Multibody System Dynamics Research Articles

Computational simulation and free flight validation of body vibration of flapping-wing MAV in forward flight

FWMAVs (Flapping Wing Micro Air Vehicles) turn to be a flexible multi-body dynamic (FMBD) system when the inertia and flexibility of flapping wing are considered. The vibration caused by interaction of unsteady aerodynamics, structural dynamics and multi-body dynamics makes the analysis of aerodynamic and acquisition of equilibrium become full of challenge. In this study, a method coupled three-dimensional CFD (Computational Fluid Dynamics) and CSD (Computational Structural Dynamics) considering FMBD (flexible multi-body dynamics) between flexible wings and body is developed. And a trim algorithm is developed to satisfy three aspects of conditions including convergence of structural deformation and periodic condition of body's vibration in longitudinal direction and conditions of equilibrium. The computational results show that the trim conditions when body's vibration is taken into account are different from that when body's vibration is ignored. The vibration of body mainly increases the aerodynamic drag while having a little effect on lift. When the flight is trimmed, the corresponding flapping frequency increases and angle of attack decreases. In order to validate the method of simulation, the free flight data including the time course of oscillated plunging acceleration and pitch angle is collected based on the steady flight ability of “DOVE” FWMAV. Through comparison, though there is slight discrepancy between computational results and free flight data, it proves that CFD/FMBD method provides a sufficiently good accuracy for the simulation of body vibration of FWMAVs. Based on the proposed and validated model, the influence of various take-off mass on the vibration of body is studied and it indicates that a proper mass ratio between wing to body can suppress the maximum acceleration of vibration to protect the precise sensors and equipment.

Stable Parking Control of a Robot Astronaut in a Space Station Based on Human Dynamics

Controlling a robot astronaut to move in the same way as a human astronaut to realize a wide range of motion in a space station is an important requirement for the robot astronauts that are meant to assist or replace human astronauts. However, a robot astronaut is a nonlinear and strongly coupled multibody dynamic system with multiple degrees of freedom, whose dynamic characteristics are complex. Therefore, implementing a robot astronaut with wide-ranging motion control in a space station is a tremendous challenge for robotic technology. This article presents a wide-ranging stable motion control method for robot astronauts in space stations based on human dynamics. Focusing on the astronauts' parking motion in a space station, a viscoelastic dynamic humanoid model of parking under microgravity environment was established using a mass-spring-damper system. The model was used as the expected model for stable parking control of a robot astronaut, and the complex dynamic characteristics were mapped into the robot astronaut system to control the stable parking of the robot astronaut in a manner similar to a human astronaut. This provides a critical basis for implementing robots that are capable of steady wide-ranging motion in space stations. The method was verified on a dynamic system of a robot astronaut that was constructed for this research. The experimental results showed that the method is feasible and effective and that it is a highly competitive solution for robot astronauts with human-like moving capabilities in space stations.

A Symplectic Instantaneous Optimal Control for Robot Trajectory Tracking With Differential-Algebraic Equation Models

Robot trajectory tracking control based on differential-algebraic equation (DAE) models is still a thorny issue, because the DAEs of such systems are inherently complex and unstable, such as the high-index problem. In this paper, a symplectic instantaneous optimal control (IOC) method for robot trajectory tracking with input saturation based on controlled DAEs is proposed. Based on the discrete variational principle and the canonical transformation, a symplectic discretization form for the controlled DAEs is first constructed. Then, the continuous trajectory tracking problem is approximated for a series of IOC problems at every time step, and the linear complementarity problem (LCP) can be derived for solving the IOC problems. Finally, the control inputs can be obtained by solving the corresponding standard LCP. The proposed method provides a unified framework for solving the trajectory tracking control problems of robot multibody dynamic systems. Numerical simulations and virtual experiments are conducted to verify the robustness and the efficiency of the proposed method, i.e., the input saturation constraints are satisfied at the discrete time points, and high accuracy tracking control results can be obtained at low computational cost.

An overview of formulae for the higher-order kinematics of lower-pair chains with applications in robotics and mechanism theory

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed.

