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This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group $SE(3)$ S E ( 3 ) . Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.

The classical local impact laws of Newton and Poisson are able to capture the behaviour observed in single-impact collisions in many situations. However, in the case of collisions with multiple impacts, the simultaneous enforcement of local impact laws does not reproduce essential features of the physical process, such as propagation effects. The aim of this work is to broaden the applicability of the classical Newton impact law to problems involving multiple impacts by assuming instantaneous local impact times and a rigid behaviour of the bodies in contact. The proposed method is implemented as an extension of the nonsmooth generalized- $$\alpha $$ method. In order to model events involving multiple impacts, a sequence of impact problems is defined on a vanishing time interval and the active set of each velocity-level sub-problem is redefined in such a way that closed contacts with zero pre-impact velocity are considered inactive. This simple redefinition allows us to deal successfully with many situations involving multiple impacts, by generating a sequence of impact problems which is amenable to be modelled by the simultaneous enforcement of classical impact laws. Additionally, the methodology fits well under the algorithmic structure of the nonsmooth generalized- $$\alpha $$ scheme or any scheme dealing with linear complementary problems at velocity level. Several examples are analyzed in order to assess the performance of the method and to discuss its main features.

Trajectory tracking problems for underactuated manipulators represent an actual research topic, which is sustained by the interest in a lighter and faster automatic class of mechanical systems, bringing some benefits as lower energy consumption, higher productivity and a more convenient human–machine interaction. This work presents a feedforward design method, which is based on the inverse dynamics of underactuated manipulators. To achieve this aim, an optimal control problem is formulated based on a direct multiple shooting method and the mechanical model is formulated according to the nonlinear finite element approach. Based on the proposed formulation, a bounded solution of the inverse dynamics problem can be achieved. The main contributions of this work are: (1) the development of an alternative formulation for the trajectory tracking problem of underactuated manipulators; (2) a parallel computation method for the inverse dynamics of underactuated manipulators; (3) a comparison/validation with the direct transcription method and the stable inversion method. A planar underactuated manipulator with one passive joint is considered as an illustrative example, but the methodology is general and could be applied to more complex systems, e.g. with flexible bodies, with parallel kinematics and in 3D.

Lightweight and flexible robots offer an interesting answer to industrial needs for safety and efficiency. The control of such systems should be able to deal properly with the flexible behavior in the links and the joints. In this paper, a feedforward control action is computed by solving the inverse dynamics of the system. Flexibility in the system is modeled using finite elements formulated in the local frame. The inverse problem is then solved using a constrained optimization formulation. This local frame representation reduces the nonlinearity in the equations of motion and improves the convergence of the numerical scheme. To illustrate the method, numerical examples of a serial and a parallel 3D robot are shown.

The aim of this work is the development of a robust and accurate time integrator for the simulation of the dynamics of multibody systems composed of rigid and/or flexible bodies subject to frictionless contacts and impacts. The integrator is built upon a previously developed nonsmooth generalized-α scheme time integrator which was able to deal well with nonsmooth dynamical problems avoiding any constraint drift phenomena and capturing vibration effects without introducing too much numerical dissipation. However, when dealing with problems involving nonlinear bilateral constraints and/or flexible elements, it is necessary to adopt small time-step sizes to ensure the convergence of the numerical scheme. In order to tackle these problems more efficiently, a fully decoupled version of the nonsmooth generalized-α method is proposed in this work, avoiding these inconveniences. Several examples are considered to assess its accuracy and robustness. Fil: Cosimo, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Galvez, Javier. University Of Liège, Department Of Aerospace And Mechan; Bélgica Fil: Cavalieri, Federico José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Brüls, Olivier. University Of Liège, Department Of Aerospace And Mechan; Bélgica

Given the potential consequences of falls among older adults, a major challenge is to identify people at risk before the first event. In this context, gait parameters have been suggested as markers of fall risk. To examine, among older people, the prospective relationship between gait patterns assessed in comfortable and challenging walking conditions, and future fall(s). A total of 105 adults older than 65 years, living independently at home and without a recent fall history were included in a 2-year, longitudinal, observational study. All underwent physical and functional assessment. Gait speed, stride length, frequency, symmetry and regularity and Minimum Toe Clearance (MTC) were recorded in comfortable (CW), fast (FW) and dual task walking (DTW) conditions. Gait parameter changes occurring between CW and FW and between CW and DTW were calculated and expressed in percent. DTW cost was calculated as the change of DTW relative to CW. Fall events were recorded using fall diaries. Comparisons according to fall occurrence were performed by means of univariate analysis and multivariate binary logistic regression analysis. Two-year follow-up was available for 96 participants, of whom 35 (36.5%) fell at least once. Comparative analysis showed that future fallers had shorter FW stride length and higher symmetry DTW cost than non-fallers (p

The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. The nonsmooth generalized-α (NSGA) scheme is adopted, which imposes bilateral and unilateral constraints both at position and velocity levels avoiding drift phenomena. This scheme can be implemented in a general purpose simulation code with limited modifications of pre-existing elements. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the NSGA scheme within the context of a general finite element framework. This example has already been studied by many authors who generally adopted a model with a minimal set of coordinates and small rotations. It is shown that good results are obtained using a general purpose finite element code for multibody dynamics, in which the equations of motion are assembled automatically and large rotations are easily taken into account. In addition, comparing results between different models of the woodpecker toy, the importance of modeling large rotations and the horizontal displacement of the woodpecker's sleeve is emphasized.

