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The paper considers the contactless transportation of space debris by means of an ion beam generated by an active spacecraft electrodynamic engine. The three-dimensional motion of a space debris object relative to its center of mass is studied. Space debris is assumed to be a dynamically symmetric cylindrical rigid body. The aim of the paper is to develop a control of the engine thrust, which ensures the stabilization of spatial oscillations of cylindrical space debris. A simplified mathematical model describing the motion of a dynamically symmetric rigid body in a Keplerian orbit is developed. For the case of a circular orbit, stationary motions relative to the center of mass are found. A feedback control law for the thrust of an electrodynamic engine creating an ion beam, which is aimed at stabilizing the space debris object in a stationary angular position, is proposed. The results of numerical research confirm the effectiveness of this control. The research results can be used in the preparation of space debris removal missions.

The research is aimed at the study and validation of an impact attenuator to be installed on roads. Its main function is to absorb the energy generated by an impact, therefore, the different regulations (national and international) are analyzed together with the materials that lead to reduce the severity of the accident. From this point, the best material is selected through a decision matrix under specific parameters, the design of the shape of the attenuator using a Pugh matrix ideal for the selection of completely new designs and the dynamic simulation is established to observe the behavior. The modeling of the attenuator geometry is created by engineering software and its geometry itself, it is designed in sections with mitigating elements among them. For the validation of the design, the one with the greatest capacity to dissipate energy is chosen, for this purpose, the behavior of the impact attenuator in the event of a vehicle crash is observed using finite element analysis software, defining simulation variables and varying geometry parameters, resulting after several simulations that the 0.8 mm thick impact attenuator design is the most suitable to reduce the crashing effect by reducing the kinetic energy of the rigid body by 92.72%.

Floating vertical axis wind turbines (VAWTs) have many advantages over floating horizontal axis wind turbines (HAWTs) at large scales in deep water; however, there are several key challenges to overcome as well. One of the challenges is accurate prediction of the dynamic motion and loads performance of a floating VAWT. A new semi-coupled aero-servo-hydro method is developed to assess dynamic responses of a floating VAWT by modeling the system as a 7-degree-of-freedom (7-DOF) model: the supporting platform is considered as a 6-DOF rigid body; the rotation of the rotor is considered as the 7th DOF. Aerodynamic, hydrodynamic, and mooring loads and control of the rotor speed are fully considered. This model can predict performance of floating VAWTs with reasonable fidelity according to validation with OrcaFlex through static and dynamic responses of a floating VAWT with Darrieus rotor operating on a new tension-leg platform (TLP). Being a reduced complexity model, the 7-DOF model can be efficiently applied to assess performance of the newly designed floating VAWT. This model is used to examine the relative contributions of aerodynamic and wave loads imparted to the floating system and the benefits of a three-bladed VAWT over a two-bladed VAWT through dynamic and fatigue analysis.

Aiming to simulate the experimentally observed three kinds of one-stepping characteristics in stick-slip piezoelectric actuators, i.e., backward motion, smooth motion, and sudden jump, a new dynamic model is proposed with consideration of the deformation of overall system. Being different from the existing dynamic models that consider the overall system as a rigid body, the stiffness coefficient and damping coefficient of the overall system are introduced in the newly proposed model. By adjusting the parameters according to the experimental conditions, these three kinds of characteristics are successfully simulated for the first time in this field. By comparison with the existing dynamic models of stick-slip piezoelectric actuators, the effectiveness, advancement, and necessity of the proposed dynamic model are demonstrated. This model is expected to be helpful for the structure design and performance prediction of stick-slip piezoelectric actuators.

Aircraft and helicopter often fly above open waters and thus have to observe regulations to ensure safe water landing under emergency conditions. This practice is also referred to as ditching - one of several types of slamming problems that are under review by the current regulations of the Federal Aviation Administration (FAA) and the European Aviation Safety Agency (EASA). Ditching is related to the controlled landing on water, with distinctive features such as hydrodynamic slamming loads, complex hydromechanics at tremendous forward speeds, as well as the interaction of multiphase fluid dynamics (air, water, and vapor). This paper presents the knowledge on system mechanics during helicopter ditching. The discussion begins with the fundamental kinetics of the rigid body, and then delves into dynamic relations to describe the effect of forces on motions. In the end, the paper discusses several relevant theories to further contribute to the understanding of the problem of impact.

A method for analysing the vehicle–bridge interaction system with enhanced objectivity is proposed in the paper, which considers the time-variant and random characteristics and allows finding the power spectral densities (PSDs) of the system responses directly from the PSD of track irregularity. The pseudo-excitation method is adopted in the proposed framework, where the vehicle is modelled as a rigid body and the bridge is modelled using the finite element method. The vertical and lateral wheel–rail pseudo-excitations are established assuming the wheel and rail have the same displacement and using the simplified Kalker creep theory, respectively. The power spectrum function of vehicle and bridge responses is calculated by history integral. Based on the dynamic responses from the deterministic and random analyses of the interaction system, and the probability density functions for three safety factors (derailment coefficient, wheel unloading rate, and lateral wheel axle force) are obtained, and the probabilities of the safety factors exceeding the given limits are calculated. The proposed method is validated by Monte Carlo simulations using a case study of a high-speed train running over a bridge with five simply supported spans and four piers.

