Linearized Kinematic Model Research Articles

Design of a spherical parallel mechanism with controllable center of rotation using a spherical reconfiguration linkage

It is well known that Remote Center of the motion (RCM) mechanisms are highly suitable for many medical applications. While it is sometimes preferable that the mechanism can control their Center of Rotation (CoR), most RCM mechanisms do not have this possibility without being mounted on large and heavy translational platforms. By using a new concept of Spherical Reconfigurable Linkage (SRL), the present study offers an alternative solution. These new linkages are designed to control their radius and they are connected to form an RCM mechanism with controllable CoR. The newly mounted mechanism now has two linear Degrees of Freedom (DoF) for the displacement of its CoR in addition to its two angular DoF. The linear kinematic model is derived along with the angular kinematic one while taking into account the reconfiguration of the SRL. The velocity model is calculated and all singular configurations are identified. The mechanism performances in terms of workspace and kinematic performances are is also assessed. Finally, motion capture experiments on a prototype validated the models.

Повышение технологичности и эксплуатационной надежности гидроразжимного соединения сваи с основанием морской стационарной платформы

Object and purpose of research. This paper discusses hydraulic-release couplings of pillars and substructures for fixed marine platforms. This topic is relevant because at some platforms hydraulic-release couplings contribute to crack initiation. The purpose of this study was to work out design solutions that would mitigate residual strains so as to preclude pillar cracking due to hydraulic release, thus making the pillars more durable. Achieving this purpose will make hydraulic release more suitable for routine operation, and will also make Russian manufacturers of fixed marine platforms more independent from Western patent holders of hydraulic release system designs. Subject matter and methods. Design solutions suggested in this study were tried out through finite-element simulation of hydraulic release process. Plastic straining of pillars was taken into account by means of a linear kinematic model of hardening. Main results. The study covered seven possible designs of hydraulic release units and yielded load diagrams for both plastic straining of pillar over the entire working cycle of hydraulic release (with indication of maximum accumulated plastic strain) and subsequent pillar pull-out from substructure. Conclusion. The study yielded an optimal design solution for hydraulic release joint that both reduces plastic straining of pillar and increases axial stiffness of the joint itself.

An aero-hydro coupled method for investigating ship collision against a floating offshore wind turbine

Ship collision hazards with floating offshore wind turbines (FOWTs) has been identified and the dynamic responses of FOWT under ship collision scenarios are necessary to be investigated. This paper develops a numerical solver to address the challenge of considering wind-wave loads in the ship-FOWT collision analysis. The user-defined load subroutine, LOADUD, in LS-DYNA is utilized to model the wind, wave and mooring loads. A simplified aerodynamic model considering blade pitch strategy is used and the hydrodynamic loads are calculated based on potential-flow theory with a linear wave kinematic model. The mooring forces are considered with a linearized model. The implementation of the coupled solver is verified by conducting free decay test, wave-only and wind-only analysis, respectively and comparing them with the reference values. Good agreement has been achieved, indicating that the aero-hydro coupling effects can be accurately simulated by the numerical solver. With the developed method and solver, cases of ship collision with a spar-type floating wind turbine are simulated and both local structural deformation and global motions in 6DOF are obtained. The influence of velocity, flexibility of tower, deformability of the ship, wind-wave loads are further discussed. It is found that the impact velocity can greatly affect the structural responses and a high-speed impact can directly lead to tower collapse. By comparing the cases of ship collision with FOWT, and those with fixed-support wind turbine, the flexibility of wind turbine tower is found to rarely influence the energy dissipation under collision scenario of FOWT, while it is important for the collision scenario of fixed-support wind turbine. The wind-wave condition can be more hazardous as a smaller impact velocity can lead to structures collapsing. This is because, even though the structure can withstand the ship collision, the residual strength may not be enough for the following wind loads, which can result in the structure to finally collapse. Additionally, the proposed fully coupled method is used to validate one of the authors’ previous studies, which is a decoupled method regarding the ship-FOWT collision analysis [1]. The external dynamic results from two methods are compared and discussed. Good agreement is reached between two methods for low-velocity impact but for high-speed collision or collisions with serious deformation, limitations of decoupled method can be found because some basic assumptions of them are violated. The proposed method and solver can be used to evaluate the crashworthiness of FOWT during the engineering design phase.

H∞ controller synthesis for AGV trajectory tracking using a linearized kinematic model

This paper proposes a design procedure for H∞ optimal linear feedback controllers for trajectory tracking of an automated guided vehicle (AGV) based on a linearized kinematic model. The design specifications are expressed as a constrained H∞ norm optimization problem to assess the potential of the H∞ framework for the considered application. This problem is then solved for a linear parameter-varying (LPV), a full-block and a decoupled linear time-invariant (LTI) controller. The performance of all controllers is compared through numerical simulations and experiments on an AGV prototype targeted at agricultural applications.

