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Hydraulic transformer is a significant component to develop the future energy saving hydraulic systems; however, the speed stability is one of the problems in such a machine because the rotor is unconstrained and the rotary inertia of the rotor is small. In this paper, aiming at the rotating speed of hydraulic transformer, a hydro-dynamic model of is proposed considering the nonlinear friction, oil compressibility and leakage. Both simulation and experiment are carried out to validate the hydro-dynamic model. Moreover, this paper theoretically analyzes the low-speed stability of hydraulic transformer based on the hydro-dynamic model for the first time. The mechanism of creep is discussed and the creep judgment method is presented. The influence of each parameter on creep is investigated, and the possible ways to avoid creep are explored. The calculations of the lowest stable rotating speed and the lowest stable flow rate without creep are given. This study is significant for the design and practical application of hydraulic transformer in the future.

In recent years, several novel homopolar inductor machine (HIM) topologies, such as rotors with the rectangular, arc-shaped, sinusoidal and triangle rotor slots, are developed. However, the influence of different rotor slots on the performance of HIM is not clear, and there is no basis for selecting rotor slots. Addressing this issue, a comprehensively comparative studies of these topologies with different rotor slot shapes are implemented. Firstly, the topology and operation principle of the HIM are illustrated. Then, the influences of rotor slot shape on the performance including the no-load air gap flux density, back electromotive force, inductance, torque, torque ripple and losses are systematically studied. Moreover, the stress distribution, modal and rotary inertia of rotor with four different rotor slots are analyzed. Based on the above analyses, the HIM with arc-shaped rotor slots is selected and its prototype is developed. Some electromagnetic performance indexes are tested to verify the rationality of analyses. This work clearly points out the advantages and disadvantages of HIMs with different rotor structures, which could be good reference for the selection of rotor slot shape.

Multi-Megawatt wind turbines have long, slender and heavy blades that can undergo extremely wind loadings. Aeroelastic stability of wind turbine blades is of great importance in both power production and load carrying capacity of structure. This paper investigates the aeroelastic stability of wind turbine blades modeled as thin walled composite box beam, utilizing unsteady incompressible aerodynamics. The structural model incorporates a number of non-classical effects such as transverse shear, warping inhibition, non-uniform torsional model and rotary inertia. The unsteady incompressible aerodynamics based on Wagner’s function is used to determine the aerodynamic loads. Governing differential equations of motion are obtained using Hamilton’s principle and solved using extended Galerkin’s method. The results obtained in this paper, related to clarification of the effects of pretwist, presetting and bending-torsion elastic coupling on the aeroelastic instability boundaries of the thin-walled composite beams. The obtained results are expected to be useful toward obtaining better predictions of the aeroelastic behavior of composite rotating blades.

The offshore wind farm is connected to the onshore power grid via a modular multilevel converter based high voltage direct current (MMC-HVDC) transmission, which results in decreasing of total rotary inertia of the power system. The frequency stability of the power grid will faces bigger challenges. This paper proposes a coordinated control strategy utilizing both the capacitor energy of the MMC-HVDC submodule and the over-speed reserve capacity of the wind turbine (WT). The strategy can provide fast frequency support for the power grid within the range of DC voltage and the reserve capacity WT. It further improves system inertia and avoids secondary impact on the grid frequency in the process of rotor speed recovery. Finally, the effectiveness of the proposed coordinated control strategy is verified by time domain simulation.

This paper analyzes the essence of commutation failure of HVDC transmission systems, and points out that the load model has an important influence on commutation failure. The Commutation Failure Immunity Index (CFII) is used to quantitatively calculate the influence of the load type and percentage of the induction motor load on the commutation failure. It is proposed that the induction motor load can provide the rotary inertia to the system at the instant of fault, suppress the converter bus voltage drop and reduce the probability of commutation failure. The above discussion is verified by electromagnetic transient simulation.