This work investigates the dynamics of spherical rigid bodies subject to multiple impact collisions and sliding friction. The contact problem is solved with a mixed dual formulation based on an augmented Lagrangian technique. The equations of motion and the multiple impact collisions are solved in the frame of the nonsmooth generalized-\(\alpha \) time integrator scheme. In order to consider the mechanical and geometrical properties of the spheres, a rigid body formulation with translational and rotational degrees of freedom is implemented. Finally, in order to assess the numerical performance of the proposed methodology, a multiple impact collisions motion of three spheres over a rigid plane is studied.

In this work, the authors present two different multibody models for static analysis of airborne wind turbines (AWTs) cables. These wind turbines are composed of three main components: a buoyant blimp with a standard turbine rotor fixed within its shell, tethers connecting the system to earth ground, and a rotating base station. The tethers (or cables) are critical parts due to their multiple functions (aerostat control and power electric transmission, among others). The models/procedure presented in this article allows determining equilibrium points of the space tethers, which can be used for starting a global dynamic analysis of the complete system. An accurate initializing solution is essential for the convergence of the successive numeric non-linear aeroelastic analysis of AWTs. On these bases, the authors present two models of increasing complexity: i) a lumped-parameter model formulated in \(\mathbb {R}^{3}\), and ii) a finite element model based on a kinematically exact formulation of beams in SE(3). Both models are validated comparing results against well-documented problems (e.g. the elastic catenary).

We present a new node-to-face frictional contact element for the simulation of the nonsmooth dynamics of systems composed of rigid and flexible bodies connected by kinematic joints. The equations of motion are integrated using a nonsmooth generalized-α time integration scheme and the frictional contact problem is formulated using a mixed approach, based on an augmented Lagrangian technique and a Coulomb friction law. The numerical results are independent of any user-defined penalty parameter for the normal or tangential component of the forces and, the bilateral and the unilateral constraints are exactly fulfilled both at position and velocity levels. Finally, the robustness and the performance of the proposed algorithm are demonstrated by solving several numerical examples of nonsmooth mechanical systems involving frictional contact. Fil: Galvez, Javier. Université de Liège; Bélgica Fil: Cavalieri, Federico José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina Fil: Cosimo, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina. Université de Liège; Bélgica Fil: Brüls, Olivier. Université de Liège; Bélgica Fil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina

A tightness of the posterior structures of the throwing shoulder has been hypothesised to be associated with injuries and pain because of alterations of the scapular kinematics and muscular imbalances. The aims of this study were to identify the clinical and biomechanical profile of symptomatic and asymptomatic overhead athletes with a tight shoulder and to evaluate the efficiency of a self-applied stretching program. Twenty male overhead athletes were recruited. Half of them reported a painful shoulder at the beginning of the study. For four weeks, the volunteers performed daily stretching exercises. Before and after the stretching program, gleno-humeral mobility, scapular kinematics, rotator muscles strength and pain were evaluated. Before stretching, the main difference between the groups was more impingement syndrome and rotator cuff tendon lesion positive tests in the symptomatic group (

The trophy position is a coaching cue for the tennis serve that usually corresponds to the racquet high point (RHP) during the preparatory action for the stroke. Mastering this position and its time of occurrence seems essential in overarm movements like in the tennis serve. Clinicians and coaches have a real interest in understanding the trophy position and its evolution during the development of the elite players at different ages. A 3D motion system was used to measure the kinematics of the serve. A group of high-level tennis players were selected for three different age groups: 8 adults (ITN 1), 8 teenagers (ITN 3) and 8 children (ITN 5-6). Results show a modified pattern sequence of the tennis serve between children and adult players. RHP appears earlier relative to impact for children (-0.54 ± 0.10 s) than for adults (-0.36 ± 0.11 s) and teenagers (-0.33 ± 0.05 s) (p = 0.007). At RHP, children present lower trunk transverse plane rotation (p < 0.003) and higher shoulder external rotation (p < 0.003). These positions for the child players may represent an increased risk of shoulder and trunk injury than for older players and contribute to a lower racquet resultant velocity at impact.