Theoretical modeling and numerical solution methods for flexible multibody system dynamics

Flexible multibody system dynamics (MSD) is one of the hot spots and difficulties in modern mechanics. It provides a powerful theoretical tool and technical support for dynamic performance evaluation and optimization design of a large number of complex systems in many engineering fields, such as machinery, aviation, aerospace, weapon, robot and biological engineering. How to find an efficient accurate dynamics modeling method and its stable reliable numerical solving algorithm are the two core problems of flexible MSD. In this paper, the research status of modeling methods of flexible MSD in recent years is summarized first, including the selection of reference frames, the flexible body’s kinematics descriptions, the deductions of dynamics equation, the model reduction techniques and the modeling methods of the contact/collision, uncertainty and multi-field coupling problems. Then, numerical solution technologies and their latest developments of flexible MSD are discussed in detail. Finally, the future research directions of modeling and numerical computation of flexible MSD are briefly prospected.

A robust nonsmooth generalized-$\alpha $ scheme for flexible systems with impacts

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-$\alpha $ 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-$\alpha $ method is proposed in this work, avoiding these inconveniences. Several examples are considered to assess its accuracy and robustness.

In Memoriam: Subhash C. Sinha

In Memoriam: Subhash C. Sinha

Multibody dynamic modelling of a direct wind turbine drive train

Wind turbines normally have a long operational lifetime and experience a wide range of operating conditions. A representative set of these conditions is considered as part of a design process, as codified in standards. However, operational experience shows that failures occur more frequently than expected, the costlier of these including failures in the main bearings and gearbox. As modern turbines are equipped with sophisticated online systems, an important task is to evaluate the drive train dynamics from online measurement data. In particular, internal forces leading to fatigue can only be determined indirectly from other locations’ sensors. In this contribution, a direct wind turbine drive train is modelled using the floating frame of reference formulation for a flexible multibody dynamics system. The purpose is to evaluate drive train response based on blade root forces and bedplate motions. The dynamic response is evaluated in terms of main shaft deformation and main bearing forces under different wind conditions. The model was found to correspond well to a commercial wind turbine system simulation software (ViDyn).

Fuzzy dynamics of multibody systems with polymorphic uncertainty in the material microstructure

This paper deals with the fuzzy dynamics of multibody systems with polymorphic uncertainty in the material microstructure. Macroscopic material properties are obtained using fuzzy-stochastic FEM based computational homogenization. In particular, the spectral stochastic local FEM is utilized to simulate a representative volume element of the microstructure. Forward dynamics of the macroscopic system is modeled using the Graph Follower algorithm. Thereby we propagate the uncertainty from the lowest level of material microstructure to the highest level of multibody dynamics. Differences in the propagation of epistemic and aleatoric uncertainties to the macroscale and their influence on the multibody dynamics are discussed. A particular example of a multibody system used in this paper is a multistory frame, whereby the considered heterogeneous material is a cement-based concrete.

Cone complementarity approach for dynamic analysis of multiple pendulums

The multibody system dynamics approach allows describing equations of motion for a dynamic system in a straightforward manner. This approach can be applied to a wide variety of applications that consist of interconnected components which may be rigid or deformable. Even though there are a number of applications in multibody dynamics, the contact description within multibody dynamics still remains challenging. A user of the multibody approach may face the problem of thousands or millions of contacts between particles and bodies. The objective of this article is to demonstrate a computationally straightforward approach for a planar case with multiple contacts. To this end, this article introduces a planar approach based on the cone complementarity problem and applies it to a practical problem of granular chains.

L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

An L-stable method over time intervals for differential-algebraic equations (DAEs) of multibody system dynamics is presented in this paper. The solution format is established based on equidistant nodes and nonequidistant nodes such as Chebyshev nodes and Legendre nodes. Based on Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula are obtained by comparison with Pade approximation. Newton iteration method is used during the solution process. Taking the planar two-link manipulator system as an example, the results of L-stable method presented are compared for different number of nodes in the time interval and the step size in the simulation, and also compared with the classic Runge-Kutta method, A-stable method, Radau IA, Radau IIA, and Lobatto IIIC methods. The results show that the method has the advantages of good stability and high precision and is suitable for multibody system dynamics simulation under long-term conditions.

A Multibody Dynamics Approach to Limit Cycle Walking

SummaryThough significant efforts are made to develop mathematical models of the limit cycle walking (LCW), there is still a lack of a general and efficient framework to study the periodic solution and robustness of a complex model like human with knees, ankles and flat feet. In this study, a numerical framework of the LCW based on general multibody system dynamics is proposed, especially the impacts between the feet and the ground are modeled by Hunt–Crossley normal contact force and Coulomb friction force, and the modeling of the knee locking is presented as well. Moreover, event-based operating strategies are presented to deal with controls for the ground clearance and the knee locking. Importantly, a fast and efficient two-step algorithm is proposed to search for stable periodic gaits. Finally, maximum allowable disturbance is adopted as the index for stability analysis. All these features could be readily implemented in the framework. The presented solution is verified on a compass-like passive dynamic walking (PDW) walker with results in the literature. Based on this framework, a fairly complicated level-walking walkers with ankles and knees under control are analyzed and their periodic gaits are obtained, and surprisingly, double stable periodic gaits with, respectively, low speed and high speed are found.

