has been proposed to assess whether the joints are predominantly driven or stabilized.

Gravity-induced coronal plane joint moments in adolescent idiopathic scoliosis

Background Adolescent Idiopathic Scoliosis is the most common type of spinal deformity, and whilst the risk of progression appears to be biomechanically mediated (larger deformities are more likely to progress), the detailed biomechanical mechanisms driving progression are not well understood. Gravitational forces in the upright position are the primary sustained loads experienced by the spine. In scoliosis they are asymmetrical, generating moments about the spinal joints which may promote asymmetrical growth and deformity progression. Using 3D imaging modalities to estimate segmental torso masses allows the gravitational loading on the scoliotic spine to be determined. The resulting distribution of joint moments aids understanding of the mechanics of scoliosis progression. Methods Existing low-dose CT scans were used to estimate torso segment masses and joint moments for 20 female scoliosis patients. Intervertebral joint moments at each vertebral level were found by summing the moments of each of the torso segment masses above the required joint. Results The patients’ mean age was 15.3 years (SD 2.3; range 11.9 – 22.3 years); mean thoracic major Cobb angle 52° (SD 5.9°; range 42°-63°) and mean weight 57.5 kg (SD 11.5 kg; range 41 – 84.7 kg). Joint moments of up to 7 Nm were estimated at the apical level. No significant correlation was found between the patients’ major Cobb angles and apical joint moments. Conclusions Patients with larger Cobb angles do not necessarily have higher joint moments, and curve shape is an important determinant of joint moment distribution. These findings may help to explain the variations in progression between individual patients. This study suggests that substantial corrective forces are required of either internal instrumentation or orthoses to effectively counter the gravity-induced moments acting to deform the spinal joints of idiopathic scoliosis patients.

The effect of lumbar support on the trunk muscle activity and pelvic tilt in a passenger vehicle car seat

In order to gain a competitive edge in the market, automotive manufacturers and automotive seat suppliers have identified seat ergonomics for further development to improve overall vehicle comfort. Adjustable lumbar support devices have been offered since long as comfort systems in either a 2-way or 4-way adjustable configuration, although their effect on lumbar strain is not well documented. The effect of a lumbar support on posture and muscular strain, and therefore the relationship between discomfort and comfort device parameter settings, requires clarification. The aim of this paper is to study the effect of a 4-way lumbar support on lower trunk and pelvis muscle activity, pelvic tilt and spine curvature during a car seating activity. 10 healthy subjects (5 m/f; age 19-39) performed a seating activity in a passenger vehicle with seven different static lumbar support positions. The lumbar support was tested in 3 different height positions in relation to the seatback surface centreline (high, centre, low), each having 2 depths positions (lumbar prominence). An extra depth position was added for the centre position. Posture data were collected using a VICON MX motion capture system and NORAXON DTS goniometers and inclinometer. A rigid-body model of an adjustable car seat with four-way adjustable lumbar support was constructed in UGS Siemens NX and connected to a musculoskeletal model of a seated-human, modelled in AnyBody. Wireless electromyography (EMG) was used to calibrate the musculoskeletal model and assess the relationship between (a) muscular strain and lumbar prominence (normal to seatback surface) respective to the lumbar height (alongside seatback surface), (b) hip joint moment and lumbar prominence (normal to seatback surface) respective to lumbar height (alongside seatback surface) and (c) pelvic tilt and lumbar prominence (normal to seatback surface) respective to the lumbar height (alongside seatback surface). This study was based on the assumption that the musculoskeletal human model was seated at the correct R-Point (SgRP), determined via the occupant packaging toolkit in the JACK digital human model. The effect of the interaction between the driver/car-seat has been investigated for factors resulting from the presence and adjustment of a 4-way lumbar support. The results obtained show that various seat adjustments, and driver’s lumbar supports can have complex influence on the muscle activation, joint forces and moments, all of which can affect the comfort perception of the driver. This study enables the automotive industry to optimise passenger vehicle seat development and design. It further more supports the evaluation of static postural and dynamic seat comfort in normal everyday driving tasks and can be applied for future car design to reduce investment and improve comfort.