The aim of the study was to assess the activation profile of scapular stabilizing muscles in dyskinetic asymptomatic people.This is a noninterventional observational study. Two groups of 20 people were included in the study. The first group involved asymptomatic athletes with scapular dyskinesis. The second one included athletes without scapular dysfunction. Muscle activation of upper trapezius, lower trapezius, and serratus anterior were recorded by a surface electromyography during shoulder flexion and shoulder abduction, in unloaded and loaded conditions.A significant increase of the activity of the upper trapezius (between 23% and 31%) and a significant decrease of the activity of the lower trapezius (between 32% and 65%) were observed in the dyskinetic group in comparison with the nondyskinetic group in asymptomatic athletes. A significant increase between 17% and 31% of the activity of the serratus anterior was also observed in dyskinetic people. Likewise, a significant increase approximately 24%-61% and 23%-70% was noted respectively in upper trapezius/lower trapezius and upper trapezius/serratus anterior ratio's in the dyskinetic group.An alteration of periscapular muscular activation exists in dyskinetic asymptomatic people. Future studies will be needed to know whether those alterations increase the risk of shoulder injuries.

Background Even though most studies normalize the surface EMG signal of the gastrocnemius muscle using a single position of maximum voluntary isometric contraction (MVIC), several studies tend to indicate that several positions are in fact needed to obtain a maximal voluntary activation (MVA) for most of the subjects. However, no combination of positions has already been described. Research question A combination of MVIC positions to normalize the EMG signal of the gastrocnemius muscle is investigated. the influence of using several positions on the reproducibility of the normalization process is evaluated. Methods Twenty healthy volunteers (45 % female – 55 % male, 25.4 years (SD 4.3), 72.6 kg (SD 13.9), 1.78 m (SD 0.12)) were recruited. Six positions for MVIC were compared and the effect of several normalization combinations on a functional task (gait) was evaluated. Results Several positions are needed to obtain at least 90 % of the MVA for 90 % of the volunteers even though the use of a single well-chosen position (unipodal standing position with knee fully extended and ankle fully plantar-flexed) will lead to no statistically significant differences of the gait evaluation during stance phase. For each position, five repetitions of the MVIC are recommended to obtain a valid MVA. Significance This study confirms that using several MVIC positions is recommended when possible to normalize the gastrocnemius muscle EMG signal. However, in the situation of a patient where limited MVIC attempts are possible, using a single well-chosen position should not significantly influence the amplitude and the reproducibility of the measures.

This paper studies the dynamics of tape springs which are characterised by a highly geometrical nonlinear behaviour including buckling, the formation of folds and hysteresis. An experimental set-up is designed to capture these complex nonlinear phenomena. The experimental data are acquired by the means of a 3D motion analysis system combined with a synchronised force plate. Deployment tests show that the motion can be divided into three phases characterised by different types of folds, frequencies of oscillation and damping behaviours. Furthermore, the reproducibility quality of the dynamic and quasi-static results is validated by performing a large number of tests. In parallel, a nonlinear finite element model is developed. The required model parameters are identified based on simple experimental tests such as static deformed configurations and small amplitude vibration tests. In the end, the model proves to be well correlated with the experimental results in opposite sense bending, while in equal sense, both the experimental set-up and the numerical model are particularly sensitive to the initial conditions.

Structural optimization of flexible multibody systems (MBS) is a challenging design problem which has received increased attention in the last decade. The weakly coupled method is a powerful method to solve this design problem as it transforms the underlying dynamic response optimization problem into a static response optimization problem subject to multiple load cases. These load cases can be conveniently defined using the so-called Equivalent Static Load (ESL) method. With the usual ESL method, ESLs are defined at a component-level assuming that each component is isolated from the rest of the system. Thus, this method cannot account for design functions involving the global response of the system but it is restricted to optimization problems that are solely formulated in terms of local responses within the components. In order to get rid of this restriction, a system-wise extension of the ESL method is proposed. It is shown that the solutions of the equivalent static optimization problem and of the initial MBS optimization problem are equivalent and that the ESL formulation naturally leads to a weakly coupled solution algorithm. Standard benchmarks exemplify the proposed method.

For coaches, the most common and easiest way to analyse the tennis serve is to refer to their own vision. However, human vision is insufficient to observe high-speed motion with great precision. With the improvement of technology, it is now possible to study the gesture from a quantitative point of view. The quantitative evaluation of the tennis serve focuses on the kinematics and kinetics of the player but also on the stroke result, which includes the ball speed and the ball trajectory. This review aims to highlight the current tools available for players, coaches, medical staffs and biomechanical researchers, to evaluate the tennis serve. This overview will provide information to the player’s entourage in order to choose the right tools depending on their specific purposes. All of these tools can be applied in performance improvement and injury prevention.

For human-robot cooperation, intrinsic safety approaches aim at reducing the energy involved in the motion of the robotic system and at increasing the system compliance in order to reduce the risk of injury in case of an unexpected collision. Robots based on lightweight and inherently flexible links exhibit attractive features in this context but the control of their motion then leads to a tremendous challenge. This paper presents a novel trajectory planning method for 3D robots which aims at improving the tracking accuracy despite the link flexibility.