Transfer matrix method for multibody systems (Rui method) and its applications

The transfer matrix method for multibody systems, namely the “Rui method”, is a new method for studying multibody system dynamics, which avoids the global dynamics equations of the system, keeps high computational speed, and allows highly formalized programming. It has been widely applied to scientific research and key engineering of lots of complex mechanical systems in 52 research directions. The following aspects regarding the transfer matrix method for multibody systems are reviewed systematically in this paper: history, basic principles, formulas, algorithm, automatic deduction theorem of overall transfer equation, visualized simulation and design software, highlights, tendency, and applications in 52 research directions in over 100 key engineering products.

The constraint-stabilized implicit methods on Lie group for differential-algebraic equations of multibody system dynamics

The implicit methods on Lie group are developed for multibody system dynamics. To avoid the violation of the displacement, velocity and acceleration constraints of the nonlinear differential-algebr...

A collaborative simulation in shipbuilding and the offshore installation based on the integration of the dynamic analysis, virtual reality, and control devices

It is difficult to observe the potential risks of lifting or turn-over operations in the early stages before a real operation. Therefore, many dynamic simulations have been designed to predict the risks and to reduce the possibility of accidents. These simulations, however, have usually been performed for predetermined and fixed scenarios, so they do not reflect the real-time control of an operator that is one of the most important influential factors in an operation; additionally, lifting or turn-over operations should be a collaboration involving more than two operators. Therefore, this study presents an integrated method for a collaborative simulation that allows multiple workers to operate together in the virtual world. The proposed method is composed of four components. The first component is a dynamic analysis that is based on multibody-system dynamics. The second component is VR (virtual reality) for the generation of realistic views for the operators. The third component comprises the control devices and the scenario generator to handle the crane in the virtual environment. Lastly, the fourth component is the HLA (high-level architecture)-based integrated simulation interface for the convenient and efficient exchange of the data through the middleware. To show the applicability of the proposed method, it has been applied to a block turn-over simulation for which one floating crane and two crawler cranes were used, and an offshore module installation for which a DCR (dual-crane rig) was used. In conclusion, the execution of the proposed method of this study is successful regarding the above two applications for which multiple workers were involved.

Coupled finite element and multibody systems dynamics modelling for the investigation of the bridge approach problem

Railways are the most common mode of transportation for both people and cargo due to its advantages in economy, safety, and comfort. The finite element method has been broadly used for more than three decades to model the different components of the railroad system such as rails, sleepers (cross ties), and substructure and has been used to investigate a variety of problems associated with rail mechanics. Different multibody systems dynamics software programs have also been developed to investigate the dynamic performance and contact behaviour between the rails and the wheels and to determine the contact forces. In this work, a full three-dimensional model that couples both the finite element method and the multibody systems dynamics has been used to study the railroad system. The main focus of this study is to model the bridge approach problem under dynamic load. The bridge approach problem arises from the sudden change in the foundation's stiffness under the rails at the bridge entry and exit, leading to high levels of stress and settlement that can also cause further problems over time. The effect of using a concrete slab at the bridge entry is also investigated in this study, using two slab designs: rectangular and inclined. The results show the effectiveness of the three-dimensional model and slab implementation on the forces and the vertical deformation, especially the inclined slab that applies a gradual change in the stiffness rather than a sudden change.

Features of solving the inverse dynamic method equations for the synthesis of stable walking robots controlled motion