Robust Time-Optimal Guidance in a Partially Uncertain Time-Varying Flow-Field

In this paper, we address the problem of guiding an aerial or aquatic vehicle to a fixed target point in a partially uncertain flow-field. We assume that the motion of the vehicle is described by a point-mass linear kinematic model. In addition, the velocity of the flow-field, which is taken to be time varying, can be decomposed into two components: one which is known a priori and another one which is uncertain and only a bound on its magnitude is known. We show that the guidance problem can be reformulated as an equivalent pursuit evasion game with time-varying affine dynamics. To solve the latter game, we propose an extension of a specialized solution approach, which transforms the pursuit–evasion game (whose terminal time is free) via a special state transformation into a family of games with fixed terminal time. In addition, we provide a simple method to visualize the level sets of the value function of the game, along with the corresponding reachable sets. Furthermore, we compare our conservative game-theoretic solution with a pure optimal control solution, for the special case in which the flow-field is perfectly known a priori.

Advanced Plasticity Modeling for Ultra-Low-Cycle-Fatigue Simulation of Steel Pipe

Pipelines and piping components may be exposed to extreme loading conditions, for instance earthquakes and hurricanes. In such conditions, they undergo severe plastic strains, which may locally reach the fracture limits due to either monotonic loading or ultra-low cycle fatigue (ULCF). Aiming to investigate the failure process and strain evolution of pipes enduring ULCF, a lab-scale ULCF test on an X65 steel pipeline component is simulated with finite element models, and experimental data are used to validate various material modeling assumptions. The paper focuses on plastic material modeling and compares different models for plastic anisotropy in combination with various hardening models, including isotropic, linear kinematic and combined hardening models. Both isotropic and anisotropic assumptions for plastic yielding are considered. As pipes pose difficulty for the measurement of plastic properties in mechanical testing, we calibrate an anisotropic yield locus using advanced multi-scale simulation based on texture measurements. Moreover, the importance of the anisotropy gradient across thickness is studied in detail for this thick-walled pipeline steel. It is found that the usage of a combined hardening model is essential to accurately predict the number of the cycles until failure, as well as the strain evolution during the fatigue test. The advanced hardening modeling featuring kinematic hardening has a substantially higher impact on result accuracy compared to the yield locus assumption for the studied ULCF test. Cyclic tension-compression testing is conducted to calibrate the kinematic hardening models. Additionally, plastic anisotropy and its gradient across the thickness play a notable, yet secondary role. Based on this research, it is advised to focus on improvements in strain hardening characteristics in future developments of pipeline steel with enhanced earthquake resistance.

A comparative evaluation of various models for prediction of displacements

One of the main subjects of Geodesy is the monitoring of position changes of artificial structures (buildings, dams, bridges etc.). Such position changes can be caused by a variety of reasons such as vehicles for cable bridges and earthquakes. Various mathematical models have been developed in order to monitor and to analyze this phenomenon. This study presents the main models which are used by geodesists for the description of points’ displacements. These are the descriptive models (which are separated into the congruence and the kinematic ones) and the cause-response models (which are separated into the static and the dynamic). Moreover, several models, which are based on time series analysis and are used mainly for the prediction of financial parameters, are referred in parallel. These are the smoothing models, the time series decomposition models, and the ARIMA models. All the abovementioned models are discussed and compared in order to emerge their advantages, disadvantages, and limitations. The goal of this study is to substantiate which of these models could be used with reliability for prediction of displacements. A case study using the most appropriate models is carried out. The experiment deals with the prediction of displacements of a set of permanent GNSS stations. The results proved that the linear kinematic models have the best performance, in comparison with the other examined models.

Realtime Application of Constrained Predictive Control for Mobile Robot Navigation

This work addresses the implementation issue of constrained Model Predictive Control (MPC) for the autonomous trajectory-tracking problem. The chosen process to control is a Wheeled Mobile Robot (WMR) described by a discrete, Multiple Input Multiple Output (MIMO), state-space and linear parameter varying kinematic model. The main motivation of the constrained MPC usage in this case relies on its ability in considering, in a straightforward way, control and states constraints that naturally arise in trajectory tracking practical problems. The efficiency of the presented control scheme is validated through experimental results on a two wheeled mobile robot using both STM32F429II and STM32F407ZG microcontrollers. The controller implementation is facilitated by the usage of the automatic C code generation and interesting optimization before real-time execution. Based on the experimental results obtained, the good performance and robustness of the proposed control scheme are established.