Hip power analysis in individuals with transfemoral amputation: A different strategy different from stabilisation during gait stance

Introduction and Objectives Joint moments and joint powers during gait are widely used to determine the effects of rehabilitation programs as well as prosthetic fitting. Following the definition of power (dot product of joint moment and joint angular velocity) it has been previously proposed to analyse the 3D angle between both vectors, αMw. Basically, joint power is maximised when both vectors are parallel and cancelled when both vectors are orthogonal. In other words, αMw < 60° reveals a propulsion configuration (more than 50% of the moment contribute to positive power) while αMw > 120° reveals a resistance configuration (more than 50% of the moment contribute to negative power). A stabilisation configuration (less than 50% of the moment contribute to power) corresponds to 60° < αMw < 120°. Previous studies demonstrated that hip joints of able-bodied adults (AB) are mainly in a stabilisation configuration (αMw about 90°) during the stance phase of gait. [1, 2] Individuals with transfemoral amputation (TFA) need to maximise joint power at the hip while controlling the prosthetic knee during stance. Therefore, we tested the hypothesis that TFAs should adopt a strategy that is different from a continuous stabilisation. The objective of this study was to compute joint power and αMw for TFA and to compare them with AB. Methods Three trials of walking at self-selected speed were analysed for 8 TFAs (7 males and 1 female, 46±10 years old, 1.78±0.08 m 82±13 kg) and 8 ABs (males, 25±3 years old, 1.75±0.04, m 67±6 kg). The joint moments are computed from a motion analysis system (Qualisys, Goteborg, Sweden) and a multi-axial transducer (JR3, Woodland, USA) mounted above the prosthetic knee for TFAs and from a motion analysis system (Motion Analysis, Santa Rosa, USA) and force plates (Bertec, Columbus, USA) for ABs. The TFAs were fitted with an OPRA (Integrum, AB, Gothengurg, Sweden) osseointegrated implant system and their prosthetic designs include pneumatic, hydraulic and microprocessor knees. Previous studies showed that the inverse dynamics computed from the multi-axial transducer is the proper method considering the absorption at the foot and resistance at the knee. Results The peak of positive power at loading response (H1) was earlier and lower for TFA compared to AB. Although the joint power is lower, the 3D angle between joint moment and joint angular velocity, αMw, reveals an obvious propulsion configuration (mean αMw about 20°) for TFA compared to a stabilisation configuration (mean αMw about 70°) for AB. The peaks of negative power at midstance (H2) and of positive power at preswing / initial swing (H3) occurred later, lower and longer for TFA compared to AB. Again, the joint powers are lower for TFA but, in this case, αMw is almost comparable (with a time lag), demonstrating a stabilisation (almost a resistance for TFA, mean αMw about 120°) and a propulsion configuration, respectively. The swing phase is not analysed in the present study. Conclusion The analysis of hip joint power may indicate that TFAs demonstrated less propulsion and resistance than ABs during the stance phase of gait. This is true from a quantitative point of view. On the contrary, the 3D angle between joint moment and joint angular velocity, αMw, reveals that TFAs have a remarkable propulsion strategy at loading response and almost a resistance strategy at midstance while ABs adopted a stabilisation strategy. The propulsion configuration, with αMw close to 0°, seems to aim at maximising the positive joint power. The configuration close to resistance, with αMw far from 180°, might aim at unlocking the prosthetic knee before swing while minimising the negative power. This analysis of both joint power and 3D angle between the joint moment and the joint angular velocity provides complementary insights into the gait strategies of TFA that can be used to support evidence-based rehabilitation and fitting of prosthetic components.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition

This paper considers various asymptotic approximations in the near-integrated firstorder autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial condition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the continuous time approximation of Perron (1991). We assess how these alternative methods provide or not an adequate approximation to the finite-sample distribution of the least-squares estimator in a first-order autoregressive model. The results show that, when the initial condition is non-zero, Perron's (1991) continuous time approximation performs very well while the others only offer improvements when the initial condition is zero.