The problem of walking robots controlled motion synthesis by the inverse dynamic method is considered. The inverse dynamic method equations are represented by the methods of multibody system dynamics as free bodies motion equations and constraint equations. The variety of constraint equations group are introduced to specify the robot gait, to implement the robot stability conditions and to coordinate specified robot links movement. The key feature of the inverse dynamic method equations in this formulation is the presence of the second derivatives of the system coordinates in the constraint equations expressing the stability conditions that ensure the maintenance of the vertical position by the robot. The determined solution of such equations in general case is impossible due to the uncertainty of the initial conditions for the Lagrange multipliers. An approximate method for solving the inverse dynamic without taking into account the inertial components in the constraint equations that determine the stability of the robot is considered. Constraint equations that determine the coordinate movement of individual robot links and required for unique problem solving based on approximate equations are presented. The implementation of program motion synthesis methods in the control system of the humanoid robot AR-600 is presented. The comparison of theoretical and experimental parameters of controlled motion is performed. It has been established that with the achieved high accuracy of the robot links tracking drives control with an error of several percent, the indicators of the robot's absolute movements, in particular, the angles of roll, yaw and pitch, differ from the programmed by 30-40%. It’s shown that proposed method allows to synthesize robot control in quasistatic mode for different movement types such as moving forward, sideways, walking on stairs, inclinations etc.

Parameterization dynamics visual design platform for missile launching system

The missile launching system is a typical complex mechanical system, which is becoming increasingly larger in scale and more complicated in structure. Designing these types of products often requires repeated complex and time-consuming model design, calculation, and analysis of the dynamics of the system. The most time-consuming is repeatedly modifying the geometric and dynamics models. In this article, we put forward a new method for bidirectional-driving parameter between CAD and CAE, by changing the geometric model parameters, which directly changes the dynamics model. A parameterized multibody system dynamics modeling and analysis software for missile launching system are proposed, which gathered modeling, solving, visual simulation as a whole, and realized design parameters seamless transfer between geometric models and dynamics models for missile launching system. In order to examine the correctness of the simulation results, a parameterized experimental platform for missile launching system is designed, which can modify the key parameters as designed in simulation software. Finally, a missile launching system simulation and test examples are given, and the simulation analysis and experiment results demonstrate that the overall trend of the simulation results of multi-rigid and rigid-flexible coupling dynamics model is consistent with the experiment results.

Multibody dynamical modeling of the FPSO soft yoke mooring system and prototype validation

The Soft Yoke Mooring System (SYMS) is a single point mooring system for shallow water. It is composed of a mooring framework, mooring legs, yoke, and single point, and is located at the Floating Production Storage and Offloading (FPSO) through 13 hinge joints, such as universal joints and thrust bearings. Mooring restoring force, motions and postures of mooring components, and mechanical behaviors of hinge joints are major criteria for the structural design of the SYMS. Aiming at the difficulties of the multibody dynamics in traditional design of the SYMS, a multi-body dynamic mathematical modeling with seven independent degrees of freedom (DOFs) which is applicable to prototype field engineering was developed in this study. The proposed mathematical modeling of the SYMS multibody dynamic system has several advantages: 1. Internal tribological behaviors in hinge joints are considered within the presented multibody dynamics model to illustrate the good dynamic effects of the SYMS. 2. The multibody dynamic model can be applied in field service. Correctness and feasibility of the proposed multibody dynamic simulation method for describing motions and postures of hinges and single-body were validated by the prototype monitoring data. 3. The horizontal restoring force of the SYMS was calculated according to field measurement data. The motion state of each single body and internal stress distributions at each hinge joint in the SYMS are given. 4. The multibody dynamics calculation program can be directly used for the real-time monitoring of mechanical behaviors of the SYMS under the service state. The simulated results can provide real-time guarantee for safety alarming of the system. The vulnerability of the mooring system in service was evaluated based on long-term monitoring data analysis.

Use of mixed coordinates in modeling wind turbines including tubular tower

Abstract. This paper studies the effect of the tower dynamics upon the wind turbine model by using mixed sets of rigid and/or nodal and/or modal coordinates within multibody system dynamics approach. The nodal model exhibits excellent numerical properties, especially in the case where the rotation of the rotor-blade is extremely high, and therefore, the geometric stiffness effect can not be ignored. However, the use of nodal models to describe the flexibility of large multibody systems produces huge size of coordinates and may consume massive computational time in simulation. On the other side, the dynamics of the tower as well as other components of wind turbine remain exhibit small deformations and can be modeled using Cartesian and/or reduced set of modal coordinates. The paper examines a method of using mixed sets of different coordinates in the same model, although there are differences in the scale and the physical interpretation. The equations of motion of the wind-turbine model is presented based on the floating frame of reference formulation. The mixed coordinates vector consists of three sets: Cartesian coordinates set to present the rigid body motion (nacelle and rotor bodies), elastic nodal coordinates for rotating blades, and reduced-order modal coordinates for low speed components and those that deflect by simple motion shapes (circular Tower). Experimental validation has been carried out successfully, and consequently, the proposed model can be utilized for design process, identification and health monitoring aspects.