In this paper, the nonlinear three-dimensional dynamics of a micro-needle driven at ultrasonic operating frequencies is briefly derived. The micro-needle is simulated as an Euler-Bernoulli cantilever beam attached to a moving base. The equations of motion of cutting micro-needle are derived with Kane's method. The shear and rotary inertia effects are neglected by considering a slender-shaped beam with homogeneous and isotropic material properties. Furthermore, the elastic and centroidal axes of the cross-section of the micro-needle coincide so that eccentricity effects are not considered. The micro-needle is modelled with contact with an embryo zone pellucida, submerged in a fluid medium. The surrounding fluid is modeled as incompressible using the Morison equation. From the simulation model, resonant frequencies are determined. Experimental work is presented for perforation of mouse zona pellucida with the micro-needle PZT actuator driven at different frequencies. Experimental tests are conducted to determine a threshold frequency below which PZT actuated zona perforation is unsuccessful.

In this paper, the nonlinear dynamic behavior of the pre-twisted blades based on the Timoshenko beam theory has been investigated. The main purpose of the present work is to study the nonlinear dynamic response of uniform, rotating, cantilever pre-twisted blades. To this end, firstly, the coupled nonlinear equations of motion considering diverse parameters such as the hub radius, rotating velocity of the blade, pre-twist and pre-cone angles, shear strain, rotary inertia and warping of cross section have been derived step by step using Hamilton's principle. The obtained nonlinear partial differential equations (PDEs) of motion, which are included the bending-bending-torsion coupling terms, have been converted to the time dependent ordinary differential equations (ODEs) by applying the Galerkin partial discretization method. Finally, Euler-Gauss step by step numerical method has been employed to solve the obtained nonlinear ODEs. The obtained results illustrate that, considering the nonlinear strain terms in the formulation has significant effects on the dynamic responses of the pre-twisted blades. Furthermore, the results show that, increasing the pre-twist angle of the blade, decreases the amplitude of the blade response and the period of oscillations for bending vibration (in the Z direction) and torsional vibration. Furthermore, because of the stiffing effect of the centrifugal force, the amplitude of the blade response and the period of oscillations decrease with increasing the rotational speed. Besides, for evaluation purpose, the natural frequencies of the studied blades have been obtained by linearization of the obtained nonlinear equations of motion. The comparison of the obtained natural frequencies in this paper with those are available in the literature shows a good agreement.

This paper presents an investigative work about the direct speed control (DSC) of interior permanent magnet synchronous motor (IPMSM) based on finite control set model predictive control (FCS-MPC). A compensation is applied to the speed prediction model because of the unknown load torque and varied rotary inertia. And a multi-constrained cost function with dynamically adjustable weight factors is designed to realize speed tracking and guarantee the currents operating points lay on q-axis in d-q axis frame. The effectiveness of the proposed strategy is evaluated through simulations.

The on-line identification of the moment of inertia is researched, in order to improve the performance of servo system. The identification of the moment of inertia based on the recursive forgetting factor least squares(RFFLS), gradient descent (GDM)and model reference adaptive (MRA)methods is designed respectively. And the advantages and disadvantages of the three methods are summarized. The factors affecting the identification accuracy of the algorithm and convergence time are studied by simulation experiment. In physical experiment, the estimated values of RFFLS and GDM converge faster, but they have obviously oscillation. The estimated value of MRA converges slowly, but it has little oscillation. The estimated errors in steady state of RFFLS, GMD and MRA are 11%,24%and 10%. In order to reduce the estimated errors, the friction obtained by friction model is applied to the identification of the moment of inertia. The effectiveness of this method is demonstrated by experimental results.

This paper presents a study of the large angle maneuvers and high-accuracy attitude control of a small satellite which uses a variable inertia reaction wheel(VIRW). Based on the traditional kinetic model of a reaction wheel, a kinetic model of a VIRW with three-axis orthogonal variable inertia is established which takes rotational inertia as the physical variable. A characteristics model of the small satellite attitude motion is then established. This model takes rotational inertia change rate and rotational angular acceleration of the VIRW as a state variable and the satellite attitude angle as the output. The Golden-section control(GSC) law is designed for the attitude control of small satellites, and also tests the function of the control system designed in this paper through simulation. The simulation shows that the small satellite attitude control system based on the VIRW, which uses the GSC law designed in this paper, can achieve a stable control system and smooth transient process. When there is no external perturbed moment, this design won't produce any steady-state errors, and under the perturbed moment of 20mNm, there will be 0.005° error of attitude angle positioning. The simulation shows a good signal tracking performance under a 5°/s attitude angular velocity.

