Multibody system dynamics is based on classical mechanics and its engineering applications originating from mechanisms, gyroscopes, satellites and robots to biomechanics. Multibody system dynamics is characterized by algorithms or formalisms, respectively, ready for computer implementation. As a result simulation and animation are most convenient. Recent developments in multibody dynamics are identified as elastic or flexible systems, respectively, contact and impact problems, and actively controlled systems. Based on the history and recent activities in multibody dynamics, recursive algorithms are introduced and methods for dynamical analysis are presented. Linear and nonlinear engineering systems are analyzed by matrix methods, nonlinear dynamics approaches and simulation techniques. Applications are shown from low frequency vehicles dynamics including comfort and safety requirements to high frequency structural vibrations generating noise and sound, and from controlled limit cycles of mechanisms to periodic nonlinear oscillations of biped walkers. The fields of application are steadily increasing, in particular as multibody dynamics is considered as the basis of mechatronics.

The vast mechanical systems could be classified as closed loop system, open loop system and open & closed (switching) system. In the closed loop system, the kinematics and dynamics of 3-D mechanisms will be reviewed and closed form solutions using the direction cosine matrix method and reflection transformation method will be introduced. In the open loop system, kinematic & dynamic analysis methods regarding the redundant system which has more degrees of freedom in joint space than those of task space are reviewed and discussed. Finally, switching system which changes its phase between closed and open loop motion is investigated with the principle of dynamical balance. Among switching systems, the human gait in biomechanics and humanoid in robotics are presented.

In this paper, a practical bushing model is proposed to improve the accuracy of the vehicle dynamic analysis. The results of the rubber bushing are used to develop an empirical bushing model with an artificial neural network. A back propagation algorithm is used to obtain the weighting factor of the neural network. Since the output for a dynamic system depends on the histories of inputs and outputs, Narendra algorithm of 'NARMAX' form is employed to consider these effects. A numerical example is carried out to verify the developed bushing model. Then, a full car dynamic model with artificial neural network bushings is simulated to show the feasibility of the proposed bushing model.

Randomness exists in engineering. Tolerance, assemble-error, environment temperature and wear make the parameters of a mechanical system uncertain. So the behavior or response of the mechanical system is uncertain. In this paper, the uncertain parameters are treated as random variables. So if the probability distribution of a random parameter is known, the simulation of mechanical multibody dynamics can be made by Monte-Carlo method. Thus multibody dynamics simulation results can be obtained in statistics. A new concept called functional reliability is put forward in this paper, which can be defined as the probability of the dynamic parameters(such as position, orientation, velocity, acceleration etc.) of the key parts of a mechanical multibody system belong to their tolerance values. A flexible mechanical arm with random parameters is studied in this paper. The length, width, thickness and density of the flexible arm are treated as random variables and Gaussian distribution is used with given mean and variance. Computer code is developed based on the dynamic model and Monte-Carlo method to simulate the dynamic behavior of the flexible arm. At the same time the end effector's locating reliability is calculated with circular tolerance area. The theory and method presented in this paper are applicable on the dynamics modeling of general multibody systems.

A vehicle driving simulator is a virtual reality device which makes a man feel as if he drove an actual vehicle. Unlike actual vehicles, the simulator has limited kinematical workspace and bounded dynamic characteristics. So it is difficult to simulate dynamic motions of a multi-body vehicle model. In order to overcome these problems, a washout algorithm which controls the workspace of the simulator within the kinematical limitation is needed. However, a classical washout algorithm contains several problems such as generation of wrong sensation of motions by filters in tilt coordination, requirement of trial and error method in selecting the proper cut-off frequencies and difficulty in returning the simulator to its origin using only high pass filters. This paper proposes a washout algorithm with new tilt coordination method which gives more accurate sensations to drivers. To reduce the time in returning the simulator to its origin, an algorithm that applies selectively onset mode from high pass filters and return mode from error functions is proposed. As a result of this study, the results of the proposed algorithm are compared with the results of classical washout algorithm through the human perception models. Also, the performance of the suggested algorithm is evaluated by using human perception and sensibility of some drivers through experiments.