In certain applications, native surface patterns can be used in place of speckle patterns in digital image correlation (DIC). This paper explores the feasibility of using text as a native speckle pattern in DIC. Five text speckle patterns are tested in three different scenarios: a rigid body translation test, a rigid body rotation test, and an out of plane bending test. The patterns are benchmarked against a sixth, random speckle pattern applied using traditional DIC speckling methods. Rigid body translation tests are additionally performed on text patterns with varying font types and line spacings. In general, text patterns have good contrast, but low density as line spacing increases. Measurement uncertainty for the text patterns was comparable to measurement uncertainty in the random speckle pattern. Results from these tests show that while text patterns cannot be expected to perform better than a traditional DIC speckle pattern, text patterns can be effective speckle patterns in situations where already present on a specimen and applying a traditional speckle pattern is difficult.

Unreinforced masonry buildings undergoing seismic actions often exhibit local failure mechanisms which represent a serious life-safety hazard, as recent strong earthquakes have shown. Compared to new buildings, older unreinforced masonry buildings are more vulnerable, not only because they have been designed without or with limited seismic loading requirements, but also because horizontal structures and connections amid the walls are not always effective. Also, Out-Of-Plane (OOP) mechanisms can be caused by significant slenderness of the walls even if connections are effective. The purpose of this paper is to derive typological fragility functions for unreinforced masonry walls considering OOP local failure mechanisms. In the case of slender walls with good material properties, the OOP response can be modeled with reference to an assembly of rigid bodies undergoing rocking motion. In particular, depending on its configuration, a wall is assumed either as a single rigid body undergoing simple one-sided rocking or a system of two coupled rigid bodies rocking along their common edge. A set of 44 ground motions from earthquake events occurred from 1972 to 2017 in Italy is used in this study. The likelihood of collapse is calculated via Multiple Stripe Analysis (MSA) from a given wall undergoing a specific ground motion. Then, the single fragility functions are suitably combined to define a typological fragility function for a class of buildings. The procedure is applied to a historical aggregate in the city center of Ferrara (Italy) as a case study. The fragility functions developed in this research can be a helpful tool for assessing seismic damage and economic losses in unreinforced masonry buildings on a regional scale.

The effects of geocell reinforcement on the behavior of shell foundations were studied using PLAXIS 3D finite element software. For this purpose, conical and pyramidal geometries were adopted as shell foundations. The real honeycomb shape of geocell and rigid body behavior of shells were simulated in PLAXIS 3D. The numerical models for shell foundations and geocell reinforced foundations were separately validated using several laboratory studies in the literature. The validated models were extended to the shell foundations resting on geocell reinforced sandy beds. The inclusion of geocell-reinforcement provided more than 70% reduction in the settlement of pyramidal and conical shell foundations. The stress transferred to the sand beds were reduced and distributed a wider area compared to the unreinforced cases. The maximum improvement in the bearing capacity and the settlement were observed in the case of conical shell foundation. The effect of adopted geocell and shell configuration on the foundation behavior was also analyzed for realistic prototype foundation size.

Derivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

Abstract In this paper, an improved procedure for strongly coupled prediction of sailing yacht performance is developed. The procedure uses 3D RANS CFD to compute the hydrodynamic forces. When coupled to a rigid body motion solver and a sail force model, along with a rudder control algorithm, this allows sailing yacht performance to be predicted within CFD software. The procedure provides improved convergence when compared to a previously published method. The grid motion scheme, partially using overset grid techniques, means that correct alignment between the free surface and the background grid is ensured even at large heel angles. The capabilities are demonstrated with performance predictions for the SYRF 14 m yacht, at one true wind speed, over a range of true wind angles, with up- and downwind sailsets. The results are compared to predictions from the ORC-VPP for a yacht with similar main particulars.

In order to optimize the shape of the compound slope at the end of the open-pit mine under the condition of non-irregular boundary, the compound slope composed of the stope end and the inner dump in the south of the open-pit mine in Pingshuo is studied. Due to the impact of land acquisition, the space of external dump is seriously insufficient, and with the development and change of mining engineering and the influence of geological structure, the problem of compound form optimization and the release and utilization of internal drain space in the south side is generated. Through field investigation and theoretical analysis and numerical analysis method, on the basis of investigating the ore party production status, to establish a 3 d geological model, select two battery profile typical position, using rigid body limit equilibrium method from the perspective of 2 d, in the full study south help shrink battery limit compound stope side slope and mine safety distance, flat width, and the direction of dump active line and the relationship between the stability design of multiple slope configuration scheme, through the various methods of slope stability, enforceability and comparing some important parameters such as displacement capacity, ultimately determine the technology feasible economic and reasonable boundary zone composite slope space form. Based on the above research results, FLAC3D software was used to study the stress-strain relationship inside the slope, revealing the deformation and failure mechanism and stability of the composite slope in the south bound area. The results show that the landslide mode and stability of the composite slope in the south bound area of pingshuoAndaobao open-pit coal mine are mainly controlled by the safe distance between stope and dump and the weak layer of 11 coal floor. According to the design, the economic and reasonable parameters of the composite slope in the south slope shrinkage boundary area are as follows: the safe distance between the stope end side and the dump site is 50m, the width of the dump flat plate is 60m, and the working line Angle of the dump line with the abandonment height of 255m is 125°, the total discard space was95,934,100 m3.

In the quaternion formulation, we consider the problem of the time-optimal rotation of a spacecraft (SC) as a rigid body of an arbitrary dynamic configuration under arbitrary specified boundary conditions. In the class of generalized conical motions, the optimal rotation problem is modified, which makes it possible to obtain its analytical solution. The analytical solution to the modified problem can be considered as an approximate (quasi-optimal) solution to the traditional time-optimal rotation problem. An algorithm for the quasi-optimal rotation of an SC is given. Numerical examples are given showing that the solution of the modified problem closely approximates the solution of the traditional problem of the time-optimal rotation of an SC.