Inverse dynamics methods are presented and analyzed in detail for the feedforward control of underactuated manipulators. Thereby, two different exact strategies are discussed: the standard stable inversion method, which relies on the formulation of a two-point boundary value problem, and an alternative optimization problem formulation, which does not require any boundary conditions. This paper proves that the solution of the optimization problem converges to the solution of the boundary value problem in the limit case where the lengths of the pre- and post-actuation phases tend to infinity. It is also shown that both strategies can be directly based on the DAE form of the equations of motion, so that there is no need to explicitly derive the input-output normal form, and standard multibody modeling codes can be used. The developments are illustrated using examples of manipulators with passive and compliant joints.

This paper reviews the state-of-the-art methods to perform structural optimization of flexible mechanisms. These methods are based on a system-based approach, i.e. the formulation of the design problem incorporates the time response of the mechanism that is obtained from a dynamic simulation of the flexible multibody system. The system-based approach aims at considering as precisely as possible the effects of nonlinear dynamic loading under various operating conditions. Also, the optimization process enhances most existing studies which are limited to (quasi-) static or frequency domain loading conditions. This paper briefly introduces flexible multibody system dynamics and structural optimization techniques. Afterwards, the two main methods, named the weakly and the fully coupled methods, that couple both disciplines are presented in details and the influence of the multibody system formalism is analyzed. The advantages and drawbacks of both methods are discussed and future possible research areas are mentioned.

International audience; Multibody models are often coupled with other domains in order to enlarge the scope of computer-based analysis. In particular, modeling multibody systems (MBSs) in interaction with granular media is of great interest for industrial process such as railway track maintenance, handling of aggregates, etc. This paper presents a strong coupling methodology for unifying a multibody formalism using relative coordinates and a discrete element method based on non-smooth contact dynamics (NSCD). Both tree-like and closed-loop MBSs are considered. For the latter, the coordinate partitioning techniques is applied in the NSCD framework. The proposed approach is applied on the slider-crank mechanism benchmark. Results are in very good agreement with results obtained with other techniques from the literature. Finally, a multibody model of a tamping machine is coupled to a discrete element model of railway ballast in order to analyse efficiency of track maintenance. This application demonstrates that the dynamics of the machine must be taken into account so as to estimate the performance of the maintenance process correctly.

The aim of this work is to extend the finite element multibody dynamics approach to problems involving frictional contacts and impacts. Since rigid bodies and joints involve bilateral constraints, it is important to avoid any drift phenomenon. Therefore, the nonsmooth generalized-α method is used, which imposes the constraints both at position and at velocity levels. Its low intrusiveness allows one to reuse an existing library of elements without major modifications. The study of the woodpecker toy dynamics sets up a good example to show the capabilities of the nonsmooth generalized-α within the context of a general finite element framework. This example has already been studied by many authors who generally adopt a model with a minimal set of coordinates and small rotations. We show that using a finite element approach, the equations of motion can be assembled automatically, and large rotations can be easily considered.

Scapular dyskinesis is observed in 61% of overhead athletes (Burn et al., 2016). For most of them, it remains asymptomatic. However, scapular dyskinesis is considered a risk factor for shoulder injury by some authors (Clarsen et al., 2014). The aim of this study is to explore the effectiveness of kinesiotaping in modifying scapular kinematics and peri-scapular muscle activity in dyskinetic athletes. The 3-dimensional position and orientation of the scapula as well as the activation of upper trapezius, lower trapezius and serratus anterior were recorded in twenty asymptomatic athletes during shoulder movements (flexion and abduction), in loaded and unloaded conditions and in three circumstances (standard, kinesiotaping 1, kinesiotaping 2). A significant decrease between 9 and 12% in upper trapezius activity was observed with kinesiotaping 1 and 2. Lower trapezius activity was slightly increased with kinesiotaping 1 while it was significantly decreased about 15-20% with kinesiotaping 2. No change was observed in serratus anterior activity, for either kinesiotaping 1 or 2. Considering scapular kinematics, both kinesiotaping 1 and 2 significantly increased posterior tilt and upward rotation. External rotation was decreased with kinesiotaping 2, in comparison to standard condition. Kinesiotaping, and especially taping 1, seems to be an effective method for changing periscapular muscle activity and scapular kinematics.