Accurate seismic analyses of large deformable moving structures are still unsolved problems in the field of earthquake engineering. In order to analyze these problems, the nonlinear finite element method formulated by the absolute nodal coordinate approach is noticed. Because, this formulation has several advantages over the standard procedures on mass matrix, elastic forces and damping forces in the case of large displacement problems. But, it has not been fully studied to build frame structure models by using beam elements in the absolute nodal coordinate formulation. In this paper, we propose the connecting method of the beam elements formulated by the absolute nodal coordinate. The coordinate transformation matrix of this element is introduced into the frame structure. This beam element has the characteristic that the mass matrix and bending stiffiness matrix are constant even if in the case of large displacement problems, and this characteristic is being kept after the transformation. In order to verify the proposed method, we show the numerical simulation results of frame structures for a vibration problem and a large displacement problem.

In this paper we present the linearized equations of motion for a bicycle as a benchmark. The results obtained by pencil-and-paper and two programs are compared. The bicycle model we consider here consists of four rigid bodies, viz. a rear frame, a front frame being the front fork and handlebar assembly, a rear wheel and a front wheel, which are connected by revolute joints. The contact between the knife-edge wheels and the flat level surface is modelled by holonomic constraints in the normal direction and by non-holonomic constraints in the longitudinal and lateral direction. The rider is rigidly attached to the rear frame with hands free from the handlebar. This system has three degrees of freedom, the roll, the steer, and the forward speed. For the benchmark we consider the linearized equations for small perturbations of the upright steady forward motion. The entries of the matrices of these equations form the basis for comparison. Three diffrent kinds of methods to obtain the results are compared : pencil-and-paper, the numeric multibody dynamics program SPACAR, and the symbolic software system Auto Sim. Because the results of the three methods are the same within the machine round-off error, we assume that the results are correct and can be used as a bicycle dynamics benchmark.

This research presents a three-dimensional modeling technique for a flexible sheet. A relative coordinate formulation is used to represent the kinematics of the sheet. The three-dimensional flexible sheet is modeled by multi-rigid bodies interconnected by out-of-plane joints and plate force elements. A parent node is designated as a master body and is connected to the ground by a floating joint to cover the rigid motion of the flexible sheet in space. Since the in-plane deformation of a sheet such as a paper and a film is relatively small, compared to out-of-plane deformation, only the out-of-plane deformation is accounted for in this research. The recursive formulation has been adopted to solve the equations of motion efficiently. An example is presented to show the validity of the proposed method.

For real time dynamic simulation, two different subsystem synthesis methods with independent generalized coordinates have been developed and compared. In each formulation, the subsystem equations of motion are generated in terms of independent generalized coordinates. The first formulation is based on the relative Cartesian coordinates with respect to moving subsystem base body. The second formulation is based on the relative joint coordinates using recursive formulation. Computational efficiency of the formulations has been compared theoretically by the arithmetic operational counts. In order to verify real-time capability of the formulations, bump run simulations of a quarter car model with SLA suspension subsystem have been carried out to measure the actual CPU time.

A new mechanism for hyper redundant manipulator (HRM) is presented, which comprises of serially assembled compound three-bar linkages (CTL). The CTL mechanism has some unique properties. This paper presents the forward and inverse kinematics of this mechanism and shows the simulation of the HRM havig 9 CTL units. The recursive algorithm of the inverse kinematics that the author originally developed is employed. It is fast and stable ; moreover, it enables us to obtain a solution in which the end-point of the HRM is controlled by a portion of joints. It also presents the method of the dynamical analysis. There exist kinematical constraints in the proposed closed linkage mechanism. In the dynamic analysis constraints are sufficiently sustained by the constraint stabilization method that the author developed. The mechanical structure of the HRM having some CTL units that is under construction is shown.

For high speed railway vehicles, we consider a vibration of flexible track/wheel system. It is very important to deal with the complex phenomena of high-speed vehicles that can be occurred in the vertical vibration of the system. From a viewpoint of multibody dynamics, this kind of problem needs accurate analysis because the system includes mutual dynamic behaviors of rigid body and flexible body. The simulation technique for the complex problems is also discussed. We consider the high-speed translation, rail elasticity, elastic supports under the rail and contact rigidity. Eigen value analysis is also completed to verify the mechanism of the coupled vertical vibration of the system.