Enhanced non-linear material modelling for analysis and qualification of rollover protective structures

Finite element simulations of a rollover protective structure are an important aspect in its design, as it provides a means of structural integrity qualification prior to the required destructive testing. A good understanding of the rollover protective structure behaviour under simulated loading offers engineering practitioners the opportunity to optimize the design. The testing conditions, which are outlined in the applicable standards, result in plastic deformation of the rollover protective structure, associated with material hardening of various areas of the structure. An accurate description of the material behaviour is important for finite element simulations of the structural response. This research examines some of the hardening models commonly used in simulations of rollover protective structures, which are available in most finite element commercial software, including linear and multi-linear isotropic and kinematic hardening models and non-linear kinematic hardening models. The numerical performance of the plasticity models in representing the material behaviour was compared with the experimental data for commonly used rollover protective structure material. Analysis revealed the potential benefits and drawbacks of the various models. Moreover, a damage-induced softening model was implemented at the structure joints in conjunction with the non-linear hardening models. Enhanced computational results were obtained through this modelling variation, highlighting the importance of material modelling at the primary structure and the joints of a rollover protective structure.

Effect of vorticity on the generation of rogue waves due to dispersive focusing

The kinematic and dynamic of steep two-dimensional focusing wave trains on a shearing flow in deep water are investigated analytically and numerically. In the absence of waves, the vorticity due to the vertical gradient of the horizontal current velocity is assumed constant. A linear kinematic model based on the spatio-temporal evolution of the frequency is derived, predicting the focusing distance and time of a chirped wave packet in the presence of constant vorticity. Furthermore, a linear model, based on a Fourier integral, is used to describe the evolution of the free surface on shearing current. To compute the fully nonlinear evolution of the wave group in the presence of vorticity, a new numerical model, based on a BIEM approach, is developed. On the basis of these different approaches, the role of constant vorticity on rogue wave occurrence is analysed. Two main results are obtained: (1) the linear behaviour expected in the presence of constant vorticity is significantly different from what is commonly expected in the presence of constant current and (2) the nonlinear effects are found to be of significant influence in the case at hand.

A dangerous use of the fading memory term for non linear kinematic models at variable temperature

Abstract The purpose of this note is to shed the light on a specific problem linked to the use of a variable fading memory parameter in a nonlinear kinematic rule. A strong variation of this parameter versus temperature may generate cumbersome behaviours even with very simple temperature histories. A better solution is to use several non linear kinematic variables with a constant fading memory term.

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

Flow over two fish (modeled by two flexible plates) in tandem arrangement is investigated by solving the incompressible Navier---Stokes equations numerically with the DSD/SST method to understand the differences between the geometrically linear and nonlinear models. In the simulation, the motions of the plates are reconstructed from a vertically flowing soap film tunnel experiment with linear and nonlinear kinematic models. Based on the simulations, the drag, lift, power consumption, vorticity and pressure fields are discussed in detail. It is found that the linear and nonlinear models are able to reasonably predict the forces and power consumption of a single plate in flow. Moreover, if multiple plates are considered, these two models yield totally different results, which implies that the nonlinear model should be used. The results presented in this work provide a guideline for future studies in fish swimming.

Capture zone of linear strategies in interception problems with variable structure dynamics

The paper considers planar interception engagements against maneuverable targets using a linearized kinematic model with constant velocities. Both the interceptor and the target have bounded controls and first-order linear dynamics. Due to the linearization, the duration of the interception is prescribed. The target dynamics is fixed, but the interceptor has variable structure dynamics, switching from one mode to another once during the engagement. For such engagements the capture zone of a given linear feedback control is constructed. Numerical examples demonstrate that proper change of the interceptor dynamic mode leads to an enlarged capture zone.

Surface plastic strain in contact problems: Prediction by a simplified non-linear kinematic hardening model

A previously published model for plasticity assessment in rolling contact, based on a simplification of the non- linear kinematic and isotropic hardening model of Chaboche and Lemaitre, is discussed, and an update is introduced in order to improve its accuracy in the plastic strain prediction within the region just underneath the contact surface. The update is based on a correction of the yield limit and of the strain rate as a function of the load ratio of the tensile stress in the direction parallel to the contact surface. The effectiveness and the accuracy of the updated model in not too severe conditions are demonstrated through comparisons with results obtained by finite element model (FEM) analyses. An application of the model to some experimental results obtained on rail and railway wheel steels is also carried out, and quite good agreement is found in plastic strain prediction, although some discrepancies are found. The method appears to be a valid tool for practical application, especially for its ability of combining the effects of different phenomena and of simulating a number of cycles of the order of millions in a reasonable time.