Apport d’une évaluation biomécanique 3D du genou dans la prise en charge orthopédique de patients ayant une rupture du ligament croisé antérieur

Parmi les blessures sportives reliées au genou, 20 % impliquent le ligament croisé antérieur (LCA). Le LCA étant le principal stabilisateur du genou, une lésion à cette structure engendre une importante instabilité articulaire influençant considérablement la fonction du genou. L’évaluation clinique actuelle des patients ayant une atteinte au LCA présente malheureusement des limitations importantes à la fois dans l’investigation de l’impact de la blessure et dans le processus diagnostic. Une évaluation biomécanique tridimensionnelle (3D) du genou pourrait s’avérer une avenue innovante afin de pallier à ces limitations. L’objectif général de la thèse est de démontrer la valeur ajoutée du domaine biomécanique dans (1) l’investigation de l’impact de la blessure sur la fonction articulaire du genou et dans (2) l’aide au diagnostic. Pour répondre aux objectifs de recherche un groupe de 29 patients ayant une rupture du LCA (ACLD) et un groupe contrôle de 15 participants sains ont pris part à une évaluation biomécanique 3D du genou lors de tâches de marche sur tapis roulant. L’évaluation des patrons biomécaniques 3D du genou a permis de démontrer que les patients ACLD adoptent un mécanisme compensatoire que nous avons intitulé pivot-shift avoidance gait. Cette adaptation biomécanique a pour objectif d’éviter de positionner le genou dans une condition susceptible de provoquer une instabilité antérolatérale du genou lors de la marche. Par la suite, une méthode de classification a été développée afin d’associer de manière automatique et objective des patrons biomécaniques 3D du genou soit au groupe ACLD ou au groupe contrôle. Pour cela, des paramètres ont été extraits des patrons biomécaniques en utilisant une décomposition en ondelettes et ont ensuite été classifiés par la méthode du plus proche voisin. Notre méthode de classification a obtenu un excellent niveau précision, de sensibilité et de spécificité atteignant respectivement 88%, 90% et 87%. Cette méthode a donc le potentiel de servir d’outil d’aide à la décision clinique. La présente thèse a démontré l’apport considérable d’une évaluation biomécanique 3D du genou dans la prise en charge orthopédique de patients présentant une rupture du LCA; plus spécifiquement dans l’investigation de l’impact de la blessure et dans l’aide au diagnostic.

Asymétries locomotrices réelles et perçues lors de différentes conditions de marche sur tapis roulant chez les personnes saines et hémiparétiques

L'asymétrie locomotrice chez les personnes hémiparétiques à la suite d'un accident vasculaire cérébral (AVC) est fréquemment observée en clinique. Les causes sous-jacentes à cette asymétrie et sa persistance malgré les interventions sont source de nombreuses interrogations. Ce projet avait donc pour objectif de développer de nouvelles connaissances sur les facteurs pouvant expliquer l'asymétrie locomotrice après un AVC. Les objectifs principaux étaient de 1) quantifier les moments et les niveaux d'effort musculaire des membres inférieurs lors de différentes conditions de marche sur le tapis roulant à double courroie (DC) afin de déterminer si ceux-ci sont explicatifs de l'asymétrie locomotrice, et de 2) quantifier la capacité de perception de l'asymétrie locomotrice des personnes saines et hémiparétiques. L’hypothèse générale était que l’asymétrie locomotrice est une stratégie utilisée par les personnes hémiparétiques pour symétriser ou limiter les niveaux d’effort musculaire, tels qu’évalués par le taux d'utilisation musculaire mécanique (TUM). Les résultats ont été présentés dans quatre articles (#2 à #5). La première étude a quantifié l'effet d'un protocole sur tapis roulant à DC visant à modifier l'asymétrie spatio-temporelle sur les moments musculaires aux membres inférieurs des personnes saines et hémiparétiques. Globalement, les résultats ont démontré que placer le membre inférieur parétique sur la courroie lente augmentait le moment fléchisseur plantaire (FP) parétique en post-adaptation et que cette augmentation était corrélée avec l'augmentation de la longueur de pas controlatérale. La deuxième étude a démontré que les personnes présentant de hauts niveaux d'effort dans les FP parétiques avaient une asymétrie des efforts dans leurs FP et extenseurs de hanche (EH) alors que le groupe avec de bas niveaux d'effort dans les FP avait des efforts symétriques. De plus, les deux groupes présentaient des moments FP asymétriques, mais cette asymétrie était reliée à l'asymétrie de forces résiduelles seulement chez ceux présentant de hauts niveaux d'effort. Cela suggère que la faiblesse musculaire joue un rôle important dans la réduction du moment FP parétique chez ceux avec de hauts niveaux d'effort alors que d'autres facteurs doivent être considérés pour expliquer l'asymétrie des moments à la marche des personnes avec de bas niveaux d'effort. La troisième étude a démontré que la symétrisation du patron de marche (temporelle ou spatiale) amenait des efforts musculaires élevés dans les FP parétiques, atteignant des niveaux moyens supérieurs à 85 %. La quatrième étude a évalué la capacité de perception de l'asymétrie locomotrice des personnes saines avec un protocole sur tapis roulant à DC et a démontré qu'elles percevaient leur patron de marche comme asymétrique lorsque leur ratio d'asymétrie temporelle atteignait le seuil de 1,05, avec une variabilité intra-individu faible, suggérant une bonne capacité de ces personnes à détecter l'asymétrie. Les résultats supplémentaires de cette thèse ont démontré que les personnes hémiparétiques percevaient mieux l'asymétrie temporelle que spatiale. En somme, ces résultats suggèrent que la force musculaire et les efforts musculaires des FP parétiques sont à considérer comme des facteurs explicatifs de l'asymétrie locomotrice des personnes hémiparétiques. D'autres études sont nécessaires pour statuer sur les capacités de perception de l'asymétrie locomotrice des personnes hémiparétiques.