The DC motor of a vehicle may cause noise and vibration due to high-speed revolution, which can make a driver feel uncomfortable. There have been various studies attempting to solve these problems, mostly focusing on the causes of noise and vibration and a means of preventing them. The CAE methodology is more efficient than a real test for the purpose of looking for various design parameters to reduce the noise and vibration of the DC motor. In this study, a design process for reducing brush noise is presented with the use of a computer model, which is made by using a multi-body dynamics program (DADS). The design parameters to reduce the brush noise and vibration were proposed using a computer model. They were used to reduce the noise and vibration of the DC motor and verified by the test results of the fan DC motor in the vehicle. This method may be applicable to various DC motors.

There are many things in common between hemodynamics in arterial systems and multibody dynamics in mechanical systems. Hemodynamics is concerned with the forces generated by the heart and the resulting motion of blood through the multi-branched vascular system. The conventional hemodynamics model has been intended to show the general behavior of the body arterial system with the frequency domain based linear model. The need for detailed models to analyze the local part like coronary arterial tree and cerebral arterial tree has been required recently. Non-linear analysis techniques are well-developed in multibody dynamics. In this paper, the studies of hemodynamics are summarized from the view of multibody dynamics. Computational algorithms of arterial tree analysis is derived, and proved by experiments on animals. The flow and pressure of each branch are calculated from the measured flow data at the ascending aorta. The simulated results of the carotid artery and the iliac artery show in good accordance with the measured results.

A method of dynamic analysis of mechanical systems considering probabilistic properties is proposed in this paper. Probabilistic properties that result from manufacturing tolerances can be represented by means and standard deviations (or variances). The probabilistic characteristics of dynamic responses of constrained multi-body systems are obtained by two ways : the proposed analytical approach and the Monte Carlo simulation. The formerpaper, necessitates sensitivity information to calculate the standard deviations. In this a direct differentiation method is employed to find the sensitivities of constrained multi-body systems. To verify the accuracy of the proposed method, numerical examples are solved and the results obtained by using the proposed method are compared to those obtained by Monte Carlo simulation.

The non-minimum phase characteristic of a flexible manipulator makes tracking control of its tip difficult. The level of the tip tracking performance of a flexible manipulator is significantly affected by the characteristics of the tip reference trajectory as well as the characteristics of the flexible manipulator system. This paper addresses the question of how to best specify a reference trajectory for the tip of a flexible manipulator to follow in order to achieve the objectives of reducing : tip tracking error, residual tip vibration, and the required actuation effort at the manipulator joint. A novel method of tip-based learning controller for the flexible manipulator system is proposed in the paper, where a model of the flexible manipulator system with a command shaping filter is used to generate a smooth and realizable tip reference trajectory for a tip-based learning controller.

A stable walking pattern generation method for a biped robot is presented in this paper. In general, the ZMP (zero moment point) equations, which are expressed as differential equations, are solved to obtain a stable walking pattern. However, the number of differential equations is less than that of unknown coordinates in the ZMP equations. It is impossible to integrate the ZMP equations directly since one or more constraint equations are involved in the ZMP equations. To overcome this difficulty, DAE (differential and algebraic equation) solution method is employed. The proposed method has enough flexibility for various kinematic structures. Walking simulation for a virtual biped robot is performed to demonstrate the effectiveness and validity of the proposed method. The method can be applied to the biped robot for stable walking pattern generation.

Relative contributions of lower extremity joints on the support moment were investigated in this study. Three-dimensional gait analyses were performed in normal walking and in unexpected step-down walking. For both gait studies, inverse dynamics were performed to obtain each joint moment of the lower extremity, which was applied to the forward dynamics simulation to determine the contributions on the support moment at different phases of walking. The forward dynamic simulation results showed that, in normal walking, the ankle plantar flexors contributed significantly during single-limb-support. However, the ankle plantar flexors, knee extensors and hip extensors worked together during double-limb-support. In unexpected step-down walking, the important contributors on the support of the body during single-limb-support were not only ankle plantar flexors but also knee extensors. This study, analyzing the relative contributions of the lower limb joint moments for the body support, would be helpful to understand different unexpected walking conditions and compensatory mechanisms for various pathological gaits.