To meet the demand of a player’s entourage (e.g., coaches and medical staff), it is important for the biomechanics specialist to perform repeatable measures. To the best of our knowledge, to date, it has not been demonstrated whether similar results are obtained between two sessions of testing or between laboratory and field sport kinematic protocols with regard to the tennis serve. This study had two primary aims. First, the inter-session repeatability of biomechanical variables of a tennis serve was evaluated. Second, the differences between laboratory and field evaluations were studied. Thirteen national tennis players (ITN 3) performed the same 28 markers’ set laboratory test twice two weeks apart, and other thirteen national players (ITN 3) performed two 4 markers’ set tests both in the laboratory and on an official tennis court one week apart. A 3D motion system was used to measure lower-limb, pelvis, trunk, dominant arm and racket kinematics. A force plate was used to evaluate kinetics of legs’ drive in the laboratory. A personal method based on a point scoring system was developed to evaluate the ball landing location accuracy. We observed that the majority of the studied variables were acceptable for excellent relative reliability for the inter-session analysis. We also showed that the impact of the laboratory versus field context on the player’s serve was limited

Gait patterns of healthy aging are needed to allow a comparison with pathological situations. However, little data is available. To present gait pattern of healthy older specially selected to be “healthy walkers”. Fifty-seven older people benefited from a geriatric assessment including clinical and functional evaluations to include only those without gait disorders. Gait data were simultaneously recorded using a tri-axial accelerometer placed on the waist and four 3D position markers placed on the feet at the level of the heel and the toe. Volunteers walked at comfortable self-selected speed (CW), fast self-selected speed (FW), and finally in dual task walking condition (DTW). The extracted gait parameters were: gait speed, stride length, stride frequency, regularity and symmetry, swing, stance and double support time and ratio and minimum toe clearance. Gait speed and stride length were normalized to the right leg length. Fifty-seven older people with a mean age of 69.7 ± 4.2 years old (range from 65 to 82 years) were included. Data were analyzed according to the gender and according to the age (

This paper describes the development of a complete methodology for the aeroservoelastic modelling of horizontal axis wind turbines at the conceptual design stage. The methodology is based on the implementation of unsteady aerodynamic modelling, advanced description of the control system and nonlinear finite element calculations in the Samcef Wind Turbines design package. The aerodynamic modelling is carried out by means of fast techniques, such as the blade element method and the unsteady vortex lattice method, including a free wake model. The complete model also includes a description of a doubly fed induction generator and its control system for variable speed operation. The Samcef Wind Turbines software features a nonlinear finite element solver with multi-body dynamics capability. The full methodology is used to perform complete aeroservoelastic simulations of a realistic 2 MW wind turbine model. The interaction between the three components of the approach is carefully analysed and presented here.

In order to increase the production of power on small satellites, solar panels are commonly deployed and, in some cases, reflectors are added to improve the concentration factor on solar cells. In this work, reflectors are deployed by the means of compliant mechanisms known as tape springs. Their attractive characteristics are, among others, their passive behaviour, their self-locking capacity, their elastic deformations and their robustness. However, their mechanical behaviour is highly nonlinear and requires thorough analyses in order to develop predictive numerical models. It is shown here through parametric studies that the nonlinear behaviour of a tape spring is mainly governed by its geometry. Thus, for each specific application, its dimensions can be determined in order to minimise two critical features: the maximum stress affecting the structure and the maximum motion amplitude during deployment. In this paper, an optimisation procedure is proposed to meet these requirements.

Summary The equivalent static load (ESL) method is a powerful approach to solve dynamic response structural optimization problems. The method transforms the dynamic response optimization into a static response optimization under multiple load cases. The ESL cases are defined based on the transient analysis response whereupon all the standard techniques of static response optimization can be used. In the last decade, the ESL method has been applied to perform the structural optimization of flexible components of mechanical systems modeled as multibody systems (MBS). The ESL evaluation strongly depends on the adopted formulation to describe the MBS and has been initially derived based on a floating frame of reference formulation. In this paper, we propose a method to derive the ESL adapted to a nonlinear finite element approach based on a Lie group formalism for two main reasons. Firstly, the finite element approach is completely general to analyze complex MBS and is suitable to perform more advanced optimization problems like topology optimization. Secondly, the selected Lie group formalism leads to a formulation of the equations of motion in the local frame, which turns out to be a strong practical advantage for the ESL evaluation. Examples are provided to validate the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

The proper orthogonal decomposition (POD) is an efficient model-order reduction (MOR) technique for linear problems in computational sciences, recently gaining popularity in electromagnetics. However, its efficiency has been shown to considerably degrade for nonlinear problems. In this paper, we propose a method to reduce nonlinear magnetodynamic problems by combining POD with an interpolation on manifolds, which interpolates the reduced bases to efficiently construct the appropriate reduced model. This method, new in electromagnetics, is applied on an inductor-core system and showed good results compared with the classical MOR approaches, e.g., direct POD reduction and a standard interpolation of pre-computed reduced bases (i.e., Lagrange interpolation).