In the quaternionic setting, we consider the problem of optimal control of a spatial attitude maneuver of a spacecraft viewed as a rigid body with one symmetry axis without a constraint on the control function. For the optimality criterion we use a functional combining the time and energy spent on turning the spacecraft. Based on the Pontryagin maximum principle for this problem, new analytical solutions are obtained in the classes of conical and generalized conical motions. Numerical examples are given.

We propose a formulation of the finite horizon optimal control problem (FHOCP) based on inverse dynamics for general open-chain rigid-body systems, which reduces the computational cost from the conventional formulation based on forward dynamics. We regard the generalized acceleration as a decision variable and inverse dynamics as an equality constraint. To treat under-actuated systems with inverse dynamics that are well defined only to fully actuated systems, that is, to consider passive joints in this FHOCP, we add an equality constraint to zero the corresponding generalized torques. We include the contact forces in the decision variables of this FHOCP and treat the contact constraints using Baumgarte's stabilization method for numerical stability. We derive the optimality conditions and formulate the two-point boundary-value problem that can be efficiently solved using the recursive Newton–Euler algorithm (RNEA) and the partial derivatives of RNEA. We conducted three numerical experiments on model predictive control based on the proposed formulation to demonstrate its effectiveness. The first experiment involved simulating a swing-up control of a four-link arm with a passive joint and showed that the proposed formulation is effective for under-actuated systems. The second one involved comparing the proposed formulation with the conventional forward-dynamics-based formulation with various numbers of joints and showed that the proposed formulation reduces computational cost regardless of the number of joints. The third experiment involved simulating a whole-body control of a quadruped robot, a floating-base system having four contacts with the ground, and showed that the proposed formulation is applicable even for floating-base systems with contacts.

Solid object water entry is a common problem in various natural, industrial and military applications, which involves large deformation of free surfaces and violent fluid–structure interactions. In computational fluid dynamics (CFD), this is a type of problem that tests the robustness and capacity of any CFD numerical algorithm. In this work, the newly-developed updated Lagrangian particle hydrodynamics (ULPH) method, which is a fluid version of peridynamics, is enhanced and applied to simulate solid object water entry problems. ULPH method is Lagrangian meshfree particle method that can ensure the specific free surface conditions automatically satisfied. The density filter and artificial viscosity diffusion are adopted in the ULPH scheme to stabilize and smooth the pressure field. In the process of a rigid body entering water, it may induce negative pressure in some areas of impact region, which can cause spurious tensile instability in some meshfree particle simulations, such as SPH and ULPH. A tensile instability control technique based on the ULPH framework has been developed to overcome the numerical instability. To validate the stability and accuracy of the ULPH approach in simulating water entry problems, several 2D and 3D examples of water entry have been carried out in this work. The necking and cavity pinch-off phenomena are visible in the numerical results. The simulation results of the ULPH method are well compared with experimental data and other numerical solutions. The water crown, cavity shapes and stream pattern formed around the rigid body entering the water can be well captured. The computation results show that the ULPH method has the ability to simulate the complex solid object water entry precess accurately.

This paper presents the results of our research regarding the use of a meshless method, namely element-free Galerkin method, in solving an impact problem between a rigid body and a foam plate. Next, the paper gives two answers to two usual questions appearing when modeling foam materials. These questions refer to the choice of a material model and to the extension of the stress–strain curve of the foam material. Solutions start from some experimental data of a foam material and continue by numerical simulations using Ls-Dyna software. The results are very interesting and especially useful in numerical modeling of the foam material. The results are presented in a comparative way, graphically and in tabular form.

In this letter, we propose a novel method for the on-ground simulation of a space robotic mission, while exploiting a robotic hardware-in-the-loop facility. The simulated dynamics replicated by the robots are defined with respect to a nominal motion. This approach enables simulating the motion of large satellites. In particular, we exploit a Lagrangian matching relative to the nominal motion for a satellite (client) and a manipulator-equipped spacecraft (servicer), which are modeled as a rigid body and a multi-body system, respectively. Stability of the proposed method is also analyzed. The effectiveness of the method is demonstrated through experiments on the OOS-Sim facility for the capture of Envisat, a free-tumbling satellite and the largest space debris in Low-Earth-Orbit.

This work presents a novel RGB-D SLAM approach to simultaneously segment, track and reconstruct the static background and large dynamic rigid objects that can occlude major portions of the camera view. Previous approaches treat dynamic parts of a scene as outliers and are thus limited to a small amount of changes in the scene, or rely on prior information for all objects in the scene to enable robust camera tracking. Here, we propose to treat all dynamic parts as one rigid body and simultaneously segment and track both static and dynamic components. We, therefore, enable simultaneous localisation and reconstruction of both the static background and rigid dynamic components in environments where dynamic objects cause large occlusion. We evaluate our approach on multiple challenging scenes with large dynamic occlusion. The evaluation demonstrates that our approach achieves better motion segmentation, localisation and mapping without requiring prior knowledge of the dynamic object's shape and appearance., 8 pages, 11 figures. IEEE Robotics and Automation Letters (2021)