The equations of motion of two-wheeled vehicles, e.g. bicycles or motorcycles, are developed by using Lagrange's equations for quasi-coordinates. The pure rolling constraints between the ground and the two wheels are considered in the dynamical equations of the system. For each wheel, two nonholonomic and two holonomic constraints are introduced in a set of differential-algebraic equations (DAE). The constraint Jacobian matrix is obtained by collecting all the constraint equations and converting them into the velocity form. Equilibrium, an algorithm for searching for equilibrium points of two-wheeled vehicles and the associated problems are discussed. Formulae for calculating the radii of curvatures of ground-wheel contact paths and the reference point are also given.

Recently, the authors have developed a method for real-time dynamics of multibody systems, which combines a semi-recursive formulation to derive the equations of motion in dependent relative coordinates, along with an augmented Lagrangian technique to impose the loop closure conditions. The following numerical integration procedures, which can be grouped into the so-called structural integrators, were tested : trapezoidal rule, Newmark dissipative schemes, HHT rule, and the Generalized-${\alpha}$ family. It was shown that, for large multi body systems, Newmark dissipative was the best election since, provided that the adequate parameters were chosen, excellent behavior was achieved in terms of efficiency and robustness with acceptable levels of accuracy. In the present paper, the performance of the described method in combination with another group of integrators, the Implicit Runge-Kutta family (IRK), is analyzed. The purpose is to clarify which kind of IRK algorithms can be more suitable for real-time applications, and to see whether they can be competitive with the already tested structural family of integrators. The final objective of the work is to provide some practical criteria for those interested in achieving real-time performance for large and complex multibody systems.

This paper deals with modeling and computer simulation of a full multibody vehicle model for a driving simulator. The multibody vehicle model is based on the recursive formulation and a corresponding simulation code is generated automatically from AUTOCODE, which is a symbolic computation package developed by the authors using MAPLE. The paper describes a procedure for automatically generating a highly efficient simulation code for the full vehicle model, while incorporating realistically modeled components. The following issues have been accounted for in the procedure, including software design for representing a mechanical system in symbolic form as a set of computer data objects, a multibody formulation for systems with various types of connections between bodies, automatic manipulation of symbolic expressions in the multibody formulation, interface design for allowing users to describe unconventional force-and torque-producing components, and a method for accommodating external computer subroutines that may have already been developed. The effectiveness and efficiency of the proposed method have been demonstrated by the simulation code developed and implemented for driving simulation.

Many daily appliances for examples copiers, printers and ATMs contain the media transport system (MTS) and the slippage between the medium in the MTS deteriorates the performance quality of the whole system. The slippage of the medium in the MTS is affected by many parameters including the friction coefficient between the feeding rollers and the medium, the velocity of the feeding rollers, and the normal force exerted on the medium by feeding rollers. This paper focuses on the effect of the normal force on the slippage while the medium is being fed. For this purpose, we developed a two-dimensional simulation model for a paper feeding system. Using the simulation model, we calculated the slippage of the paper for different normal forces. We have also constructed a testbed of the paper feeding system to verify the simulation results. Experimental results are compared with the simulation results.

The development and implementation of an appropriate methodology for the accurate geometric description of track models is proposed in the framework of multibody dynamics and it includes the representation of the track spatial geometry and its irregularities. The wheel and rail surfaces are parameterized to represent any wheel and rail profiles obtained from direct measurements or design requirements. A fully generic methodology to determine, online during the dynamic simulation, the coordinates of the contact points, even when the most general three dimensional motion of the wheelset with respect to the rails is proposed. This methodology is applied to study specific issues in railway dynamics such as the flange contact problem and lead and lag contact configurations. A formulation for the description of the normal contact forces, which result from the wheel-rail interaction, is also presented. The tangential creep forces and moments that develop in the wheel-rail contact area are evaluated using : Kalker linear theory ; Heuristic force method ; Polach formulation. The methodology is implemented in a general multibody code. The discussion is supported through the application of the methodology to the railway vehicle ML95, used by the Lisbon metro company.