ROBUST SOLUTION OF A TIME-VARIABLE INTERCEPTION PROBLEM: A CHEAP CONTROL APPROACH

A planar interception problem of a maneuverable target is considered using the linearized kinematic model with variable velocities and first-order dynamics of the interceptor and target. The maneuverabilities of the interceptor and target are assumed to be variable. By using an auxiliary zero-sum linear-quadratic differential game with cheap controls of both players, an interception guidance law, linear with respect to the state vector, is derived. An analytical description of the set of initial positions (capture set) is obtained, from which this guidance law provides zero miss distance, subject to given maneuverabilities of the interceptor and target. A numerical example illustrating the analytical results is presented.

The continental margin in Iceland — A snapshot derived from combined GPS networks

The tectonical setting in Iceland is quite complex due to the interaction of the Iceland hot spot and the Mid Atlantic Ridge. While in the north of the island one active spreading zone exists, the divergent motion in the centre and the south is distributed over at least two volcanic rift zones. The spreading rate increases linearly along the Western Volcanic Zone from north to south up to 8 mm/yr at the Hengill triple junction. On the contrary, the spreading rate of the parallel Eastern Volcanic Zone decreases from 16 mm/yr down to 6 mm/yr at the island's southern coast. The Hreppar microplate between the two predominant rift zones has an independent motion, which is distinct from that of the Eurasian and North American plates. A new detected feature is the spreading activity around the Hofsjökull volcanic zone located in the centre of Iceland with a significant rate of 6 mm/yr. During this investigation the coordinate sets of nearly 20 years of GPS data acquisition on Iceland were combined to get a velocity field for the surface of Iceland. This velocity field is based on a linear kinematic model with the consideration of local non-linear effects like volcano up-doming and displacements due to major earthquakes.

A three‐DOF compliant micromotion stage with flexure hinges

Micromanipulation has enabled numerous technological breakthroughs in recent years, from advances in biotechnology to microcomponent assembly. Micromotion devices commonly use piezoelectric actuators (PZT) together with compliant mechanisms to provide fine motions with position resolution in the nanometre or even sub‐nanometre range. Many multiple degree of freedom (DOF) micromotion stages have parallel structures due to better stiffness and accuracy than serial structures. This paper presents the development of a three‐DOF compliant micromotion stage with flexure hinges and parallel structure for applications requiring motions in micrometres. The derivation of a simple linear kinematic model of the compliant mechanism is presented and simulation results before and after calibration are compared with results from finite element (FE) modeling and experiments. The position control system, which uses an experimentally determined constant‐Jacobian, and its performance are also presented and discussed.

Zero Miss Interception Guidance: Cheap Control Approach

A planar interception problem of a highly maneuverable target is considered based on linearized kinematic model with variable velocities and first-order dynamics of both missiles. This problem can be embedded into the framework of a more general robust controllability problem. By using an auxiliary zero-sum linear-quadratic differential game with cheap controls of both players, an interception guidance control law, linear with respect to the state vector, is derived. This control provides zero miss distance, i.e. a “hit-to-kill” interception accuracy. Numerical example illustrating the analytical results is presented.

Pendulation control of an offshore crane

This paper considers a control system for a crane that reduces pendulation of suspended loads in offshore lifting operations. The modelling of the ship crane is studied and an anti-pendulation arm is designed and proposed. Two different types of models are derived, one based on torque and one kinematic. For the torque model, Lyapunov analysis and non-linear control design is applied on the vertical plane. Linear control design techniques for the linearized kinematic model are applied in both vertical and horizontal planes. These techniques are based on linear quadratic Gaussian (LQG) and generalized predictive control (GPC). The advantage for the linear control designs is the explicit use of the vessel dynamics and sea wave disturbances in the control design that considerably improves the controlled pendulation of the crane. Design issues, simulation results and comparison studies are considered.

Modeling of large simple shear using a viscoplastic overstress model and classical plasticity model with different objective stress rates

Large simple shear deformation, which usually has been used to test the applicability of various models, is studied by applying the classical plasticity model and the viscoplasticity theory based on overstress (VBO) with the logarithmic stress rate. Hypo-elastic, elastic-perfectly plastic, elastic-plastic linear kinematic and isotropic hardening models are employed. In addition to the logarithmic rate, the influences of the convected Truesdell and co-rotational Jaumann and Green-Naghdi rates on stress-strain behavior in simple shear are investigated. It is observed that unlike the Jaumann rate the logarithmic rate does not exhibit any oscillatory response. The responses of the logarithmic rate to every type of model discussed here are acceptable except for the elastic-perfectly plastic case. The finite viscoplasticity theory based on overstress, which has been developed by Krempl and his co-workers, with zero isotropic stress rate and nonzero hardening modulus and elastic-plastic kinematic hardening model gives the same results at the rate of 10−5 1/s. It is shown that elastic-perfectly plastic, elastic-plastic kinematic hardening can be modeled with FVBO.