Based on a formulation on the special Euclidean group S E ( 3 ) , a geometrically exact thin-walled beam with an arbitrary open cross-section is proposed to deal with the finite deformation and rotation issues. The beam strains are based on a kinematic assumption where warping deformation and Wagner effects are included such that the nonlinear behavior of a thin-walled beam is predicted accurately, particular under large torsion. To reduce the nonlinearity of rigid motion, static and dynamic equations are derived in the S E ( 3 ) framework based on the local frame approach. As the value of the iteration matrix, including the Jacobian matrix of inertial and internal forces, is invariable under arbitrary rigid motion, the number of updates required during the computation process decreases sharply, which drastically improves the computational efficiency. Furthermore, the isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBS) basis functions, which promotes the integration of computer-aided design (CAD) and computer-aided engineering (CAE), is adopted to interpolate the displacement, rotation, and warping fields separately. The interpolated strain measures satisfy the objectivity by removing the rigid motion of the reference point. To obtain the symmetric Jacobian matrix of internal forces, the linearization operation is conducted based on the previously converged configuration. A Lie group S E ( 3 ) extension of the generalized- α time integration method is utilized to solve the equations of motion for thin-walled beams. Finally, the proposed formulation is successfully tested and validated in several static and dynamic numerical examples.

Optimal Control methods are increasingly used for the control of multibody systems (MBS). This work analyzes the different dynamic formulations and compare their performances in solving Optimal Control Problem. The focus is on minimal coordinates and the derivation of the dynamics via the recursive methods for tree-like MBS (i.e., the so-called Newton-Euler and Order-N recursive algorithms). The different formulations are introduced and their derivations are discussed. A benchmark case study (i.e., a 3D series manipulator balancing an inverted pendulum) is modeled and a series of manipulation tasks (movement of the end effector in the 3D space) are performed. The OCP is formulated and solved with the help of the CasADi software while the dynamic formulations are generated by the Robotran software. Results show that the implicit and semi-explicit formulations derived via the Newton-Euler recursive algorithm lead to faster computation of the OCP than the explicit formulations. This is explained by a more compact expression for the implicit dynamics. However, a lower number of high local minima is observed with the explicit formulations for the most extreme robot manipulations.

Future robots will rely more than today on high precision, better energy efficiency and safe handling (e.g. human-machine interaction). An inevitable step in the development of new robots is therefore the improvement of existing mechanisms, since better sensors and algorithms do not satisfy the demands alone. During the last three decades, Parallel Redundant Mechanisms (PRM) came more into the focus of research, as they are advantageous in terms of singularity avoidance, fast movements and energy efficiency. Subsequently, yet another technology - the Variable Impedance Actuator (VIA) - emerged which proposes to change its inherent stiffness allowing an adaptation to its environment and to handle for example dynamic movements or shock absorptions. This work aims to create a new mechanism where a stiffness and position control for 2 degrees of freedom (DOF) is achieved by 3 actuators with flexible elements. It is thus a combination of the PRM and VIA, while taking advantage of both technologies but asking for a more sophisticated mathematical description. Practical implementation is intended for a humanoid ankle mechanism. Kinetostatic and stiffness models are derived and incorporated into the simulation of the mechanism. The simulations show that improvements in terms of singularity removal and dexterity are achieved. Furthermore, the adaptation of human like gait performances is presented.

Multibody systems are often modeled as interconnected multibody and modal components: multibody components, such as rigid bodies, beams, plates, and kinematic joints, are treated via multibody techniques whereas the modal components are handled via a modal reduction approach based on the small strain assumption. In this work, the problem is formulated within the framework of the motion formalism. The kinematic description involves simple, straightforward frame transformations and leads naturally to consistent deformation measures. Derivatives are expressed in local frames, which results in the remarkable property that the tangent matrices are independent of the position and orientation of the modal component with respect to an inertia frame. This implies a reduced level of geometric non-linearity as compared to standard description. In particular, geometrically non-linear problems can be solved with the tangent matrices of the reference configuration, without re-evaluation and re-factorization.Copyright © 2018 by ASME

International audience; The simulation of flexible multibody systems with unilateral contact conditions and impacts requires advanced numerical methods. The nonsmooth generalized-α method was developed in order to combine an accurate and second-order time discretization of the smoother part of the dynamics and a consistent but first-order time discretization of the impulsive contributions. Compared to the Moreau-Jean scheme, this approach improves the quality of the numerical solution especially for the representation of the vibrating response of flexible bodies. It entirely relies on the formal definition of a so-called smooth motion that captures a non-impulsive part of the total nonsmooth motion. This definition may account for some contributions of the bilateral constraints and/or of the active unilateral constraints at velocity or at acceleration level. This chapter shows that the formulation of the constraints strongly influences the numerical stability and the computational cost of the method. A strategy to enforce the bilateral and unilateral constraints simultaneously at position, velocity and acceleration levels is also established with a careful formulation of the activation criteria based on augmented Lagrange mul-tipliers. In the special case of smooth systems, a comparison is made with more standard solvers for differential-algebraic equations. The properties of this method are demonstrated using illustrative numerical examples of smooth and nonsmooth mechanical systems.