A knowledge of the inertia tensors and centre of gravity locations of rigid bodies and rigid mechanical systems is required in precise control of motion and in many other applications whenever the dynamics of them is significantly determined by these inertia parameters. This paper presents a new method for identifying the inertia tensor and coordinates of the centre of mass of a rigid body or of a rigid mechanical system. The proposed method is based on the work-energy principle and provides high accuracy of identification even on devices with essential dissipation. The tensor and centre of gravity location are defined on a single spherical motion — symmetric precession. The paper gives a survey of existing inertia parameter identification methods, the theoretical fundamentals of the proposed identification method, the hybrid identification device and data processing procedure with error estimation on dissipative systems using proposed and classical methods.

The disturbances of flexible spacecraft, such as the uncertainty of rotary inertia and the external disturbances, can be classified as norm bounded variable, harmonic variable, gradient bounded variable, etc. These disturbances severely impact the attitude stabilization of flexible spacecraft. Aiming at the attitude control of flexible spacecraft, a nonlinear controller combining sliding mode variable structure control and internal model principle is designed, which can suppress both the constant interference and the periodic interference. The close-loop system is proved to be stable based on the Lyapunov method and the numerical simulation results verified the effective of the control approach. Moreover, the results show the rapid convergence and high accuracy of steady state error, and the controller can reduce disturbances efficiently.

For the rotor speed of variable speed wind turbine (VSWT) is decoupled from system frequency, the system equivalent rotary inertia and primary frequency control ability are decreased with wind power penetration growing continuously. To solve the problems, VSWT with additional frequency control was studied. The dynamic characteristics of input and output power of VSWT during participating in system frequency regulation are analyzed, and the relationships between the active power increments and the duration of VSWT is quantified. A coordination frequency control strategy base on time sequence control is proposed. According to the control strategy, the VSWTs can participate in frequency regulation depending on the coordination of wind speed, power increments and duration. The simulation results demonstrate the effectiveness of the proposed control strategy, which can make full use of the frequency regulation ability of VSWTs as well as minimize the negative effects on system frequency.

Time-consuming calculations of overlapping areas among objects have become a bottleneck that restricts further improvement of evolutionary algorithms for circle and rectangle packing problems. This paper proposes a heuristic ant colony optimization (HACO) algorithm for the circle and rectangle packing problems with rotary inertia constraints (ICCRPP). The proposed heuristic method is used by artificial ants to construct the feasible layout schemes. Through the ant colony optimization, the optimal layout scheme can be gotten for ICCRPP. Because the introduction of the related layout knowledge in the ordering and positioning rules can make both the envelope radius and rotary inertia of the constructing layout scheme less. The numerical experimental results show that the computational efficiency and solution accuracy of HACO algorithm are satisfactory for ICCRPP.

The transmission mechanisms in servo systems have finite stiffness, therefore the elastic deformation and the rotary inertia would cause mechanical resonance in servo systems. Based on the theoretical analysis of the mechanical resonance, the quantitative relation between transfer function of the resonance and system parameters (including torsional elastic coefficient and load rotary inertia) is built. In this paper, the rational approximation of mechanical resonance amplitude frequency characteristics is calculated by vector fitting method in the presence of known system parameter. With different given system parameters, the nonlinear mapping between system parameters and the transfer function of mechanical resonance through sample training is established through sample training. Therefore, the effective prediction of the transfer function of mechanical resonance with regards to the variation of servos conditions can be realized.

Backdrivability is an important property in applications like haptics, where force or torque is exerted by the user onto the motor. Gears cause higher friction, which results in a reduction of the backdrivability. This paper investigates how the backdriving torque can be reduced without the additional use of expensive force-torque sensors. The friction compensation uses a predetermined mapping, that adapts the motor's supporting torque depending on the measured velocity. The inertia compensation depends on the acceleration multiplied by the motor's moment of inertia. The method was objectively evaluated by using a robot. Kinetic friction compensation with inertia compensation significantly reduced the backdriving torque by 66.67 % over all median, and 23.58 % over all average values from measurements with different velocity and acceleration profiles. However, the variance and torque peaks were increased. The inertia compensation showed slight benefits in comparison to kinetic compensation alone, but not throughout all measurements.

Piezoelectric inertia motors use the inertia of a body to drive it by means of a friction contact in a series of small steps. These motors can operate in “stick-slip” or “slip-slip” mode, with the fundamental frequency of the driving signal ranging from several Hertz to more than 100 kHz. To predict the motor characteristics, a Coulomb friction model is sufficient in many cases, but numerical simulation requires microscopic time steps. This contribution proposes a much faster simulation technique using one evaluation per period of the excitation signal. The proposed technique produces results very close to those of timestep simulation for ultrasonics inertia motors and allows direct determination of the steady-state velocity of an inertia motor from the motion profile of the driving part. Thus it is a useful simulation technique which can be applied in both analysis and design of inertia motors, especially for parameter studies and optimisation.

This paper presents a new method for identifying the inertia tensor of a rigid body on a specific spherical motion. This motion contains a stage of slowed rotation and a stage of reverse symmetric accelerated rotation, where one of the stages can be chosen to be non-program. The moments of inertia of a body about five positions of its instantaneous axis are defined on a single precession. The sixth moment of inertia is defined on an additional program rotation about a fixed axis. The method can be used on devices with essential dissipation.

Inertia momentum wheel is widely used for satellite attitude-control that requires fine pointing accuracy and stability. But, the inner disturbance torque and noises produced by the inertia momentum wheel seriously deteriorate the output torque precision. Accordingly, this paper adopts the adjustable PID algorithm, regulated by RBF network with a simple disturbance compensator in the torque-mode control system of inertia momentum wheel. Based the dynamics and analysis of disturbance torque, the RBF-PID controller with disturbance compensator are designed. The performance comparisons of the proposed method with conventional PID are performed to show the advantages of the former over the latter on many aspects, such as response time, overshot, anti-disturbance ability, etc.

Dynamic analysis and trajectory planning for a rigid-flexible manipulator is considered here. The manipulator under consideration consists of two links, the first link is rigid while the second link is flexible. Euler-Bernoulli's beam theory is utilized to model the elastic link where shear deformation and rotary inertia can be neglected if the cross sectional area is small compared to the length of the beam. The tangential coordinate frame is employed to describe the elastic deflection of the flexible link. The equations of motion of the manipulator are derived using the Extended Hamilton's Principle. The joints trajectory will be designed based on two different trajectories and the joints torques required to move the manipulator joints according to a prescribed trajectory will be obtained through the solution of the inverse dynamics problem. To validate the applicability of soft motion trajectory for flexible manipulators, a comparison with fifth-order polynomial trajectory is carried out for the first three mode shapes of the flexible link.

With the instruction of computational dynamics of multi-body systems theory, considering factor of the crankshaft system with variable inertia, the torsional vibration model of crankshaft system was established. Based on kinetic energy equivalence principle, the variable inertia of crankshaft system was analyzed by computational dynamics of multi-body systems method; and the characteristic relation curve between torsional vibration frequency and crank angle was attained; then the belt type distribution characteristic of critical speed was obtained. The analysis considering the nonlinear factor of variable inertia was complicated, but the result was much more approach to the fact. The whole analysis laid the foundations of diesel structure design, and provided a simple and feasible approach to torsional vibration analysis with variable inertia of other systems.

The advance of high-frequency response and micro-torque electric actuator motivates the study on high performance motor for load simulator. A novel high-precision swing-arm Voice Coil Motor (VCM) has been proposed in this paper. The research investigates the feasibility of this new structure applied to the VCM. Abiding by the equivalent rotary inertia idea, mechanical structure and magnetic field interactive design have been implemented with the electromagnetic simulation software-Ansoft's Maxwell. An iterative optimal design process is then proposed to maximize the force constant of the VCM and to minimize the inertia of the rotor. Simulation results are given to illustrate that the proposed design procedure can preliminarily achieve a satisfactory performance.

Flywheel is used to compensate the energy difference and to suppress the shafting torsional vibration in the diesel generator due to its pulsed load. In this paper, the relation between the rotational inertia of flywheel and the dynamic speed droop of generator unit and the shafting torsional vibration is analyzed on the basis of preliminary estimate of rotational inertia of flywheel. At last, a conclusion is made that kinds of factors should be considered fully while determining flywheel rotational inertia to achieve optimal performance.

The design of a dual-mode inertia motor involves an actuator that can generate translational and rotational motion without connecting the actuators serially. Traditionally, translational or rotational actuators should be stacked serially to have multi-axis degrees-of-freedom. The experimental results of this study display performance characteristics such as linearity, resolution, velocity and the most excellent operating frequency.

In this study, extension and flapwise bending vibration analysis of a rotating piezolaminated composite Timoshenko beam is performed both analytically and via finite element method. In the analytical part, energy expressions are derived by including the parameters for the hub radius, rotational speed, rotary inertia, shear deformation, slenderness ratio and ply orientation. The Differential Transform Method is used to transform the differential equations of motion and the boundary conditions into simple analytical expressions. In the finite element part, derived energy expressions are used to obtain the element stiffness and mass matrices. In order to model the piezoelectric effect correctly, some preliminary steps are performed and not only loads but also structural properties of the piezoelectric layers are added to the beam model. Numerical examples are solved to validate the correctness and accuracy of the built models.

the end position addition mass and activation joint rotary inertia have important effect on elastic motion stability of flexible manipulator arm. On the basis of mode analysis, the dynamics model of flexible manipulator arm is deduced using Lagrange equation, the state space expression and transfer function are deduced after state variable and input-output are selected. The necessary and sufficient condition of input-output stability and stability criterion of flexible manipulator arm are deduced, based on this, the effect of end position addition mass and activation joint rotary inertia on the motion stability of flexible manipulator arm is analysed.

The necessary and sufficient condition of input-output stability of control system and its significance to the desigan and control application of flexible manipulator arm are described in the place,then the necessary and sufficient condition of input-output stability is simplified to make the criterion simple and easy. It is pointed out in the end that the input-output stability criterion may be used to analyse the effect of end position addition mass and drive joint rotary inertia and mode rotary inertia on the input-output stability of control system of flexible manipulator arm.

Understanding the velocity response characteristic of the variable valve timing system under parameters of different work status has a very important influence on drawing up the system's control strategy. In this text, a simulation mold of the VVT system has been established based on AMESim. The system changed the engine's timing phase through turning the camshaft. The simulation results have registered that the speed of the engine and the engine oil pressure have a great influence on Phase-adjuster response characteristic as well as the structure parameters of Phase-adjuster. The engine oil's temperature and the rotary inertia of rotor were so small that can be ignored. We also got the flow feature of the oil control valve under control signal of different duty ratio.

The inertia force and moment of inertia of engine piston-connecting rod-crank is the main vibration source of motorcycle vibration. In order to reduce the strength of the vibration source, the method of singular balancing shaft is adopted to counterbalance the first-order inertial force based on the structure of single cylinder diesel engine. For the additional first-order moment of inertia of the balancing shaft and moment of inertia of piston-connecting rod-crank, the stiffness of the rubber suspension that along three different directions is optimized so that the corresponding torque of suspension mount reach the lowest level and in that way to isolate the vibration. Finally the vibration that results from the inertia force of engine and the moment of inertia is reduced synthetically.