Herramienta de detección y medición de las condiciones de riesgo laborales asociadas a la presentación de los desórdenes por trauma acumulativo en hombro

El movimiento en el complejo articular de hombro, al igual que en las demás partes del cuerpo se realiza gracias a los sistemas óseo, articular y muscular. Cuando se presentan movimientos repetitivos, posturas y fuerzas en el lugar de trabajo al desarrollar las tareas, se pueden originar una serie de patologías profesionales en los trabajadores ocupacionalmente expuestos. Estas patologías no solamente se asocian a estos factores de riesgo, sino también, a una concepción inadecuada del diseño del puesto de trabajo en dónde los trabajadores desarrollan su actividad laboral. se pretende a través de este proyecto de investigación dar a conocer una herramienta de observación, detección de éstos, y medición tridimensional de los movimientos que puedan llegar a representar un riesgo, facilitando la recolección de datos de forma precisa y rápida, así como la apreciación de las condiciones de trabajo, por parte de los profesionales interesados en Salud Ocupacional.

Development of a continuum mechanics model of passive skeletal muscle

Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model.

Gait analysis of the hind limb in Labrador Retrievers with and without cranial cruciate ligament disease

Cranial cruciate ligament (CCL) deficiency is the leading cause of lameness affecting the stifle joints of large breed dogs, especially Labrador Retrievers. Although CCL disease has been studied extensively, its exact pathogenesis and the primary cause leading to CCL rupture remain controversial. However, weakening secondary to repetitive microtrauma is currently believed to cause the majority of CCL instabilities diagnosed in dogs. Techniques of gait analysis have become the most productive tools to investigate normal and pathological gait in human and veterinary subjects. The inverse dynamics analysis approach models the limb as a series of connected linkages and integrates morphometric data to yield information about the net joint moment, patterns of muscle power and joint reaction forces. The results of these studies have greatly advanced our understanding of the pathogenesis of joint diseases in humans. A muscular imbalance between the hamstring and quadriceps muscles has been suggested as a cause for anterior cruciate ligament rupture in female athletes. Based on these findings, neuromuscular training programs leading to a relative risk reduction of up to 80% has been designed. In spite of the cost and morbidity associated with CCL disease and its management, very few studies have focused on the inverse dynamics gait analysis of this condition in dogs. The general goals of this research were (1) to further define gait mechanism in Labrador Retrievers with and without CCL-deficiency, (2) to identify individual dogs that are susceptible to CCL disease, and (3) to characterize their gait. The mass, location of the center of mass (COM), and mass moment of inertia of hind limb segments were calculated using a noninvasive method based on computerized tomography of normal and CCL-deficient Labrador Retrievers. Regression models were developed to determine predictive equations to estimate body segment parameters on the basis of simple morphometric measurements, providing a basis for nonterminal studies of inverse dynamics of the hind limbs in Labrador Retrievers. Kinematic, ground reaction forces (GRF) and morphometric data were combined in an inverse dynamics approach to compute hock, stifle and hip net moments, powers and joint reaction forces (JRF) while trotting in normal, CCL-deficient or sound contralateral limbs. Reductions in joint moment, power, and loads observed in CCL-deficient limbs were interpreted as modifications adopted to reduce or avoid painful mobilization of the injured stifle joint. Lameness resulting from CCL disease affected predominantly reaction forces during the braking phase and the extension during push-off. Kinetics also identified a greater joint moment and power of the contralateral limbs compared with normal, particularly of the stifle extensor muscles group, which may correlate with the lameness observed, but also with the predisposition of contralateral