The paper concerns a detailed comparison between two optimization methods that are used to perform the structural optimization of flexible components within a multibody system (MBS) simulation. The dynamic analysis of flexible MBS is based on a nonlinear finite element formulation. The first method is a weakly coupled method, which reformulates the dynamic response optimization problem in a two-level approach. First, a rigid or flexible MBS simulation is performed, and second, each component is optimized independently using a quasi-static approach in which a series of equivalent static load (ESL) cases obtained from the MBS simulation are applied to the respective components. The second method, the fully coupled method, performs the dynamic response optimization using the time response obtained directly from the flexible MBS simulation. Here, an original procedure is proposed to evaluate the ESL from a nonlinear finite element simulation, contrasting with the floating reference frame formulation exploited in the standard ESL method. Several numerical examples are provided to support our position. It is shown that the fully coupled method is more general and accommodates all types of constraints at the price of a more complex optimization process.

The structural optimization of the components in multibody systems is performed using a fully coupled optimization method. The design's predicted response is obtained from a flexible multibody system simulation under various service conditions. In this way, the resulting optimization process enhances most existing studies which are limited to weakly coupled (quasi-) static or frequency domain loading conditions. A level set description of the component geometry is used to formulate a generalized shape optimization problem which is solved via efficient gradient-based optimization methods. Gradients of cost and constraint functions are obtained from a sensitivity analysis which is revisited in order to facilitate its implementation and retain its computational efficiency. The optimizations of a slider-crank mechanism and a 2-dof robot are provided to exemplify the procedure.

Compliant mechanisms such as tape springs are often used on satellites to deploy appendices, e.g. solar panels, antennas, telescopes and solar sails. Their main advantage comes from the fact that their motion results from the elastic deformation of structural components and the absence of actuators or external energy sources. The mechanical behaviour of a tape spring is intrinsically complex and nonlinear involving buckling, hysteresis and self-locking phenomena. In the majority of the previous works, dynamic simulations were performed without any physical representation of the structural damping. These simulations could be successfully achieved because of the presence of numerical damping in the transient solver. However, in this case, the dynamic response turns out to be quite sensitive to the amount of numerical dissipation, so that the predictive capabilities of the model are questionable. In this work based on numerical case studies, we show that the dynamic simulation of a tape spring can be made less sensitive to numerical parameters when the structural dissipation is taken into account.

1. Comparisons of multiple-impact laws for multibody systems: Moreau’s law, binary impacts, and the LZB approach -- 2. Variational analysis of inequality impact laws for perfect unilateral constraints -- 3. Periodic motions of coupled impact oscillators -- 4. Mathematical aspects of vibro-impact problems -- 5. Nonsmooth modal analysis: from the discrete to the continuous settings -- 6. Variational and numerical methods based on the bipotential and application to the frictional contact -- 7. Passive control of differential algebraic inclusions - General method and a simple example -- 8. Experimental validation of torsional controllers for drilling systems -- 9. On the constraints formulation in the nonsmooth generalized-α method -- 10. On solving contact problems with Coulomb friction: formulations and numerical comparisons.

Integrated optimization techniques for mechatronic systems aim at designing simultaneously the trajectory, the control system and the mechanical structure in order to minimize a performance index. The key advantage of such an integrated approach is the capability to search in a wide design space, to account for many dynamic couplings in an early design stage and to avoid simplifying assumptions which would induce a suboptimal design. This work considers that technique for robotic manipulators with flexible links. It is known that a flexible multibody system is often non-minimum phase, here, no restriction is imposed to avoid it. This allows a free choice of the optimization process to select a lighter weight controlled system. Furthermore, the amplitudes of the non-actuated degrees-of-freedom should be reduced in order to limit bodies deformation. The mechanical model is derived using a nonlinear finite element method, which is a useful approach to represent systems with elastic bodies. An optimal control problem is considered to perform that integrated analysis and its time dicretization relies the direct transcription method.

Movement patterns during landing have been suggested to be related to injury risk. The purpose of this study was to determine the inter-session reliability of kinematic variables and ground reaction forces during landing in a population of male recreational athletes after a counter movement jump. Both unipodal and bipodal landings were evaluated. Furthermore, the possibility to improve landing reliability with a verbal instruction was also studied. Twenty-four male volunteers with no history of lower extremity trauma were randomly assigned to two groups (with and without verbal landing instruction). An optoelectronic 3D system and force plates were used to measure the lower limb joint angles and the ground reaction forces during landing. Intraclass correlation values show moderate to excellent inter-session reliability for the bipodal task (ICC average: 0.80, range: 0.46-0.97) and poor to excellent reliability for the unipodal task (ICC average:0.75, range: 0.20-0.95). However, large standard errors of measurement values at the ankle joint at impact (27.6 ± 11.5°) and for the vertical ground reaction forces (394 ± 1091 N) show that some variables may not be usable in practice. The verbal instruction had a negative effect on the reliability of unipodal landing but improved the reliability of bipodal landing. These findings show that the reliability of a landing task is influenced by its motor complexity as well as the instruction given to the subject.

