Physical and mathematical characteristics of fractal have been shown by many researchers since 1975. Many structures like fractal were discovered in nature and then some applications of fractal also have been developed in informatics or other engineering fields. But almost all of them use static characteristics of fractal. In this study, vibration characteristics of 2-dimensional fractal trees are discussed through vibration tests. The structures as a binary fractal tree and a ternery factal tree were produced as test pieces by using milling machine with numerical controller. The structure as a binary fractal tree showed dynamic behaviors like dynamic dampers in experiments.

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It is thought that it is effective to measure the change in the tilt-angle and the change in the intrinsic period for evaluation of structure. The field test with the bridge was executed by using a combined tilt-angle and acceleration sensor, and the control panel that had been developed this time. It is thought that the measurement of a steady tilt-angle and the measurement of the intrinsic period by the acceleration are possible as a result of the test.

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Considering the tooth profile error, the rattle of one pair of helical gear system is analyzed numerically. Two cases are treated, the case A where the effect of the profile error on the mesh stiffness is not considered, and the case B where the effect is considered. Because of tooth profile error, the amplitude of resonance curve becomes large. In low frequency region the amplitudes in the case A are larger than those in the case B, and in high frequency region the amplitudes in the case B are larger than those in the case A. (3) Chaos generates in wide frequency region in the case A.

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This paper treats the problem of analysis of steady-state vibration of a frame structure with breathing cracks. The breathing crack opens and closes during vibration. Since the opening and closing of the breathing crack depends on the sign of the bending moment and tensile force in the axial direction, the key point to this problem is explicit treatment of the bending moment and tensile force. In a previous paper, one of the authors presented a method to analyze vibration of a beam with breathing cracks. The presented method is based on the mixed variational principle which allows one to use deflection as well as bending moment as primary variables in the governing equation. In this paper the presented method is generalized so that it becomes applicable to frame structures. First the governing equations of a frame structure with breathing cracks are derived by the finite element procedure based on the mixed variational principle. Then a method to solve the derived governing equations by combining the iteration method and the harmonic balance method is presented.

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Recently, there is a high expectation for viscometer to measure polymeric solutions, adhesive agents, coating materials, abrasives, and so on. Vibration-type viscometer is known as a sensor to be able to measure time variation of the viscosity with change of the material characteristics. However, conventional vibration-type viscometer uses Quality factor of frequency response curve under external excitation, and requires the observation of the frequency response curve near the resonance peak. In this research, to overcome the drawback, we theoretically proposed a viscometer based on self-excited oscillation under positive linear feedback. The critical feedback gain which produces the self-excited oscillation corresponds to the viscosity. Also, from experimental results, the validity of the proposed method is discussed.

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In this research, we consider a three-link underactuated manipulator, whose first link is actuated and second link and third link are not actuated. According to the previous our research on two-link underactuated manipulator, we analytically investigate nonlinear dynamics and by using high frequency excitation of first link, we clarify through bifurcation analysis that the free links can be swung up and are stabilized at some configurations without state feedback of free joint.

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We apply the external feedback control technique to microcantilevers in tapping-mode atomic force microscopy. This approach enables us not only to control vibrations of the cantilevers but also to measure the sample surfaces simultaneously. The efficiency and validity of our approach is demonstrated by numerical simulations.

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This paper deals with the problem of vibration quenching using a Hula-Hoop. Quenching of perpendicular vibration is compared with that of horizontal one. Following was made clear from the numerical analysis: (1) The device using Hula-Hoop is very effective for not only horizontal vibration quenching but also perpendicular one in the region exceeding the resonant frequency. (2) Smaller damping of the hula-hoop is more effective in vibration quenching. (3) The Hula-Hoop without parametric excitation relation with the main system is more effective than the one with parametric excitation relation.

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This paper presents a method to calculate the critical flow velocity of fluidelastic vibration of tube array in the heat exchangers. The method is based upon the modal analysis technique, which combines the fluid dynamic force caused by cross flow and the vibration characteristics of the complicated tube array to obtain its response. The analytical method enables us not only to take into account the vibration mode of tube array and distribution of the flow velocity, but also to estimate the effect of anti-vibration devices such as spacer, connecting band and so on. Based on the numerical results of the fluidelastic vibration mode shape of no constrained tube array, the mode shape constrained devices along the flow direction are offered and its availability are confirmed by the numerical analysis and experimental evaluation.

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In this paper, we describe the response characteristics of vortex-induced vibration and random vibration of a circular cylinder behind another cylinder of five times larger diameter. Free vibration tests of an elastic circular cylinder whose both ends were clamped were conducted in a water tunnel for three different relative locations of the upstream cylinder as well as single cylinder tests. The onset flow velocities of in-line vortex-induced vibration and response amplitudes of random vibration obtained by the tests were compared with values predicted using the JSME standard 012-1998 to verify the evaluation methods in the guideline.

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To predict natural frequencies of high-pressure centrifugal compressor impellers accurately, we measured the natural frequencies of an impeller vibrating in a high-pressure gas environment. In order to clarify the effect of gaseous species, we used four different gasses as the surrounding gas. It is known that natural frequencies of pump impellers in water decrease compared with their natural frequencies in air due to the added mass effect. However, in our experiments in a high-pressure gas environment, the natural frequencies of the impeller not only decreased but also increased compared with those conducting under atmospheric condition.

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In the present papers, we propose a new approach for simulating the aerodynamic vibration of structures in a wind tunnel and discuss its application. The concept of the proposed approach is a step-by-step computer simulation using the measured external wind force acting on a structural model in the air flow of a wind tunnel. This approach is referred as to the New Hybrid Aerodynamic Vibration Technique (NHAT). In the part 1, at first, the concept and advantages are explained. In the next place, the development of a simulation system based on this approach and the accuracy of this system are described. In additional, the outline of conducted simulation by means of this approach is indicated.

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In the part 2, in order to verify and demonstrate the application of NHAT, two simulations are performed. First, the aerodynamic vibration of a square prism on a single-degree-of freedom elastic model is simulated in three-dimensional flow. Then, the air pressure field acting on the model is analyzed by means of the Proper Orthogonal Decomposition. Second, the aerodynamic vibration of a square prism is simulated using a multi-degree-of freedom elasto-plastic model. These simulations prove the broad applicability of NHAT. In additional, it is discussed whether NHAT can simulate the vibration of structures in liquid sodium even under in air flow or not.

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The FDC (Flow Dynamics Conveyer) has been often used in power plants and iron works because of superiority in quiet compared with a roller type conveyer and it is excellent in a low noise and low power. The FDC consists of a trough and a belt, and the air is supplied from a lot of holes provided on the trough. However, large vibrations occur when the flow rate becomes a certain value. This abnormal vibration is defined to be self-excited vibration caused by leakage flow induced vibration here. It is well known that the abnormal vibration occurs when the tapered flow channel is formed. The purpose of this study is to clarify the generation mechanism of the abnormal vibration. The experiment was carried out to examine the effect of various parameters such as taper angle θ, floating amount H on the abnormal vibration. As a result, the damping ability becomes small with increase of the taper angle and decrease of the floating amount. Furthermore it was clarified that the abnormal vibration occurs in θ>0.11H.

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This paper deals with theoretical stability analysis of an active feedback control of web flutter which occurs to the web with both ends fixed and tensioned. In this paper, a non-contact active feedback control method of web flutter by using movable plates set at inlet or outlet of the passage are developed and its analytical model is constructed. The equations of motion of the flexible sheet coupled with the fluid flow controlled by the movable plates are obtained. The characteristic equation of the system is derived as a function of the flow velocity in the narrow gap. As a result, it is shown that the web flutter occurs to the web with increasing the flow velocity, and is effectively suppressed by the proposed non-contact flow control devices and active feedback control method. Furthermore, calculation results are verified by the experiments.

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Flow-induced vibration occurs in the structures subjected to annular flow such as elastic beam in the narrow passage. Once the vibration occurs, the vibration becomes larger. In this paper, active control of the vibration of the axisymmetric elastic beam subjected to annular flow is investigated. The fluid-structure coupled equations based on the Euler-Bernoulli type partial differential equation and Navier-Stokes equation are derived including control terms. In this paper, two kinds of control methods are proposed. Applying the optimal control law to the coupled system, the unstable behavior is stabilized. Simulation studies are performed to investigate the efficiency of the proposed control method and the effect of the position of actuator on control performance.

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The evaluation methodologies for the flow-induced vibration instability of a long flexible beam due to an axial flow confined in a narrow passage have been reported. In this paper, by using this proposed analytical method, the parameter-studies are performed on the dynamic stability of elastic beam subjected to axial flow confined a narrow passage. The effects of support conditions of structures, structural damping, and fluid characteristics on the dynamic stability are clarified for safety dynamic design in industries. Especially, paying an attention on the vicinity of critical velocity, the effects as for stabilization and destabilization on flutter or divergence phenomena is investigated by changing fluid viscosity and structural damping.

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In this paper, we propose a new concept of tuned sloshing damper with variable damping system. This system suppresses sloshing by controlling fluid flow with a baffle plate, which is set in the TSD, and increases damping ratio of sloshing while TSD diffuses the vibration energy. Characteristics of the vibration control performance of TSD are investigated with RMS displacement ratio of structure with control the one against without control. As a result, it is found that vibration displacement of structure is suppressed as damping ratio of sloshing increases by controlling fluid flow.

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The liquid storage container (tank) is listed up as one of facilities which are apt to be damaged by earthquake in industrial facilities. As for earthquake damages of tanks, the sloshing phenomenon of the liquid free surface and the bulging one which is due to the interaction between the tank structure rigidity and the liquid pressure force become problems. Of these, we investigate a nonlinear sloshing. Although there are many papers which introduce the small parameter till its 3 power term for nonlinearity based the Galerkin's method in their theories, a modal approach to the nonlinear sloshing which superposes the linearized solutions using Fourier series representations is presented in the seismic response analysis on the nonlinear sloshing of a rectangular liquid storage container.

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This paper describes the experimental study of nappe oscillation at weir. We present how to suppress low frequency sound from nappe oscillation. Its sound can be suppressed by setting equipment at the lower end of a falling water sheet. Experimental results show the characteristic of nappe oscillation and effectiveness of the equipment on low frequency sound.

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In the present paper, the effect of twist-serrated fins around a bare tube on the Aeolian tone was experimentally investigated. We measured the intensity of velocity fluctuation, spectrum of velocity fluctuation, coherence of Karman vortex in the spanwise direction, and SPL of the aerodynamic noise generated from finned tubes with various fin pitches. An Aeolian tone induced by Karman vortex shedding was observed in the case of a finned tube. When the pitch of the fins decreased, the peak level of the sound pressure spectrum decreased. A correlation analysis between the flow field and Aeolian tone was carried out.

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In the present paper the attention is focused on effect of arrangement of in-line tube banks on vortex shedding, acoustic damping and acoustic resonance which occurred in the two-dimensional model of boiler. We have examined the characteristics of vortex shedding, acoustic damping and acoustic resonance generated from in-line tube banks with tube pitch ratio of 1.33, 1.44, 1.56, 1.67, 1.76 and 2.0 in the flow direction. As the tube pitch ratio in the flow direction decreased, the acoustic damping increased and the vortex shedding frequency became broad-band. The resonance mode of low acoustic damping was generated in the broad-band vortex shedding frequency. It was easy to generate acoustic resonance of low order transverse mode as the tube pitch ratio in the flow direction increased.

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Acoustic resonance may occur in heat exchangers such as gas heaters or boilers which contain tube bundles. The purpose of this study is to develop modeling method of vortex shedding synchronization because this is the most essential part of critical flow velocity prediction. Here, acoustic resonance level dependence of spatial correlation of vortex shedding is expressed by coherence function between wake-oscillator behaviors in any two locations in the cavity. The feedback effect in synchronization of vortex shedding is represented by resonant level dependence of the wake-oscillator phase fluctuation range. This method gives the result that when resonance level increases, synchronization level in the tube bundles also increases, which seems to be a reasonable conclusion. Experimental method to identify the undefined parameters in the proposed method is also mentioned.

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The present study intended that search for turbulent flow noise source in a wing profile centrifugal blower. First, we examined velocity and direction of flow with flow visualization of blade around. These brought out large change in flow in blade trailing edge of impeller center. At best efficiency point, it becomes small. Next, fluctuating pressure in blade trailing edge was measured with probe microphone. These brought out turbulent flow element of sound pressure level that was high from impeller center to lateral plate side.

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The present study intended mechanism clarification of blade passing frequency (BPF) noise generation in wing profile centrifugal blower. First, visualized flow in the vicinity of cut-off that source of BPF noise brought out relation between blade passing and flow. Next, fluctuating pressure on cut-off surface was measured by probe microphone. Distribution of fluctuating pressure pinpointed major source of BPF noise. Measurement of fluctuating pressure on cut-off by probe microphone and detection of blade position by laser brought out relation between blade passing and fluctuating pressure. Measuring transfer function in casing cleared that the noise was amplified by resonance.

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In the previous report, the concentrated mass model was proposed to analyze a nonlinear pressure wave phenomenon in a rigid cylindrical straight tube. In this paper, we apply the model to an elastic pipe. To confirm the validity of the proposed elastic pipe model, we perform experiments on a silicone tube, and compare the experimental results with the numerical results. The numerical computational results agree very well with the the experimental results. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem in an elastic pipe.

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To make progress the technique of forecasting a serious plant trouble caused by acoustic resonance and sympathetic vibration, vibration experiments were performed using an actual mock-up piping by sweep test and steady operations of pump, and numerical simulations for the experiments were performed. When experimental condition of the valve opening ratio were changed from 5% to 30% or when experimental condition of the pipe diameter were changed from 3/ 4B to 1B, the simulation results were agreement with the experiment ones on the whole.

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Fluid in the channel can be transported by vibrating the wall of the channel, and this phenomenon has been researched for the application to a peristaltic pump. This study aimed to investigate the relationship between the motion pattern of the wall of the closed channel and transportation volume of flow and evaluate the transport efficiency of a peristaltic pump. In order to simulate the volume of flow, cellular automata was used. The rule for cellular automata considered wall attenuation and pressure loss for quantitative evaluation. The results of simulation show that there is the best vibration form of the wall that maximizes the transport efficiency of the fluid.

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In this study, the combustion oscillation model which includes effects of various fuel components is presented. The model is based on ignition-delay model, which is proposed by Z. M. Ibrahim, but didn't consider the effect of fuel components to ignition-delay time. So, we evaluated the ignition-delay time by using CHEMKIN and considered the effects of various fuel components. As a result, H_2 tends to cause unstable thermo acoustic oscillations. And incombustible components, such as CO_2 and N_2 tend to suppress the combustion oscillation. In addition, we investigated the effect of 2-staged combustion and swirl number in MGT combustor.

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This paper concerns an analysis of a quasi-passive dynamic walking (quasi-PDW) biped robot on level ground. In this study, a linearized "simplest walking model" is adopted as the biped walker model, and the constant torque inputs at the hip joints which simulate the effect of the gravity on a slope are introduced to make the quasi-PDW on level ground to have a periodic walking motion. The equilibrium points of the Poincare map and their dependence on the input torque are numerically studied, and the structure of the domains of attraction is investigated. A control algorithm which enhances the stability of the equilibrium is proposed based on the linearized Poincare map, and the optimal gain is designed in terms of the pole assignment to maximize the local stability of the equilibrium. In addition, a study concerning the stride control is carried out, and based on the structure of the domains of attraction, the existence of a control law that can direct the walker from one equilibrium to another for a desired stride is suggested.

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By recent researches, heel and toe of human is clarified important element in human walking. However, previous many researches of passive dynamic walking has omitted heel and toe from foot, and these researches has hardly been argued about the influence that heel and toe gives to passive dynamic walking. So, the purpose of this study is to clarify effect of heel and toe in passive dynamic walking. As a first step in this study, this paper clarify that passive dynamic walker with heel, ankle and toe enables stable walking. Experimental results showed that passive dynamic walker with heel and toes enable stable walking.

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In Passive walking robot, kinetic energy is lost whenever its leg is landing. An expression of this energy loss is derived as speed ratio from equations of plastic collision between typical biped waking model and the ground. According to a derived expression of speed ratio, energy loss increases as a step is lengthened. However, it is necessary to lengthen a step to increase walking speed. In this paper, first, a walking model using spring for saving kinetic energy as potential energy is proposed. Then, performances of proposed walking model are evaluated by numerical simulation based on rigid multibody dynamics. Finally, parametric excitation by the vibration of spring is examined about a proposed walking model.

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We examine the control method that doesn't use angular sensors of the thigh link in the leg of the six-legged robot. Concretely, an observer (Kalman Filter) is designed by using a mathematical model in which the inputs are the driving torque of the thigh links in the supporting legs and the outputs are the body height, pitching angle, and rolling angle. It is shown that the proposed control method controls the posture by using the state vector estimated by this observer, and the six-legged robot can achieve stable walking by the 3D simulations and the experiments.

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Mobile inverted pendulums are expected to be applied to personal mobility and robots which is used in near human living space. Although this mobility always need to be stabilized, main approaches to control it has been methods based on a linearized model or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied and a nonlinear controller is constructed. Usable methods to select controller parameters and estimate the domain of attraction are also introduced. Simulation results showed that the IDA-PBC controller performs fast responses theoretically ensuring sufficient domain of attraction.

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This paper discusses SSM (Sensor Steering Mechanism) for lateral guided vehicle with an articulated body which is allowing the vehicle to change moving directions. The last paper demonstrates the geometry of SSM for the articulated vehicle of which bending joint is located at the center of wheel base. SSM presents a stable lateral guiding characteristics for automated vehicle which follows a straight and curved path created by guideway. A control system of articulated robotic vehicle is constructed with a line following controller and an articulation angle controller. The former outputs a target angle of articulation angle of body and the latter controls the articulation joint by a PD control law. The PD controller exists a control delay. This paper is focuses on the control delay of articulation joint controller and reconstructs an experimental robotic vehicle used in previous paper to improve the control performance. The effectiveness of control delay is demonstrated by the simulated and experimental data.

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This paper proposes the synthesis procedure for the motion control system to reduce slippage in a planetary rover. The slippage in the rover is mainly due to degree of contact force against the loose soil on the planetary surface. In this paper, particularly, it is confirmed that the slippage generating in early phase of the rover motion is involved with acceleration and deceleration in the driving mechanism through the experiment. Hence, we propose the command shaping method of the target acceleration to prevent the increase of the slippage and the acceleration profile is then derived only by solving a regulator problem with an initial velocity and taking account of the maximum value in acceleration.

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This paper addresses a problem of tracking control for a two-wheeled mobile robot with sideslip. A nonlinear mathematical model based on kinematics and dynamics is developed, which includes a adhesion model between the pneumatic tiers and the ground, and is more practical than non-holonomic constrained model. Then, a nonlinear controller is designed via back-stepping approach. Simulation results illustrate the effectiveness of the proposed control law.

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Recently, a new tendency has emerged control not only linear motion but also rotational motion in high accuracy manufacturing fields. Many five axis-controlled machining centers are therefore in use. However, it is difficult to achieve the flexible manufacturing systems by means of the methods based on the use of these machine tools. An industrial dual-arm robot has gained attention as a new method to control both linear motion and rotational motion accurately, in attempt to control a working plate like a machine tool table. In the present report, the cooperating dual-arm motion is demonstrated to make it feasible to perform a stable operation control, such as an application of controlling the working plate to keep a ball rolling around a circular path on it.

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This paper proposes a horizontal locomotion method for a hopping mechanism which utilizes resonance. The system has two mass that can be resonated by actuators on them. Each mass is captured in a certain level of compression by latch mechanism and release of each latch mechanism with time lag yields the system's hop which realizes horizontal locomotion. Numerical analyses and experiment validates the proposed system.

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Recently, the needs of autonomic robot have risen in the point of production. So, it is necessary for these robots to recognize the external environment by using vision sensor such as camera. When camera is used in robot system, camera calibration have to be performed to calculate three dimension position from image gotten by the camera. In this research, we decide on the optimal camera position to fulfill improving object position recognition accuracy and verify it by handling task using robot hand.

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Since the reduction gears of motors in robotic arms have rotational stiffness, residual rotational vibration occurs in robotic arms after the motor stops. The input shaping method is effective for suppression of residual vibration in machining tools. However, this method can be applied only to time-invariant system. Therefore, an improved method is proposed for suppression of residual vibration to time-variant systems. The effectiveness of the proposed method is verified through simulation.

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Pneumatically controlled and actuated planar snake-like device has been developed. Each joint is controlled by hardware-implemented algorithm inspired by snake's lateral undulatory locomotion. Therefore the device progresses forward whenever the lateral movement is constrained, such as a winding groove by which the tip element is guided. Without lateral constraint, the device behaves like a elephant trunk. This paper focuses on the behavior as an manipulator. Endoscopic manipulation through a complicated cavity is demonstrated by experiments.

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Recently, research has focused on pneumatic robot. Here, we present artificial muscle-type pneumatic actuators as the driving source of a robot hand that is both safe and flexible. We develop a five-fingered robot hand with pneumatic actuators of low-pressure and low-volume. To control this hand in high accuracy, we construct the spring-damper model of the pneumatic actuator. We produce a I-link arm. We construct the model of 1-link arm that considers moment of inertia and the viscous friction coefficient. We construct a control system for 1-link arm. In addition, the effectiveness of the constructed model is verified by the experiment.

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This paper describes motion control of two-degree-of-freedom parallel manipulator which used pneumatic artificial actuators. This parallel manipulator uses three pneumatic artificial actuators. We adopted minimum number of pneumatic artificial actuators that could move two-degree-of-freedom joint, because this manipulator is applied to a joint of robot hand. It is known that high-nonlinearity with the hysteresis characteristic exists in the relationship between inner pressure and contraction ratio of pneumatic artificial actuators. Therefore, in this study, we perform motion control by using the control system which integrated hysteresis compensation.

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In recent year, it is reported the analysis of roll and lateral vehicle behaviors due to the road input. However, there are few researches about the suspension control which considered the suspension characteristic that influences these dynamics. In this paper, a vehicle model including the suspension characteristic that influences these dynamics is constructed, Pade approximation of the time delay of the road input from the front wheel to the rear wheel is carried out, and the robust control system design which sets the lateral acceleration of the vehicle to one of the amounts of evaluation function is proposed. As the result, it was confirmed that proposed control system is effective in reducing the lateral behavior of the vehicle due to antiphase road disturbance.

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Many studies have been done on improving ride comfort and driving stability for vehicles. Semi-active suspensions with variable dampers and variable stiffness stabilizers have attracted much attention recently due to their low cost, low energy use, and safety. Several systems have been put into practical use. However there is a possibility that these devices interfere in each other, because they are separately controlled. Therefore, it is desirable that these devices are controlled by an integrated control design method for suspension system. This study aims at establishing the integrated control design method for the semi-active suspension system which consists of variable dampers and variable stiffness stabilizers. The computer simulations were carried out to verify the availability of the proposed method.

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This paper presents a method to suppress the vertical bending vibration of electric railcar by using traction motor. Dynamics of the truck with parallel cardan drives can be controlled by torque of the traction motors. This paper proposes a control scheme to reduce vertical vibration of truck frame by the traction motor torques, and shows that they can decrease vertical bending vibrations of carbody. The motor torques are added with the traction torques of the control scheme in reverse phase for two traction motors of a truck, and they are designed based on the sky-hook control theory. The simulations show that the control scheme using traction motor torque improves ride quality level about 9 dB at the center of carbody.

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The vertical elastic vibrations of railway vehicle carbodies are needed to reduce from the viewpoint of riding quality. The first bending mode and diagonal distortion mode are commonly observed almost all railway vehicle carbodies. The natural frequencies of the two modes exist around 10Hz which is known to be a sensitive frequency for human. In this paper, a vibration reduction method about the two modes by using active mass dampers is suggested. A stationary excitation test for an actual railway vehicle is conducted to confirm the feasibility of this method. As a result of the excitation test, two modes of above mentioned elastic vibration of the carbody are reduced successfully.

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This paper concerns the suppression of the contact force fluctuation between the pantograph and the overhead contact catenary of high-speed railway vehicles based on the concept of the impedance control. For the better compliance, the mechanical impedance of the pantograph at the contact point is to be reduced in the dominant frequencies of the disturbance which are determined by the span length and the vehicle velocity. To this end, an impedance control law which imitates a pantograph structure with a virtual Maxwell damper is designed to introduce a resonance characteristic tuned to the dominant frequency. Numerical simulations and experiments are presented to show the performance of the proposed control strategy.

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The critical steering angle that the self-centering of the steering wheel occurs is one of the important measures for steering maneuverability. It is shown that this critical angle is influenced by the damping coefficient of the torsion bar if slight steering torque is applied just before releasing the steering wheel. Meanwhile, torque assistance device equipped vehicle generates assistance torque based on the deflection angle of torsion bar. Hence, the exceedingly high damping coefficient may cause deterioration of the assistance torque. Analytical results on the adequate range of the damping coefficient in view of both assistance torque and self-centering is shown.

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