limbs to CCL deficiency in dogs. For the first time, surface EMG patterns of major hind limb muscles during trotting gait of healthy Labrador Retrievers were characterized and compared with kinetic and kinematic data of the stifle joint. The use of surface EMG highlighted the co-contraction patterns of the muscles around the stifle joint, which were documented during transition periods between flexion and extension of the joint, but also during the flexion observed in the weight bearing phase. Identification of possible differences in EMG activation characteristics between healthy patients and dogs with or predisposed to orthopedic and neurological disease may help understanding the neuromuscular abnormality and gait mechanics of such disorders in the future. Conformation parameters, obtained from femoral and tibial radiographs, hind limb CT images, and dual-energy X-ray absorptiometry, of hind limbs predisposed to CCL deficiency were compared with the conformation parameters from hind limbs at low risk. A combination of tibial plateau angle and femoral anteversion angle measured on radiographs was determined optimal for discriminating predisposed and non-predisposed limbs for CCL disease in Labrador Retrievers using a receiver operating characteristic curve analysis method. In the future, the tibial plateau angle (TPA) and femoral anteversion angle (FAA) may be used to screen dogs suspected of being susceptible to CCL disease. Last, kinematics and kinetics across the hock, stifle and hip joints in Labrador Retrievers presumed to be at low risk based on their radiographic TPA and FAA were compared to gait data from dogs presumed to be predisposed to CCL disease for overground and treadmill trotting gait. For overground trials, extensor moment at the hock and energy generated around the hock and stifle joints were increased in predisposed limbs compared to non predisposed limbs. For treadmill trials, dogs qualified as predisposed to CCL disease held their stifle at a greater degree of flexion, extended their hock less, and generated more energy around the stifle joints while trotting on a treadmill compared with dogs at low risk. This characterization of the gait mechanics of Labrador Retrievers at low risk or predisposed to CCL disease may help developing and monitoring preventive exercise programs to decrease gastrocnemius dominance and strengthened the hamstring muscle group.

Effects of surgical joint destabilization on load sharing between ligamentous structures in the thoracic spine : a finite element investigation

Background: In vitro investigations have demonstrated the importance of the ribcage in stabilising the thoracic spine. Surgical alterations of the ribcage may change load-sharing patterns in the thoracic spine. Computer models are used in this study to explore the effect of surgical disruption of the rib-vertebrae connections on ligament load-sharing in the thoracic spine. Methods: A finite element model of a T7-8 motion segment, including the T8 rib, was developed using CT-derived spinal anatomy for the Visible Woman. Both the intact motion segment and the motion segment with four successive stages of destabilization (discectomy and removal of right costovertebral joint, right costotransverse joint and left costovertebral joint) were analysed for a 2000Nmm moment in flexion/extension, lateral bending and axial rotation. Joint rotational moments were compared with existing in vitro data and a detailed investigation of the load sharing between the posterior ligaments carried out. Findings: The simulated motion segment demonstrated acceptable agreement with in vitro data at all stages of destabilization. Under lateral bending and axial rotation, the costovertebral joints were of critical importance in resisting applied moments. In comparison to the intact joint, anterior destabilization increases the total moment contributed by the posterior ligaments. Interpretation: Surgical removal of the costovertebral joints may lead to excessive rotational motion in a spinal joint, increasing the risk of overload and damage to the remaining ligaments. The findings of this study are particularly relevant for surgical procedures involving rib head resection, such as some techniques for scoliosis deformity correction.