To reduce the errors caused by the rigid body hypothesis in the aerodynamics-structure coupling calculation and improve the structural performance, an optimum structure design with the consideration of the fluid-structure interaction are performed for the H-type vertical axis wind turbine (VAWT) blade. Based on the ANSYS Workbench platform, the geometric model, computational domain and grids of the wind wheel are constructed, the turbulence model, boundary conditions and composite material layers are set up, and the fluid and solid domains are solved in a coupled way. The single-objective structural optimization model in which the thicknesses of glass clothes, foam and gel coat, and the positions of two webs are taken as design variables is solved using the response surface optimization method to minimize the wind wheel mass. The frequencies and vibration modes of original and optimized blades with and without pre-stress and the transient characteristics of wind wheels in different wind speeds are investigated. The results indicate that after the blade optimization, the first-order frequency and critical speed become larger and other frequencies reduce for the static, single pre-stress and multiple pre-stresses states, and the maximum displacement, stress and strain of the wind wheel decrease under rated and extreme wind speeds, confirming significant performance improvements. The research provides useful guidance for the integrated design of structure and aerodynamics of wind turbine blades.

In many robotic applications, the environment setting in which the 6-DoF pose estimation of a known, rigid object and its subsequent grasping is to be performed, remains nearly unchanging and might even be known to the robot in advance. In this paper, we refer to this problem as instance-specific pose estimation: the robot is expected to estimate the pose with a high degree of accuracy in only a limited set of familiar scenarios. Minor changes in the scene, including variations in lighting conditions and background appearance, are acceptable but drastic alterations are not anticipated. To this end, we present a method to rapidly train and deploy a pipeline for estimating the continuous 6-DoF pose of an object from a single RGB image. The key idea is to leverage known camera poses and rigid body geometry to partially automate the generation of a large labeled dataset. The dataset, along with sufficient domain randomization, is then used to supervise the training of deep neural networks for predicting semantic keypoints. Experimentally, we demonstrate the convenience and effectiveness of our proposed method to accurately estimate object pose requiring only a very small amount of manual annotation for training., GitHub code: https://github.com/rohanpsingh/ObjectKeypointTrainer

The dynamic in-plane instability process of pin-ended arches under a central radial impact applied is analyzed with numerical simulation method. Based on energy characteristics of arch under impact, the method for determining the critical state of dynamic stability of both elastic arch and elastic–plastic arch under impact are discussed in this paper. The calculation results show that the strain energy of the elastic arch at dynamic stable critical state is consistent with that at a state after buckling under static load in which the bearing capacity of the arch drops to zero, and the difference between them are very small and no more than 3.6 %. When impact act on the arch with dynamic critical initial conditions, the converter efficiencies from initial kinetic energy possessed by the rigid body to elastic strain energy of arch approaches 100 %, therefore a feasible method is provided to determine the dynamic stability of elastic arch under impact on the energy method. Then the impact analysis of arch considering material nonlinearity is carried out, it is proposed that the instability of elastic-plastic arch can be judged by the forming of plastic hinges at about 1/4 on both sides of the arch. It is found that the elastic strain energy of elastic-plastic arch at dynamic stability critical state is very close to maximum elastic strain energy of the arch under static load, and the differences between them are no more than 3 %.

This paper presents an analytical algorithm with appropriate software specified for the approximation of the allowed critical slope of the solid flat terrain that guarantees static and/or dynamic stability of the specified self-propelled agricultural machines and their aggregates. This algorithm assumes machine as a rigid body, having 3 or 4 contact points (defined by wheels or crawlers), under uniform motion at different constant velocities and radii of curvature trajectories. Using this algorithm, based on the principles of theoretical mechanics combined with 3D analytical geometry, the computer program SSPM ( s tability of the s elf-propelled agricultural m achines) has been coded. This software is intended to facilitate the analysis, comparison and optimization of different configurations of self-propelled agricultural machines in operation on horizontal and sloped flat terrains at constant velocities and radii of trajectory with respect to their static and dynamic stability. It calculates critical pitch and roll angles of the self-propelled machine and the maximum allowed slope of the flat terrain under the given conditions. The algorithm and the appropriate SSPM software were experimentally verified using the platform and low-scale tractor model. Average difference between calculated and experimental critical values of roll and pitch angles were about 4°

A theoretical dynamic model of vehicular driveline is presented to reveal the mechanism of low frequency interior booms within a low engine speed range. Unlike existing models, this model manifests the torsional-lateral-longitude coupling effects of the propeller shafts together with the integral rear axle assembly. Based on rotor dynamics, translational rigid body vibrations of propeller shafts due to flexible support onto the trimmed body are complemented to traditional one-dimensional torsional model. Then the kinematic equation of the Hooke’s joint is improved to illustrate the dynamic effects of the non-constant velocity coupling. In addition, pitching of the integral rear axle assembly coupled to torsional vibration through the main reducer is also considered. An application containing analyses of critical engine speed and dynamic response is performed to a rear-wheel-drive vehicle, which proves that this model shows the best balance of accuracy and efficiency compared with established models, and has a capacity to show the contributions of the Hooke’s joints. Finally, a modal sensitivity analysis is conducted to find the authentic cause of the vehicle’s boom and explain the reasons that the previous model is less accurate. At last, the sensitivity of peak value of force transmissibility is derived as a novel method to seek for optimized directions. It concludes that this model is suitable for investigation and optimizing of boom problems.

We present a practical backend for stereo visual SLAM which can simultaneously discover individual rigid bodies and compute their motions in dynamic environments. While recent factor graph based state optimization algorithms have shown their ability to robustly solve SLAM problems by treating dynamic objects as outliers, their dynamic motions are rarely considered. In this paper, we exploit the consensus of 3D motions for landmarks extracted from the same rigid body for clustering, and to identify static and dynamic objects in a unified manner. Specifically, our algorithm builds a noise-aware motion affinity matrix from landmarks, and uses agglomerative clustering to distinguish rigid bodies. Using decoupled factor graph optimization to revise their shapes and trajectories, we obtain an iterative scheme to update both cluster assignments and motion estimation reciprocally. Evaluations on both synthetic scenes and KITTI demonstrate the capability of our approach, and further experiments considering online efficiency also show the effectiveness of our method for simultaneously tracking ego-motion and multiple objects.

There are three different well-known methods for predicting the manoeuvrability of ships: (1) free running model test, (2) direct manoeuvring simulation using CFD and (3) system-based manoeuvring simulation. In this paper, the manoeuvrability of the KVLCC2 was estimated using CFD with rigid body motion and body force propeller method. The free running manoeuvre at the different time steps were also simulated. The yaw checking ability and the turning ability of KVLCC2 were predicted using CFD and could have been confirmed that the IMO criteria was satisfied. When the results were compared with the model test and system-based method, the free running simulation showed better agreement to that of the model test. It could also be confirmed that the results vary depending on the time step. Overall, the CFD results using the body force propeller method estimated most accurately the test results.

Braided structures are widely used in numerous contexts including everyday practice. In most cases, rope ends are knotted to form various types of loops or tie them to rigid body parts; however, knots take up space that may not be available in some application scenarios, thus making them unsuitable for certain purposes. Hence, this paper introduces first development steps of a method for the numerical simulation of rope ends connected by sewing stitches.

Three-dimensional reorientation of a rigid body by means of several auxiliary masses moving relative to the body is considered. The algorithm presented is based on simple circular motions of the internal point masses. It is shown that the case of several masses, especially if their number exceeds three, has certain advantages compared to the case of one moving mass. The location of domains where these masses move as well as the size of these domains can be chosen according to the design requirements. The results obtained can be of interest for the control of mobile robots and other moving objects including spacecraft.

Point-based rigid registration (PBRR) techniques are widely used in many aspects of image-guided surgery (IGS). Accurately estimating target registration error (TRE) statistics is of essential value for medical applications such as optically surgical tool-tip tracking and image registration. For example, knowing the TRE distribution statistics of surgical tool tip can help the surgeon make right decisions during surgery. In the meantime, the pose of a surgical tool is usually reported relative to a second rigid body whose local frame is called coordinate reference frame (CRF). In an n-ocular tracking system, fiducial localization error (FLE) should be considered inhomogeneous, that means FLE is different between fiducials, and anisotropic that indicates FLE is different in all directions. In this paper, we extend the TRE estimation algorithm relative to a CRF from homogeneous and anisotropic to heterogeneous FLE cases. Arbitrary weightings can be assumed in solving the registration problems in the proposed TRE estimation algorithm. Monte Carlo simulation results demonstrate the proposed algorithm's effectiveness for both homogeneous and inhomogeneous FLE distributions. The results are further compared with those using the other two algorithms. When FLE distribution is anisotropic and homogeneous, the proposed TRE estimation algorithm's performance is comparable with that of the first one. When FLE distribution is heterogeneous, proposed TRE estimation algorithm outperforms the other two classical algorithms in all test cases when ideal weighting scheme is adopted in solving two registrations. Possible clinical applications include the online estimation of surgical tool-tip tracking error with respect to a CRF in IGS. Graphical Abstract This paper provides the target registration error model considering a coordinate reference frame in surgical navigation.

Purpose To enable motion-robust diffusion weighted imaging of the brain using well-established imaging techniques. Methods An optical markerless tracking system was used to estimate and correct for rigid body motion of the head in real time during scanning. The imaging coordinate system was updated before each excitation pulse in a single-shot EPI sequence accelerated by GRAPPA with motion-robust calibration. Full Fourier imaging was used to reduce effects of motion during diffusion encoding. Subjects were imaged while performing prescribed motion patterns, each repeated with prospective motion correction on and off. Results Prospective motion correction with dynamic ghost correction enabled high quality DWI in the presence of fast and continuous motion within a 10° range. Images acquired without motion were not degraded by the prospective correction. Calculated diffusion tensors tolerated the motion well, but ADC values were slightly increased. Conclusions Prospective correction by markerless optical tracking minimizes patient interaction and appears to be well suited for EPI-based DWI of patient groups unable to remain still including those who are not compliant with markers.

The paper deals with dynamic in-plane simulation analysis of a motorcycle suspension. The motorcy-cle᾿s mechanical model is considered as a visco-elastically suspended rigid body. Two types of the kinematic excitation are considered ‒ a deterministic „hat“ shaped bump and stochastically uneven road characterized by its power spectral density. The simulation results for both the deterministic bump and stochastically uneven road show that significant reduction of the root mean square value of the motorcycle body centroid acceleration (comfort criterion) can be achieved by placing the lower end point of the rare spring-damper module closer to the beginning of the swinging arm and also by increasing deviation (tilt) of the spring-damper module from the vertical. The maximum improvement in the root mean square value of the motorcycle body centroid acceleration is 51.7 % for the deterministic „hat“ shaped bump and 37.4 % for the stochastically uneven road. The method presented in the paper can be employed in design of both touring motorcycles, which are characterized by higher requirements of comfort, and off-road motorcycles where protection from impacts generated by bumps is important.

For addressing the position and attitude control of a fully-actuated 6-degree-of-freedom (6-DOF) rigid body, a new configuration error function is designed, and the configuration error vector is deduced as the gradient of this function, where the configuration stands for the set of position and attitude and is described by the nonlinear manifold SE(3). Based on the newly designed configuration error function, a geometric terminal sliding-mode controller is proposed to stabilize the configuration tracking errors of rigid body in a bounded fixed time considering disturbances. Simulations for close range rendezvous and docking of a spacecraft in an elliptical orbit illustrate the effectiveness of the proposed control scheme.

The parameters of the monorail bridge, which have a significant effect on the vehicle, are analyzed in this paper. With Park method, a complicated solver of the second order with a variable step size, equations insolvable to traditional methods can be solved and a more complicated dynamic model could be built. Different from some traditional simulation of vehicle–bridge coupling system, the bridge is divided into the girder and piers. The finite element model of each part is created separately in Ansys and coupled with the vehicle system in UM, which helps the analysis of the interaction forces between flexible components and better simulation accuracy can be obtained. FIALA model is used to calculate the wheel force. These methods make the measurement more precise. The study shows that all the variables except for the stiffener thickness have little effect on the vibration of the vehicle due to the good vibration reduction performance of the vehicle system. The resonance of the girder could be avoided by changing the thickness of the stiffeners and web plates. In addition, high stiffness and damping of the connection point of the girder and pier are helpful in alleviating the vibration of the bridge.

This work presents the analysis of the load motion during the interaction of wind pressure. The load was treated as a rigid body, and the rope system model as a non-deformed. The influence of effective area of wind pressure on load motion was considered. The theoretical model of load motion was presented, which may be an universal approach for transporting machines equipped with a rope-lifting system. To define the orientation of the movable Cartesian coordinate system related to the load, Bryant angles were used. An algorithm and computational program were developed to allow for analysis of dynamic phenomena. The initial problem was solved with the use of the ode45 calculation procedure in the Matlab software on the basis of the Runge–Kutta 4th Order Method. The obtained results were verified with the experimental ones achieved in the wind tunnel and Tracker program. Numerical calculations using commercial software SolidWorks were also presented. In the experiment, the spatial motion of the load was analysed. Experimental tests were carried out for gust of wind and constant temperature and humidity. In addition, the paper presents the application of the proposed method for a load carried by a rotary crane. After taking into account the control functions resulting from the nature of the work of any machine, the formulated model can be a full description of the carried load motion taking into account external forces.

In recent years, the demand for inexpensive, simple, and highly accurate 3D measurement has been increasing. Representative methods, photogrammetry, and shape from focus (SfF) have limitations in terms of measurement time and labour. In order to solve them, computational photography (CP) has been proposed. A light field camera, based on CP, has also been developed. It has a feature to acquire multi-view and multi-focus images simultaneously in one shot. It is possible to perform 3D measurements with less time and labour for photographing and calculation processing using these images. In this study, we combined the photogrammetry as applied to multi-view images with the SfF as applied to multi-focus images using a light field camera. We applied the proposed method to a rigid body and verified its accuracy. We confirmed that the proposed method achieved more accurate results than the photogrammetry and the SfF method. Furthermore, we applied the proposed method to screws and cracks on walls of buildings and affirmed its applicability. Finally, we suggested future work on the developed method.

The free surface motion in moving containers is an important physical phenomenon for many engineering applications. One way to model the free surface motion is by employing shallow water equations (SWEs). The port-Hamiltonian systems formulation is a powerful tool that can be used for modeling complex systems in a modular way. In this work, we extend previous work on SWEs using the port-Hamiltonian formulation, by considering the two-dimensional equations under rigid body motions. The resulting equations consist of a mixed-port-Hamiltonian system, with finite and infinite-dimensional energy variables and ports. 2000 Math Subject Classification: 34K30, 35K57, 35Q80, 92D25

This paper provides a solution to the active vibration control of a microsatellite with two solar panels. At first, the microsatellite is processed as a finite element model containing a rigid body and two flexible bodies, according to the principles of mechanics, and that the dynamic characteristics are solved by modal analysis. Secondly, the equation involving vibration control is established according to the finite element calculation results. There are several actuators composed of macro fibre composite on the two solar panels for outputting control force. Furthermore, the control voltage for driving actuator is calculated by using fuzzy algorithm. It is clear that the smart structure consists of the flexible bodies and actuators. Finally, the closed-loop control simulation for suppressing harmful vibration is established. The simulation results illustrate that the responses to the external excitation are decreased significantly after adopting fuzzy control.

Nonlinear analysis of structures is an effective way for predicting the bearing capacity or ultimate strength of a structure. This paper will review researches on the nonlinear, buckling, postbuckling and elasto-plastic analyses of three-dimensional (3D) framed structures. Also considered are curved beams since they share the problem of joint equilibrium in simulation. The following are the key issues to be covered in this paper: (a) analytical or semi-analytical approaches; (b) formulation for incremental-iterative nonlinear analysis; (c) joint equilibrium of 3D frames at the deformed configuration; (d) rigid body test for nonlinear finite elements; (e) rigid-body-qualified geometric stiffnesses and derivation; (f) simulation of buckling of curved beams; (g) elasto-plastic analysis of steel frames; (h) mechanism of iterations in incremental analysis; (i) recovery of element forces; and (j) path-tracing scheme for the postbuckling response. In this paper, the theories and methods for solving the postbuckling responses of structures involving multi-loop curves are considered. In fact, the incremental-iterative procedure for the geometric and/or inelastic nonlinear analysis can be greatly simplified if it is well rooted in physics. Namely, if the rigid body rule is fully obeyed at each stage of analysis, then the entire incremental-iterative procedure can be made simpler and more efficient. Recently, it was demonstrated that satisfactory results can be obtained for the postbuckling response of a number of structures using the elastic stiffness alone. A total of 154 references are cited in this paper.

CFD models perform rigid body simulations and ignore the hydroelastic behavior of turbine blades. In reality, the tidal turbine blades deform due to the onset flow. Deformation of the turbine blade alters the angle of attack and pressure difference across the low pressure and high pressure surface of the blade. Therefore, the performance of a Tidal Current Turbine (TCT) is modelled in this study using Computational Fluid Dynamic (CFD) and coupled Fluid Structure Interaction (FSI) simulations to compare the predictions of both models. Results of the performance parameters predicted from both the models are also compared with experimental data. The difference between experimental value of CP and predicted value from the rigid blade CFD and FSI models is less than 10%. The FSI model accounted for the blade deformation and a maximum blade tip deflection of 0.12 mm is observed representing a case of small deformation. The extent of deformation is not enough to alter the angle of attack and flow separation behavior at the blade. The variation in predicted pressure difference across the blade surfaces between the two models resulted in different CP prediction. Almost similar wake predictions are obtained from both the models.

We propose techniques that achieve invariance to the positioning of wearable motion sensor units on the body for the recognition of daily and sports activities. Using two sequence sets based on the sensory data allows each unit to be placed at any position on a given rigid body part. As the unit is shifted from its ideal position with larger displacements, the activity recognition accuracy of the system that uses these sequence sets degrades slowly, whereas that of the reference system (which is not designed to achieve position invariance) drops very fast. Thus, we observe a tradeoff between the flexibility in sensor unit positioning and the classification accuracy. The reduction in the accuracy is at acceptable levels, considering the convenience and flexibility provided to the user in the placement of the units. We compare the proposed approach with an existing technique to achieve position invariance and combine the former with our earlier methodology to achieve orientation invariance. We evaluate our proposed methodology on a publicly available data set of daily and sports activities acquired by wearable motion sensor units. The proposed representations can be integrated into the preprocessing stage of existing wearable systems without significant effort.

A hopping rover that is driven only by internal or external attitude actuators is an ideal mobility approach for surface exploration of small solar system bodies. Without thrust control and grasping mechanisms, a hopping rover is mechanically simple to design and less prone to mechanical failures, but faces challenges during soft landing. It may rebound from the surface, causing deviations from its original landing site. In this paper, landing of a hopping rover on the surface of an asteroid is investigated, and a strategy using only attitude control to shorten the landing distance is proposed. Based on rigid body impact dynamics, the edge impact configuration is investigated in detail. The factors that affect the impact states of a cube-shaped hopping rover are studied. Then, controlled edge landing is analyzed, in which the post-impact velocity of the hopping rover is changed by controlling its attitude prior to impact. Three guidance schemes are developed, followed by attitude profile generation and finite time stable attitude control. Finally, simulations are performed on an ideal flat surface and uneven terrain. The results show that controlled edge landing can effectively reduce the landing distance and settling time, compared with uncontrolled landing. This study on hopping motion on the surface of an irregular-shaped asteroid with attitude control, can provide a reference for hopper trajectory plan in future asteroid surface explorations.

In this study, an impacting contact model of spur gear under lightly loaded condition is constructed by considering the pinion and the wheel as rigid body, in which the lubricant is modelled by a linear spring damper combination. The entire motion of the gear system is fell into three phases, i.e.,: meshing state, transient state and non-meshing state. An original numerical calculation method is proposed for this model, and its validation is confirmed by using the Co-simulation of Adams-Matlab/Simulink. Instead of using the Jacobian matrix, the proposed numerical method could effectively avoid the ill condition in the iteration on data resulting from the nonlinearity of gear backlash. The results in this study verified that the algorithm is useful not only can increase the accuracy, but also significantly decrease the calculation time of the entire system. And the original numerical calculation method is employed to illustrate and quantify the influences of the excitation frequency on the impacting contact model of spur gears.

The results of the analytical and numerical solution of the problem of controlling the rotational motion of an axially symmetric rigid body with a combined performance index of the control process are presented using quaternions. The performance index includes the duration of the control, impulse of the squared angular momentum magnitude, and impulse of the magnitude of the control torque applied to the body. The control must take an axisymmetric rigid body from a state of rest to another state of rest.

In this paper, we present a novel multisensor combinatory attitude determination method that enables high-accuracy measurement of the attitude of a high rotational speed rigid-body aircraft. We analyze the external moments of the aircraft during flight and develop the method using theoretical deductions based on the motion equations of a rigid body rotating around the centroid. The proposed method fuses the data measured from GPS, gyrometer, and magnetometer and uses the improved unscented Kalman filter (UKF) algorithm to perform filtering. First, appropriate assumptions and simplifying approximations are made for around-centroid motion equations of a rigid body according to the motion characteristics of the high rotational speed aircraft. Using these assumptions and approximations, the constraint equations between the Euler attitude angles and flight-path angle, trajectory deflection angle are derived to serve as the state equation. Second, the roll angle with error is calculated using the geomagnetic field model and the geomagnetic intensity measured by a three-axis magnetometer and then fused with the angular velocity information obtained from the gyroscope for constructing the measurement equations. Finally, the state equations are discretized using the Runge–Kutta method during the UKF prediction stage, improving the prediction accuracy. Simulation results show that the proposed method can effectively determine the attitude information of the high rotational speed aircraft, achieving high level of reliability and accuracy thanks to the combination of information from GPS, gyroscope, and magnetometer.

This paper presents a macro-element for simulating the seismic behavior of the soil- shallow foundation interaction. The overall behavior in the soil and at the interface is replaced by a macro-element located at the base of the superstructure. The element reproduces the irreversible elastoplastic soil behavior (material non-linearity) and the foundation uplift (geometric non-linearity) at the soil- foundation interface. This new macro-element model with three degrees-of-freedom describes the force-displacement behavior of the footing center. The single element is restrained by the system of equivalent springs and dashpots. The footing is considered as a rigid body. It is solved by a suitable Newmark time integration scheme and implemented in Matlab to simulate the nonlinear behavior of soil-shallow foundation interaction under seismic loading. A reduce scaled soil-foundation system has been tested on a shaking table at the University of Transport and Communications, Hanoi, Vietnam. Five series of earthquake motions were used with maximum acceleration increased from 0.5 to 2.5 . The comparison of numerical results obtained from the simulation and experimentations shows the satisfactory agreement of the model. The proposed macro-element can be used to predict the seismic behavior of a wider variety of configurations.

Dynamic substructuring (DS) is a research field that has gained a great deal of attention in both science and industry. The aim of DS techniques is to provide engineers in structural vibrations and sound practical solutions for analyzing the dynamic behavior of complex systems. This paper addresses the singularity problem that occurs when flexible joints are implemented as substructures into the Lagrange Multiplier Frequency-Based Substructuring (LM-FBS) coupling process. For illustration, we use rubber bushings from an automotive application. Considering the rubber isolators to exhibit hysteretic damping, we assume that only the property of the dynamic stiffness of material is given. To avoid singularity appearing in the admittance when inverting the impedance of a massless joint, we compare three different approaches to include rubber bushings in the framework of LM-FBS. One method consists in including the dynamic stiffness of material directly in the space of the interface constraints and add it to the assembled interface flexibility of the LM-FBS equation. This corresponds to a relaxation of the interface compatibility condition. In the second method, the rubber bushing is treated as a substructure by adding small masses to the equation of the joint. As a result, we obtain a nonsingular total dynamic stiffness matrix that can be included in the coupling process. The third method describes a novel extension of the LM-FBS approach, based on a solution for singular problems. If the applied forces are self-equilibrated with respect to the rigid body modes, a solution for the singular dynamic stiffness matrix exists. The methods are outlined, both mathematically and conceptually, based on a notation commonly used in LM-FBS. They facilitate the integration of connecting elements together with experimental or numerical determined system dynamics of substructures in order to predict the assembled system behavior.

PURPOSE To develop a registration method that is capable of estimating the full range of rigid body motion from three orthogonal collapsed images of the head. These images can be obtained using the collapsed FatNav, a previously introduced navigator for prospective motion correction. It combines a short duration with wide compatibility with different main sequences due to its robustness against spin history effects. THEORY AND METHODS A projection-based 3D/2D registration method is presented and then modified to take into account the peculiarities of the collapsed FatNav. Water/fat separated volumes were used in simulations to assess the accuracy of the proposed method at different resolutions by comparison with high-resolution 3D registration. The sensitivity with respect to masking strategies and starting motion parameters was investigated. Finally, prospective experiments with a healthy volunteer were performed with different types of motion patterns. A PROPELLER main sequence was chosen to compare the prospective correction with PROPELLER's own retrospective correction. RESULTS In the simulations the proposed method has shown comparable performance to 3D registration. Furthermore, evidence of its robustness with respect to masking strategies and starting motion parameters was presented. The combination with collapsed FatNav has performed well in correcting most of the motion artifacts prospectively with improved image quality compared to only using PROPELLER's retrospective motion correction. CONCLUSIONS The proposed 3D/2D registration together with collapsed FatNav is characterized by a good balance between navigator duration and estimate accuracy. Further work is needed to validate the method across a wider variety of subject anatomies.

A simple method of investigating the effect of joint clearances on landing gear retraction failure is presented and applied to the main landing gear with a single sidestay and a hydraulic actuator. A geometric model is presented with assumptions of each link as a rigid body and their relative positions geometrically determined by considering the size of the clearances. We conducted a sensitivity analysis based on a geometric model of the main landing gear. The model was calibrated using the data from the technical order. A Monte Carlo simulation (MCS) was conducted, and whose input was the distance of each clearance based on the experimental design that combined the modified Latin hypercube sampling (LHS) and central composite design (CCD). As a result, we were able to find that the joint had a high potential to operate abnormally. We validated the model by using the actual failure data. Finally, the physical meaning of the sensitivity analysis results was interpreted by comparing them with the values obtained through an amplification index method that is a modified linearization method.

The body freedom flutter characteristics of an airfoil and a fly wing aircraft model were calculated based on a CFD method for the Navier–Stokes equations. Firstly, a rigid elastic coupling dynamic model of a two-dimensional airfoil with a free–free boundary condition was derived in an inertial frame and decoupled by rigid body mode and elastic mode. In the fluid–solid coupling method, the rigid body was trimmed by subtracting the generalized steady aerodynamic force from the structural dynamic equation. The flutter characteristics were predicted by the variable stiffness method at a fixed Mach number and flight altitude. Finally, validation of the predicted body freedom flutter characteristics was performed through a comparison of theoretical solutions based on a Theodorsen unsteady aerodynamic model for airfoil and experimental results for a fly wing aircraft model. The mechanism of the influence of the bending mode stiffness and the position of the center of gravity on the body freedom flutter characteristics were briefly analyzed.