Normalization of the electromyography (EMG) signal is often performed relatively to maximal voluntary activations (MVA) obtained during maximum isometric voluntary contraction (MVIC). The first aim was to provide an inter-session reproducible protocol to normalize the signal of eight shoulder muscles. The protocol should also lead to a level of activation >90% of MVA for >90% of the volunteers. The second aim was to evaluate the influence of the method used to extract the MVA from the EMG envelope on the normalized EMG signal. Thirteen volunteers performed 12 MVICs twice (one week interval). Several time constants (100ms to 2s) were compared when extracting the MVA from the EMG envelope. The EMG activity was also acquired during an arm elevation. Our results show that a combination of nine MVIC tests was required to meet our requirements including reproducibility. Both the number of MVIC tests and the size of the time constant influence the normalized EMG signal during the dynamic activity (variations up to 15%). A time constant of 1s was a good compromise to extract the MVA. These findings are valuable to improve the reproducibility of EMG signal normalization.

The inverse dynamics simulation of the musculoskeletal system is a common method to understand and analyse human motion. The ground reaction forces can be accurately estimated by experimental measurements using force platforms. However, the number of steps is limited by the number of force platforms available in the laboratory. Several numerical methods have been proposed to estimate the ground reaction forces without force platforms, i.e., solely based on kinematic data combined with a model of the foot-ground contact. The purpose of this work is to provide a more efficient method, using a unilaterally constrained model of the foot at the center of pressure to compute the ground reaction forces. The proposed model does not require any data related with the compliance of the foot-ground contact and is kept as simple as possible. The indeterminacy in the force estimation is handled using a least square approach with filtering. The relative root mean square error (rRMSE) between the numerical estimations and experimental measurements are 4.1% for the vertical component of the ground reaction forces (GRF), 11.2% for the anterior component and 5.3% for the ground reaction moment (GRM) in the sagittal plane.

Populations considered for shoulder analysis are often composed of various ratios of men and women. It is consequently hypothesized that gender has no significant effect on the joint kinematic. However, the literature reports, for the shoulder, differences in the range of motion between genders. The specific influence of gender on the scapulo-thoracic kinematics has not been studied yet. The dominant shoulder of two populations of men and women composed of 11 subjects each were evaluated in three dimensions for three distinct motions: flexion in the sagittal plane, abduction in the frontal plane and gleno-humeral internal/external rotation with the arm abducted at 90°. Posture, kinematics and range of motion were studied separately. For flexion and abduction and with regard to the scapular kinematic, external rotation was significantly larger for women than men. The differences were of at least 5° at 120° of humeral elevation. Upward rotations were identical. Women also showed larger average active humero-thoracic range of motion. The mean differences were of 13°, 7°, 12° and 5° for abduction, flexion, internal rotation and external rotation, respectively. No difference was observed between the scapular resting positions of both populations. The observed differences concerning both the scapular and humeral patterns would indicate that the shoulder behaviour of men and women should not be expected to be similar.

Background The contralateral shoulder is often used as a reference when evaluating a pathologic shoulder. However, the literature provides contradictory results regarding the symmetry of the scapular pattern in a healthy population. We assume that several factors including gender and type of motion may influence the bilateral symmetry of the scapulae. Materials and methods The dominant and nondominant shoulders of 2 populations of men and women comprising 11 subjects each were evaluated for 3 distinct motions: flexion in the sagittal plane, abduction in the frontal plane, and glenohumeral internal/external rotation with the arm abducted at 90°. Posture, kinematics, and range of motion were studied separately. Results Asymmetries are observed for motions performed in the frontal and sagittal plane but not for internal/external rotation with the arm abducted at 90°. For both male and female populations, multiplanar asymmetries are observed and the dominant scapula has a larger upward rotation. The asymmetries mainly originate in the scapula’s kinematics and not in its original posture. Conclusion Small but significant asymmetries exist between the dominant and nondominant shoulders in terms of kinematics. One should be aware of these differences when using the contralateral shoulder as a reference.

Generalized-α methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order systems in linear spaces. Recently, they were extended to constrained systems in flexible multibody dynamics that have a configuration space with Lie group structure. In the present paper, the convergence of these Lie group methods is analysed by a coupled one-step error recursion for differential and algebraic solution components. It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction. Numerical tests for a benchmark problem from the literature illustrate the results of the theoretical investigations. Fil: Arnold, Martín Alejandro. Martin Luther University Halle-wittenberg; Alemania Fil: Brüls, Olivier. Université de Liège; Bélgica Fil: Cardona, Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina