The eigenvalue problem of Helmholtz's equation is of importance because various physical phenomena are governed by this equation. This paper presents a method for solving the boundary value problem governed by Helmholtz's equation haying a circular outer boundary and a number of eccentric circular inner boundaries. In this problem, it is difficult to satisfy the multiple connected boundary conditions. The present anlysis uses the point-matching approach for treating the inner boundary conditions, and presents the expression for finding the eigenvalues. Numerical calculations have been carried out for the system having one, two or four eccentrdc circular inner boundaries.

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An exact method using power series expansions is presented for solving asymmetric free vibration problems for thick shells of revolution having meridionally varying curvature. Based on the improved thick shell theory, the Lagrangian of the shells of revolution are obtained, and the equations of motion and the boundary conditions are derived from the stationary condition of the Lagrangian. The method is demonstrated for thick shells of revolution having elliptical, cycloidal, parabolical, catenary and hyperbolical meridional curvature. The results by the present method are compared with those by the thin shell theory and the efflects of the rotatory inertia and the shear deformation upon the natural frequencies are clarified.

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An exact method using power series expansions is presented for solving asymmetric free vibration problems for shells of revolution having meridionally varying curvature and thickness. The governing equations of motion and the boundary conditions are derived from the stationary conditions of the Lagrangian of the shells of revolution. The method is demonstrated for shells of revolution having elliptical, cycloidal, parabolical, catenary and hyperbolical meridional curvature. The natural frequencies are numerically calculated for these shells having second degree thickness variation.

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An approach is proposed for the numerical estimation of free, forced and transient vibrations of an orthotropic plate using Green's function for a static bending problem. Its merits are as follows 1) free, forced and transient vibrations can be solved using similar programs, 2) the algorithm for computation is very simple, 3) one can readily estimate a complicated system such as a plate with an attached spring-mass system ··· using Green's function for a simple system, and 4) the numerical process can be separated into two steps. One is to estimate Green's function and the other is to solve a set of simultaneous equations or an eigenvalue equation. In the present report, this numerical approach is applied to free and forced vibrations of a simply supported orthotropic rectangular plate and its accuracy is discussed. Furthermore, a free vibration of an orthotropic rectangular plate with an attached mass in the center is discussed numerically. In the second report, the transient vibration of an orthotropic plate will be discussed.

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An approach is proposed for the estimation of free, forced and transient vibrations of an orthotropic plate by using Green's function for a static bending problem. In the previous paper, free and forced vibrations of a simply supported orthotropic rectangular plate were discussed to check the accuracy of the approach. As numerical examples, a free vibration of a rectangular plate with a mass attached in the center was discussed. In the present paper, a transient vibration of an orthotropic plate is discussed by applying Wilson's θ method to a set of discrete equations of motion. First, to discuss the accuracy, numerical computations are carried out for a simply supported rectangular plate subject to a uniformly distributing stepping load. Next, the approach is applied to a simply supported rectangular plate with an attached mass.

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The bouncing and pitching oscillations of a levitated body, which is assumed to be moved in a vertical plane and suspended by the magnetic force of a guideway, are examined theoretically and experimentally. A pair of nonlinear differential equations with periodic variable coefficients and nonhomogeneous terms, which govern the oscillations of the levitated body due to the guideway roughness, are derived. Using the above equations, it is shown that the oscillations are parametrically excited by the nonlinear component of the magnetic force even if the levitated body is symmetrical about the horizontal axis passing through the center of gravity. Also, the steady-state response of the oscillations under the parametric excitation is studied in more detail. Furthermore, the experimental results are shown to be in good quantitative agreement with the theoretical ones.

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The fundamental experimental study on the torsionally excited unbalance bending vibration and modal balancing were carried out for the simple flexible rotor at the frequency of 96.4 percent of the first resonance frequency. As a result, it was found that the torsionally excited unbalance bending vibration is perpendicular to the unbalance vector and proportional to the unbalance amount as estimated from the theory. It was also found that the initial unbalance of the test rotor was mainly due to the initial deflection of the shaft and that the deflection and unbalance changed slightly according to the angular position of the rotor. The sensitivity of mass eccentricity to lateral vibration was 0.3 under the torsional excitation with frequency of 96.4 percent of the resonance frequency and an amplitude of 0.048 1 rad. This experimental value was in good agreement with the theoretical one.

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This paper is concerned with a method for solving forced vibration problems of an arbitrarily shaped plate excited by a number of eccentric circular sinusoidal forces. The analytical solution for finding the displacements in the plate has been presented by use of the Fourier expansion collocation procedure. Numerical calculations have been carried out for four cases of circular, elliptical, square, and rectangular plates which are excited by one through four vibration forces. The effects of eccentricity and the size of circular forces on the vibration response have been clarified.

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A steel rod was rubbed against the circumference of a thin steel rotating disk in its axial direction. A rotating disk serving as a railway wheel was clamped at the inner radius and free at the outer radius. A squeal occurs at low rotational speeds, when a nodal diameter mode of the disk is stationary in the space-fixed coordinate system. At relatively higher rotational speeds, a squeal with a forward or backward traveling wave is generated. Either of the two waves may occur depending on the vibration of the steel rod. Analytical responses of the rotating disk in both the disk-fixed and the space-fixed coordinate systems agreed with the experimental ones.

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An analysis is presented for the soundproof characteristics of sandwich cylindrical shells with honeycomb core excited by axially propagating internal plane acoustic waves. The shell is exposed in a free field by the length of l, however is otherwise covered with infinitely long rigid cylindrical walls. To simplify the shell equations, it is assumed that the core material resists only transverse shear forces and that the facings resist only bending moments. The sound transmission loss of the shell wall, TL, is derived and calculated numerically for various values of the physical parameters involved.

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The optimization method for the driving pattern of a stepping motor to achieve high-speed access with open loop control is presented. The transient behavior of the start-up process is determined numerically, and the power of effective torque to accelerate the rotor is calculated from the response as an evaluation function. The optimal phase switching timings are derived from maximizing the value of the evaluation function by an iterative procedure, and the relation between the compensation step number and the maximum driving speed is investigated in detail. The proposed method provides an effective tool of analysis for this class of problems.

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This paper mainly describes experimental results on a feedforward compensation in a start up and a slow down process of a stepping motor. To reduce the residual vibration in damping process, the driving pattern in slow down is analized by applying similar optimisation procedure proposed in the previous paper. And it is demonstrated to eliminate perfectly the residual vibration by the compensation of a few steps in the slow down process. The validity and the reliability of the proposed optimal driving pattern are confirmed experimentally with respect to various numbers of compensated steps and wide range of driving speed.

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When a vibration is repeatedly driven, it is difficult to identify the multipulse driving series from the observed signal contaminated by additive noise; this is the case even when the transfer system is described by an all pole model and its characteristics are known because an unstable nonlinear optimization method, such as pole-zero modeling, is necessary. Thus, an inverse filter is ordinarily used. However, when the signal-to-noise ratio is low, even this method cannot estimate the multipulse series accurately. Therefore, we propose a stable method to estimate the multipulse driving series from the observed signal by using singular value decomposition and applying a tapering window. Finally, the principle is confirmed experimentally.

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In blower vibration produced by the mutual action between machinery and a fluid, the blades of the blower are sometimes seen to vibrate considerably. Furthenrmore in some cases, blade stress exceeds the allowable limit: this may be the result of reaching the fatigue limit, of cracks or of a bloken blade due to continuous running. The authors found that the unusually large vibration and the resonance tone occur not by the surging or the rotating stall, but by the acoustic resonance with blower duct, brought about because of the low blade stiffness normally found in low-pressure blowers constructed from, steel plate.

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Chain has a heavy weight and a high tension stiffness, which are distinctive feature different from that of string. This paper describes the nonlinear harmonic and parametric resonances of a roller chain stretched horizontally, which is regarded as a system with many degree of freedom, when the elongation of the chain during vibration is taken into account. The resonance treated in this report is one of the resonances excited by combined forcing and parametric excitations in which the ratio of the frequency of the forced lateral displacement acting at the left end to that of the tension fluctuation is 1:2. The vibrationn characteristics are computed for three kinds of chain and are compared with the ones obtained from the experiments. In particular the effect of the chain weight upon the resulting vibrations is considered. A fine agreement between experimental and analytical results was confirmed.

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This paper considers the parametric resonances of cantilevered columns subjected to a pulsating generalized Reut force. Both viscous internal and external damping are taken into account. The continuous columns are discretized into a dynamic system having finite degrees of freedom by applying the finite-difference method. The regions of parametric resonances are obtained by the second-order approximation of resonance conditions proposed by the authors. The effect of damping on combination resonances of sum and difference type is demonstrated.

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Cantilever-type dynamic vibration absorbers apply not only a force but also a moment to a main vibratory system. The vibration response of the main system with this type of absorber is analyzed using receptance matrices. By analogy with a conventional absorber of one degree of freedom, a method of optimal tuning of the natural frequency and damping of the absorber is derived. An index, the equivalent mass ratio which shows the effectiveness of the absorber, is defined. Numerical calculation and experimentation are carried out, and their results suggest that the cantilever-type absorber can be more effective than the conventional absorber.

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In this paper, the optimal tuning of the natural frequency and a damping of a cantilever-type absorber which is set on a railway wheel is derived. An index, the equivalent mass ratio, with which the effectiveness of an absorber can be easily estimated and evaluated, is defined. It is found that the cantilever-type dynamic absorber can be more effective that a conventional dynamic absorber with one degree of freedom. When N absorbers are set on a wheel and N/2 is different from the number of nodal diameters, the effectiveness of the vibration reduction dose not decrease even though the wheel is rotating.

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For the optimal control problem of an active dynamic vibration absorber (active DVA), this paper considers optimal control using a reduced-order model and three kinds of output feedback controls: the acceleration, velocity and displacement feedbacks of a main structure, adding together the displacement and velocity feedbacks of an active DVA. A unified approach for the optimization of the various controls of the active DVA for multidegrees-of-freedom systems is presented by identifying these as an optimization problem with control structure constraints. By carrying out numerical calculations and experiments, the characteristics of those controls were investigated and the usefulness of the present method was demonstrated.

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A theoretical study is presented for the damping of cylindrically curved plates with an unconstrained viscoelastic layer. Natural frequencies and loss factors of flexural vibration are calculated, using the equations of motion on the basis of the Flugge's shell theory. Boundary conditions considered in this paper are as follows: Straight edges are simply supported, and curved edges are simply supported, clamped. or free. It is found that the damping properties of a curved plate depend on the existence of extensional deformation in the datum surface of displacements. In the case of the inextensional deformation, the damping properties are similar to those of a flat plate. On the other hand, if the deformation is extensional, loss factor of a curved plate is smaller than that of a flat plate, and the decrease of the loss factor with bending depends on the aspect ratio, the ratio of thickness to length, mode of vibration and boundary condition.

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This paper deals with the application of dual dynamic absorbers to nuclear piping systems to accomplish high damping value and reduce seismic response at resonance frequencies. The transfer matrix method is used for designing the dual dynamic absorbers as well as for determining the optimum mounting location. The effectiveness of the dynamic absorloer is demonstrated by suppressing the first three resonance peaks in the 3-dimensional model piping system.

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In order to guarantee the ride comfort of a high speed curving vehicle, two conditions must be fulfilled. One is that the lateral stationary acceleration felt on board the curving vehicle should not exceed 0.8 m/s². The other is that the car body should not tilt too abruptly at the entrance and exit of a curve. As it is difficult for a natural pendulum vehicle to fulfil these conditions simultaneously, the introduction of car body tilt control is necessary. In this report, fundamental aspects of the tilt control system are studied by means or a simplified physical pendulum model, in which the swing angle of the pendulum is feed-back-controlled through target value functions, and the system dealt with here is shown to be promising.

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In case an air-spring-suspended vehicle comes to a halt on the cant diminish part of a curve exit, the action of the air spring levelling valve may bring' about the extreme decrease of the wheel load of the upper rail side leading wheel. As the vehicle starting in this state is in danger of derailment, the occurence of such a state should be avoided. Numerical analyses of a quasistatic, nonlinear 18-degree-of-feedom system show that such a dangerous state can be avoided by selecting appropriate pre-set values of the differential pressure valve.

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On the truck of the general construction with the supporting stiffness both in the longitudinal and lateral directions of axle, the authors analyzed theoretically the forced hunting phenomena of a bogie truck having a small clearance in the connecting position between the truck frame and the bolster anchor where the spring and friction are connected in series against truck turning. The analysis revealed that the forced hunting phenomena of a bogie truck is affected by various factors: the wheel tread conicity, the bolster anchor stiffness, the clearance between the truck frame and the bolster anchor, the frictional force of the side bearer, the supporting stiffness of axle, the running velocity and others. According to the calculation, the authors clarified that the upper vibration of the truck disappears by selecting a suitable value for the supporting stiffness of axle and the small clearance existing between the truck frame and the bolster anchor has a bad effect on the truck vibration. Furthermore, the investigation of complicated nonlinear phenomena and the target values for the design of a high-speed truck are presented.

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The problem to suppress transient vibration at the access motion of a multidegrees-of-freedom flexible mechanical system is assessed. The procedure to derive an optimal vibrationless motion and input force are generally formulated using the modal equation of motion for a multidegrees-of-freedom flexible mechanical system. A combined control of a control point velocity tracking feedback together with the vibrationless feedforward input is describcd. Next, this method is applied to an access control for a rotational flexible arm positioning system. It is shown from the experiment that the transient vibration can be suppressed well using the combined control of collocation velocity tracking feedback and a vibrationless feedforward input.

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A tendon mechanism to control the position and the vibration of an elastic rotating arm is presented in which a motor torque is given through a driving stick and a tendon to a moment stick attached to the elastic rotating arm at a certain point. The optimal control theory taking account of the spillover of residual modes is applied to the control mechanism. By carrying out computer simulations and experiments, the usefulness of the present control mechanism and method was verified. Especially, the vibration reduction of higher modes is remarkable in comparison with the wellknown mechanism in which the edge of an arm is driven directly by a motor without a tendon.

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The step response in the axial direction of a rotor suspended by five axis-controlled active magnetic bearings was measured and compared with two kinds of numerical simulations; a simple model and an FEM model. Tests were performed up to a large rotor displacement which exceeded the linear range of the design condition. The agreement of the simulated results of the FEM model with the experiments was superior to that of the simple model. Factors considered only by the FEM model were the two-dimensionality of the magnetic field including leakage flux, voltage-current characteristics of the control coil, non-linear magnetic characteristics of the pole pieces (B-H curve), and eddy currents. The most influential factor was the magnetic leakage flux which increased the induced voltage and the time constant of the control coil.

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This paper proposes a new control method for quadruped walking robots in which the leg-support-exchange is lithely implemented. First, the authors formulate the leg-support-exchange phenomenon in 'Trot' using Lagrange's collision equation. Then the continuous walking can be numerically analyzed. Secondly, we propose a new control algorithm for leg-support-exchange. The conventional high gain local feedback causes many problems such as slip and excessive high torque in the leg-support-exchange phase of dynamic walking since it is impossible in this phase to prepare the proper reference values beforehand. In this algorithm, the control law is changed to 'free mode' or 'constant current mode' in order to adjust to the exvironment. The effectiveness of the proposed control strategy is confirmed by computer simulation and experiments using the walking robot 'COLT-1'.

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The static characteristics and damping characteristics of groove-compensated annular thrust air bearings are analyzed. The finite element method is applied to obtain a numerical solusion of the Reynolds equation, and a computer simulation method is developed to obtain a dynamic response of the shaft supported by the bearing. Based on the computed results, the effects of various specific design parameters of the bearing on the static characteristics and the damping characteristics are discussed. The principles for the optimization of the bearing design are proposed.

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An investigation of sound generated from a two-step reduction gearbox was carried out in order to obtain basic information for the reduction of sound. Four test casings having different rigidity were prepared. The rigidity was varied by material and thickness of the casing. Casing material was cast iron and aluminum cast. Furthermore, test gears having an accuracy of Class JIS 1, tooth profile error, and pitch error were used. The experiments were carried out to put one of these test gears in the gearbox for each one. The gearbox was driven with and without load, and the sound generated was picked up by a condenser microphone. Using the signal thus obtained, sound pressure level measurement, real time frequency analysis, and sound waveform observation, etc., were carried out. From the experimental results and considerations, the fundamental characteristics of the sound of a gearbox having different casing rigidity were clarified, and some basic information for reduction of sound generated from gearboxes was obtained.

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Recontly, techniques to strengthen the texture of the cast iron matrix have been studied, which has certainly resulted in an improvement of its mechanical properties. For example, the flexural fatigue strength, impact fatigue strength, etc., are markedly improved by austempering, that practically allows cast iron to be used as a functional material. In this paper, using gears manufactured from austempered ductile iron, their pitting strength was experimentally studied, and at the same time their practical serviceability was compared with that of conventional carbon steel (S 45 C) gears.

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For tightening bolted joints, the calibrated wrench method is widely used in practice. However, this method is not so accurate since the measurement of axial tension is indirect. In the previous paper, the statistical distribution of magnitude of the axial tension in bolts, which were tightened by the calibrated wrench method, was formulatcd using the ellipse of confidence limit. This paper shows the distribution of probability density of the axial tension and screw characteristics from an experimental analysis. Measurements were performed on several examples to check the analysis and to confirm the effectiveness of the proposed technique, that is, the increase of initial axial tension.

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This paper describes an entirely new theoretical approach to turbulent lubrication problems with surface roughness effects. Based on the logarithmic velocity distribution law in the turbulent boundary layer, the resistance formulas for pressure and shear flows in the lubrication films are formulated in both smooth and homogeneous rough surfaces. Moreover, introducing the concept of equivalent pressure flow, the generalized turbulent lubrication equation considering the surface roughness effects is derived. Some numerical results for the modified turbulece coeffients are presented in the graphic form for various values of relative roughness, and the effects of surface roughness on the turbulent lubrication are discussed.

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The newly proposed boundary lubrication model in the previous reports is applied to many surfaces (slideways) and the boundary lubricating ability of lubricants is examined thoroughly. The secondary microconstruction of surface asperities and the load carrying pressure distribution of adsorbed lubricant film in contact are taken into consideration in the proposed lubrication model. As a result, it is clarified that the proposed model is pertinent for estimating the boundary lubrication ability of lubricants. The boundary lubricating ability of lubricants varies with the materials and finishings of the surfaces. This may be caused by the difference of lubricant adsorbability, i. e., the lubricant adsorbability may seriously be influenced by the surface construction and the energy state of the surfaces.

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In the previous paper, the authors investigated the fluctuation of oil-film pressure and the vibration of cylinders caused by a periodical change in the width of the contact surface. The calculated results were obtained by solving a Reynolds equation and an equation of motion of the cylinder simultaneously, on the condition that the load on the cylinder is so low that the elastic deformation is negligible. In this paper, the effect of the contact-surface-width variation on the elastohydrodynamic line contact has been studied by solving the above-mentioned equations with a formula of elastic deformation and with a formula of pressure dependence of viscosity. One of these calculated results indicates that, under the condition of elastohydrodynamic lubrication, the oil film shape is changed with time similar to wave motions.

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One of the gear lubrication methods, the oil bath lubrication, is affected by an agitation loss on the temperature rise. In order to reduce the agitation loss, a visualization of the agitation appearance is required as well as the measurement of the agitation loss. The purpose of this paper is to clarify the behavior of lubricant flow in the K-H-V planetary gear unit which was used in the hydraulic drive system for heavy machines. In a visualizing experiment, adequate visualization equipment containing transparent liquid paraffin as a lubricant was used and agitation losses of the equipment were measured. The lubricant flow in the planetary gear unit was explained in terms of the changing position and movement of each component. Furthemore, some components in the equipment were modified, and the lubricant flow behavior vs. agitation loss characteristic relationships were discussed.

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A noncontact optical measuring method of surface finish in electrical discharge machining under working fluid is developed. The principle of the surface roughness measurement is based on laser reflection characteristics from a rough surface. In order to evaluate the surface roughness by angular distribution of reflected laser intensity, the 2nd-order moment and the gloss ratio of intensity distribution are introduced. The former turned out to be available for a synthetic evaluation of average roughness Ra and auto-correlation length. The latter was found to have a good correlation with Ra values. The effect of the reflactive index of working fluid on the two parameters was made clear, and it has become feasible to measure the surface roughness in electrical discharge machininq under the working fluid.

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The analysis of aerodynamic noise radiation from a circular cutting tool with a columnar tooth model is made. Particularly, this experiment deals with a circular cutting tool with a tooth length of 14.3% to 47.6% of tool diameter. Correlations between aerodynamic noise and the flow of neighboring tooth model that is a noise source are clarified. From the experimental results, an aerodynamic noise spectrum at farfield agrees with spectrum distribution of the vortex that was generated behind a columnar tooth model, and a principal noise source distributed at an appointed end of the tooth. A spectrum distribution behind a tooth model that is calculated by a tangential velocity of flow on the tooth model and a velocity of inflow to the tooth model agrees with experimental results.

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The effects of static stiffness of surface grinding machines, and the grinding conditions upon the grinding force and the surface characteristics of fine ceramics are described. There is a critical point in the relation between the table feed rate and the grinding force under the condition of constant removal rate. Fine ceramics ground at a lower table feed rate than the critical point and in an up-cut grinding condition exhibit a surface of quasi-brittle fracture and a greater grinding force. Grinding at a higher table feed rate and in a down-cut grinding exhibits a quasi-plastic flow surface and a lower grinding force. The surface grinding machine with a lower static stiffness exhibits quasi-plastic flow surfaces.

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The purpose of this paper is to finish the rotor of a screw-compressor using a fly tool. It is very useful to use a fly tool in the manufacturing of the rotor, but this has not yet been put to practical use. The reason why is as follows : Analysis of a fly tool profile requires complicated calculations, so a large computer is needed. The machining time also requires more than many other conventional methods. So this study deals with the means of solving these problems. To obtain the fly tool profile, a new method is introduced to shorten the calculating time and the memories, using only a personal computer. A new manufacturing method is introduced to shorten the machining time using a fly tool and three hob teeth.

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A determination method for redrawing ratios has been proposed by analyzing the redrawing process of cylindrical shells from flat circular blanks using an elementary theory of plasticity. These redrawing ratios were calculated using a criterion based on the reduction of the maximum deep drawing energy. Variation of redrawing ratio with profile radius, blank thickness, frictional force, blankholder load and strain-hardening exponent were obtained using a developed computer program aimed at rationalizing, planning and simulating the redrawing process. It is shown that the maximum deep drawing energy decreased about 10-40%, comparing the predicted drawing energy by the usual determination method for the redrawing ratios.