In this paper, the contact force between two colliding bodies is modeled by using Hertz's force-displacement law and nonlinear damping function. In order to verify the appropriateness of the proposed contact force model, the drop type impact test is carried out for different impact velocities and different materials of the impacting body, such as rubber, plastic and steel. In the drop type impact experiment, six photo interrupters in series close to the collision location are installed to measure the velocity before impact more accurately. The characteristics of contact force model are investigated through experiments. The parameters of the contact force model are estimated using the optimization technique. Finally the estimated parameters are used to predict the impact force between two colliding bodies in opening action of the magnetic contactor, a kind of switch mechanism for switching electric circuits.

This paper presents a precise and stable time integration method for dynamic analysis of vibration or multibody systems. A total system is divided into several subsystems and their responses are calculated separately, while the coupling effect is treated equivalently as constant force during time steps. By using iterative procedure to improve equivalent coupling forces, a precise and stable solution is obtained. Some examples such as a seismic response and multibody analyses were carried out to demonstrate its usefulness.

Controlling the friction between wheel and rail is direct and very effective measures to improve the curving performances of railway trucks, because the curving performances depend much on friction characteristics. Authors have proposed a method, 'friction control', which utilizes friction modifier ($KELTRACK^{TM}$ HPF) with onboard spraying system. With the method, not only friction coefficient, but also friction characteristics can be controlled as expected. In this study, MBD simulation is very valuable tool to foresee the effect of the control in advance of experiment with real car. And the creep characteristics of wheel/rail contact with the friction modifier takes very important role in the simulation. In this paper, authors propose a theoretical model of wheel/rail contact condition considering the creep characteristics of friction modifier, which is derived the application of principle tribological theories.

The analysis of human arm motion during steering maneuver is carried out for investigation of man-machine interface of driver and steering system Each arm is modeled as interconnection of upper arm, lower arm, and hand by rotational joints that can properly represents permissible joint motion, and both arms are connected to a steering wheel through spring and damper at the contact points. The joint motion law during steering motion is determined through the measurement of each arm movement, and subsequent inverse kinematic analysis. Combining the joint motion law and inverse dynamic analysis, joint stiffness of arm is estimated. Arm dynamic analysis model for steering maneuver is setup, and is validated through the comparison with experimentally measured data, which shows relatively good agreement. To demonstrate the usefulness of the arm model, it is applied to study the effect of steering column angle on the steering motion.

Based on an introduced optimal trajectory planning method, this paper mainly deals with the accuracy analysis during the function approximation process of the optimal trajectory planning method. The basis functions are composed of Hermit polynomials and Fourier series to improve the approximation accuracy. Since the approximation accuracy is affected by the given orders of each basis function, the accuracy of the optimal solution is examined by changing the combinations of the orders of Hermit polynomials and Fourier series as the approximation basis functions. As a result, it is found that the proper approximation basis functions are the $5^{th}$ order Hermit polynomials and the $7^{th}-10^{th}$ order of Fourier series.

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) approach. Several aspects that turned out to be crucial for the presented approach are discussed. The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist. In this paper the performance of several solvers is investigated regarding their suitability for the application to the usually highly stiff DAE. The substructures are connected with each other by nonlinear algebraic constraint equations. Further, partial derivatives of the constraints are required, which often leads to extensive algebraic trans-formations. Handcoding of analytically determined derivatives is compared to an approach utilizing algorithmic differentiation.

A three axes marine satellite antenna has been developed. As a design step, a CAD model for the antenna has been created according to the design requirements. Kinematic analyses are carried out to insure design specification and to check collision detection of the CAD model. Marine satellite antennas experience base motions, and a relevant control system should control the three antenna axis to point to the satellites accurately. A sensor fusion algorithm and a PIDA (Proportional, Integral, Derivative, Acceleration) control algorithm are designed and implemented to control the yaw, level, and cross-level angle of a small size satellite marine antenna. Antenna stabilization control experiments are performed using a test simulator which gives the antenna base motions. Experimental results show small pointing errors, which is less than 0.2 degree for the level, cross-level, and yaw axis.

This paper introduces a numerical method for integration of the linear and nonlinear differential dynamic equation of motion. The variation of acceleration in two time steps is approximated as a combination of both trigonometric cosine and hyperbolic cosine functions with weighted coefficient. From which all necessary formulae are elaborated for the direct integration of the governing equation. A number of linear and nonlinear dynamic problems with various degrees of freedom are analysed using both the suggested method and Newmark method for the comparison. The numerical results show high advantages and effectiveness of the new method.