In order to improve dynamic characteristics of electro-mechanical converter of electro-hydraulic digital valve, a novel low inertia rotating electromagnet with coreless rotor is proposed in this paper. The working principle of traditional multi-pole rotating electromagnet is discussed in detail firstly. Then the structure and magnetic circuit of low inertia rotating electromagnet is present. For the purpose of increasing the magnetic flux density of the air-gap, Nd-Fe-B and permalloy are used as permanent magnet and soft magnetic material, respectively. Dynamic response experiment is performed and results illustrate the low inertia rotating electromagnet has good dynamic characteristic which possess capability of fast rise time and smooth recurrence of sinusoidal input signal.

Low-frequency torsional resonance arising from large inertia load and elastic shaft causes vibration when industrial servo system is working, which degrades the system’s performance of motion control. This paper presents an adjustable inertia ratio control strategy based on designing disturbance observer, which the inertia ratio between the load and rotor is adjusted to an optimal ratio so as to suppress the low-frequency disturbance to the motor output shaft and load simultaneously, this algorithm allows that the servo system controls the movement of large inertia load smoothly and steadily. The effectiveness of the proposed concept is demonstrated theoretical analysis and simulation.

Material shape of car dumper during dumping is analyzed. The weight and rotary inertia of material are changed with the tipping angle during dumping. Material moment and rotary inertia on-line calculation thought is put forward. Object position measuring technology is applied to determine initial parameters and the graph display of whole dumping process is realized by coordinate conversion. The variety curve of dumping moment is drawn. The mathematics model of dumping moment is established and moment curve is analyzed, which provides for the design and test of parameters of transmission parameters.

To solve the problem of difficulty in precise locating of batch ball mill, the kinetic model was build, and parameters relationship between starting and shutting down were analyzed, control system was designed. At the stage of starting of ball mill, load torque, rotary inertia and so on could be acquired. Based on the relationship of ball mill kinetic parameters between starting and shutting off, parameters at the stage of shutting off could be predicted. With these parameters, the angle that the ball mill would roll after power off could be predicted. With the angle, the optimum spot to cut off power of ball mill could be find, and precise locating and stopping of ball mill could be implemented. The control system is simple in structure, easy for installation and suitable for the reconstruction of existing ball mills control.

The purpose of this research is introducing a mathematical model for investigating the structural dynamic stability of a three stages launch vehicle. The intended aim of this research is to reveal the effect of concentrate masses on dynamic stability of launch vehicle under a constant thrust. The launch vehicle is modeled as a free-free Timoshenko beam with variable moment of inertia and module of elasticity for each stage. Dynamic stability study with respect to: 1- the magnitude of rotary inertia and shear deformation parameters of the beam 2- the magnitude of constant follower force. Both divergence and flutter can occur over the range of free-free Timoshenko model.

This paper analyses the impact of moment of inertia on a spinning spacecraft. Spacecraft moment of inertia distribution is represented in the form of product of inertia terms in system inertia matrix. The cross product of inertia (CPI) for the body axes in the transverse plane is used to control conic motion. The attitude controller controls the spin rate in the spin axis and the angular rate in the transverse axes as well besides orienting spin axis. Dynamic equations are derived with cross product of inertia and are tested with different attitude control modes to test its effect. The analysis is done with and without cross product of inertia with a range of initial conditions to determine the maximum time taken by the individual module and finally concluded with simulation results. Finally attitude information is displayed in Attitude Control System (ACS) control panel.

For the purposes of investigating the free vibration response of the spatial curved beams, a set of deferential equations of motion are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius’ scheme and the dynamic stiffness method are then applied to solve these equations. A further numerical analysis shows that only a limited number of terms in the resultant provide a relatively accurate solution.