Errors in the knee joint forces and moments during gait depending on the foot and knee prosthetic components

Background Previously studies showed that inverse dynamics based on motion analysis and force-plate is inaccurate compared to direct measurements for individuals with transfemoral amputation (TFA). Indeed, direct measurements can appropriately take into account the absorption at the prosthetic foot and the resistance at the prosthetic knee. [1-3] However, these studies involved only a passive prosthetic knee. Aim The objective of the present study was to investigate if different types of prosthetic feet and knees can exhibit different levels of error in the knee joint forces and moments. Method Three trials of walking at self-selected speed were analysed for 9 TFAs (7 males and 2 females, 47±9 years old, 1.76±0.1 m 79±17 kg) with a motion analysis system (Qualisys, Goteborg, Sweden), force plates (Kitsler, Winterthur, Switzerland) and a multi-axial transducer (JR3, Woodland, USA) mounted above the prosthetic knee [1-17]. TFAs were all fitted with an osseointegrated implant system. The prostheses included different type of foot (N=5) and knee (N=3) components. The root mean square errors (RMSE) between direct measurements and the knee joint forces and moments estimated by inverse dynamics were computed for stance and swing phases of gait and expressed as a percentage of the measured amplitudes. A one-way Kruskal-Wallis ANOVA was performed (Statgraphics, Levallois-Perret, France) to analyse the effects of the prosthetic components on the RMSEs. Cross-effects and post-hoc tests were not analysed in this study. Results A significant effect (*) was found for the type of prosthetic foot on anterior-posterior force during swing (p=0.016), lateral-medial force during stance (p=0.009), adduction-abduction moment during stance (p=0.038), internal-external rotation moment during stance (p=0.014) and during swing (p=0.006), and flexion-extension moment during stance (p = 0.035). A significant effect (#) was found for the type of prosthetic knee on anterior-posterior force during swing (p=0.018) and adduction-abduction moment during stance (p=0.035). Discussion & Conclusion The RMSEs were larger during swing than during stance. It is because the errors on accelerations (as derived from motion analysis) become substantial with respect to the external loads. Thus, inverse dynamics during swing should be analysed with caution because the mean RMSEs are close to 50%. Conversely, there were fewer effects of the prosthetic components on RMSE during swing than during stance and, accordingly, fewer effects due to knees than feet. Thus, inverse dynamics during stance should be used with caution for comparison of different prosthetic components.

Static Balancing of Spring-loaded Planar Revolute-joint Linkages without Auxiliary Links

We present a method to statically balance a general treestructured,planar revolute-joint linkage loaded with linear springs or constant forces without using auxiliary links. The balancing methods currently documented in the literature use extra links; some do not apply when there are spring loads and some are restricted to only two-link serial chains. In our method, we suitably combine any non-zero-free-length load spring with another spring to result in an effective zero-free-length spring load. If a link has a single joint (with the parent link), we give a procedure to attach extra zero-free-length springs to it so that forces and moments are balanced for the link. Another consequence of this attachment is that the constraint force of the joint on the parent link becomes equivalent to a zero-free-length spring load. Hence, conceptually,for the parent link, the joint with its child is removed and replaced with the zero-free-length spring. This feature allows recursive application of this procedure from the end-branches of the tree down to the root, satisfying force and moment balance of all the links in the process. Furthermore, this method can easily be extended to the closed-loop revolute-joint linkages, which is also illustrated in the paper.

Inversion of moments to retrieve joint probabilities in quantum sequential measurements

A sequence of moments obtained from statistical trials encodes a classical probability distribution. However, it is well known that an incompatible set of moments arises in the quantum scenario, when correlation outcomes associated with measurements on spatially separated entangled states are considered. This feature, viz., the incompatibility of moments with a joint probability distribution, is reflected in the violation of Bell inequalities. Here, we focus on sequential measurements on a single quantum system and investigate if moments and joint probabilities are compatible with each other. By considering sequential measurement of a dichotomic dynamical observable at three different time intervals, we explicitly demonstrate that the moments and the probabilities are inconsistent with each other. Experimental results using a nuclear magnetic resonance system are reported here to corroborate these theoretical observations, viz., the incompatibility of the three-time joint probabilities with those extracted from the moment sequence when sequential measurements on a single-qubit system are considered.