In the design of mobile electronics, power is one of the most difficult restrictions to overcome; and current trends indicate this will continue to be an issue in the future. Consumer electronic equipments are becoming small, portable devices that provide users with a wide range of functionality, from communication to music playing. The battery technology and the power consumption of the device limit the size, weight and autonomous lifetime. One promising alternative to batteries is to use parasitic energy dissipated in the movement of the wearer of device to power it. In this paper we designed a system included a rotary arm extending down from the sole, which ultimately drove the small electrical generator through a stepped-up gearbox. A one- way clutch mechanism was used to transmit torque to the gearbox. This allowed for additional spin following the initial impact of a step, also preventing lockup due to rotary inertia in the gears. The entire generator system was designed to fit in the heel of a standard running shoe, with the rotary arm compressing once during each heel strike.

Large inertia is beneficial for constant speed operation, whereas low inertia is advantageous in the applications where rapid acceleration is necessary. But it is not easy to change the inertia physically. In this work, the method of increasing/decreasing inertia is proposed. To realize the virtual inertia, acceleration information of the motor is needed. So an observer is utilized to obtain acceleration and disturbance torque estimates. Effectiveness of the proposed method was supported by simulation and experimental results.

A ship propulsion method, integrated hydraulic propulsion (IHP), was put forward and its characteristic was discussed. After that, dynamic mathematic model of IHP vessel was developed. Based on the model, dynamic response character of the system and the influences of four parameters (oil bulk modulus, rotary inertia, seawater density and oil temperature) upon the system were discussed. The simulation results show that IHP method is feasible. Oil bulk modulus and rotary inertia will influence the system dynamic behavior significantly. Seawater density and oil temperature will not only influence the dynamic behavior but also the steady state, so these parameters should be taken into account when an IHP system is to be designed. IHP method offers a new idea for ship design.

The main strategy in analyzing the motion of a rigid body is to split the motion into the linear motion of the CM and the angular motion of the body about its CM. This is because all particles composing the body show the same relative angular motion about the CM. In other words, one can describe the motion of the rigid body as a whole rather than those of the particles individually. The physical characteristics of a rigid body can be described by its inertial properties: mass and moment of inertia. For this reason, a major portion of discussion will be dedicated to the inertial properties of the rigid body: moment of inertia & inertia tensor.

Many large space structures, such as satellite's solar energy plates and a space station's strut platforms, can be modeled as a rotating flexible platform. For the active control of such structures, an accurate dynamic model for rotating flexible platforms is therefore desired. As the first step toward platform control, two sets of dynamic equations for the rotation of flexible platforms are presented. The first one is based on Mindlin's plate theory, which takes the effect of both rotatory inertia and shear deformation into account, and the second one is based on Kirchhoff's plate theory, which considers only the effect of rotary inertia. While the Mindlin dynamic model has three unknown distributed functions to solve, the Kirchhoff model has only one. The dynamic models of rotating flexible platforms described can also be considered as the more accurate dynamic models of flexible manipulators. >

The present investigation involves the validation of a technique for the determination of the moment of inertia of human lower leg and of the damping coefficient of the knee joint. A method based upon the theory of small damped oscillations of a system about its equilibrium position is used to measure the moment of inertia of human lower leg. This method, in contrast with the others, is simple and does not require highly sophisticated instrumentation. The validation of this method is performed using a cylinder of known moment of inertia and the small oscillation apparatus (SOA). The results obtained were highly reproducible, however, the average difference between the known moment of inertia and that measured was less than 15%.

The influence of shear, rotary inertia on the dynamic characteristics of flexible manipulators is studied through frequency analysis. In terms of the various geometric effects, dynamic models of flexible manipulators are set up and characteristic equations are derived. By using the analysis, the influences of shear, rotary inertia, axial force on the flexible manipulator are given.

There are some important parameters that must be taken into consideration in the design process of the actuator for a flexible single link robot. Among these important factors are the hub inertia and the proper tip mass (including the payload) for optimum performance of the flexible arm system. The main objective of the paper is to study the effect of the actuator inertia as well as the tip mass in the flexible hub torque through the solution of the inverse dynamics problem. For comparison, two reference trajectories; Gaussian velocity, and a polynomial profile are applied. The equations of motion are derived with the help of the extended Hamilton principle using the virtual link coordinate system and the pinned-pinned boundary conditions.