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A determination method for the redrawing ratios has been proposed by analyzing the redrawing process of cylindrical shells from flat circular blanks using the elementary theory of plasticity, and by applying multi-objective optimization theory. These redrawing ratios were calculated using the minimax optimization of a compromise solution of multi-objective optimization theory. These theoretical results on the variations of redrawing ratio with profile radius, blank thickness, frictional force, blankholder load and strain-hardening exponent are presented using a developed computer program aimed at rationalizing, planning and simulating the redrawing process. It is shown that the maximum non-attainment value decreased to about 20-70% compared to those values of other optimization criteria.

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Based on Bassani yield function, a numerical analysis of axisymmetrical shrink-flanging is attempted, and the effect of anisotropic properties on the stress and strain distributions and the drawing force is examined. The Bassani function is found to be more useful to predict the strain distribution than Hill's conventional yield criterion. A parameter for estimating the formability of metal sheets in deep-drawing is proposed and its validity is confirmed experimentally.

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It is necessary to derive a proper method of estimating the change of angular velocity or the change of crossing angle of a rotating shaft which is driven through a universal joint. From our experiments, a rotating shaft which is driven through a universal joint has a tendency to produce a metalic sound of high frequencies. when in an abnormal state. Then we investigate the new method of estimating the condition of a rotating shaft by analyzing the distribution of frequencies of a sound due to the angular velocity variation.

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A method for determining the nodes, the inflection points, and the maximum-and minimum-curvature points of the coupler curves of Watt six-link mechanisms is proposed for the purpose of their automatic classification. The double points of the coupler curves of mechanisms, in which the fixed and driving links are the binary links or the binary and ternary links, are determined respectively as the points that the two-link chain or the compound three-link chain, in which the end pairing points are the fixed pairing point and the coupler point, can locate their inverse positions. The nodes are distinguished by two relative angles of the component two-link chains from the ordinary intersections. A curve of the curvature of the coupler curve is presented in order to determine the remaining characteristic points and to describe the properties of the coupler curve as a single-valued function.

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A index of motion-transmission characteristics τ of Stephenson six-link mechanisms which have two closed five-link loops including fixed and driving links was presented in the preceding paper. Here, we investigate the relation betweenτand the sensitivities of the angular displacements of the links to the deviations of the kinematic constants and the one between τ and the forces acting at the pairs to the external forces on the links. Generally speaking, the average of the sensitivities S and the one for the forces acting at the pairs F decrease rapidly in the interval [0, 0.3] and slowly in [0.3, 1] as τ increases. The τ-S and τ-F relations are approximated by the regions bounded by two rectangular hyperbolas which are modified by the coefficients determined from kinematic constants. Consequently, it is possible to estimate the values of S and F of any mechanism at the given crank angle by means ofτ.

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Knowledge engineering is applied in the area ol production engineering, and an expert system for process planning in production facility design is researched. This expert system is developed in order to assist an inexperienced planner to make a decision in process planning. In this system, the knowledge data dealing with machine types and those makers are described using frame and ruled representation, and the system is programmed with UTILISP. An inexperienced planner uses this system to select the value corresponding to the required product quality from the knowledge data base. After all the machine types have been reviewed, the sequence and the optimum numbers o f those machines are decided. Through the application of the developed system to a process planning of parts like a shaft, it is ascertained that the Artificial Intelligence technology is effective as a tool assisting process planners in production facility design.

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In the grafting operation of vascular prostheses, decision variables are tensile force (F) during pre-clotting and required time (t) for pre-clotting. An optimization problem is constructed which contains three objective functions; maximize the porosity (Q₁) (to maintain initial porosity over a long period of time), minimize the porosity (Q₂) after pre-clotting (to reduce bleeding from the vascular prosheses during grafting), and minimize the required time (t) for pre-clotting (to reduce required time for grafting). The following regression equations are formulated using experimental data: Q₁=2850+8.7F and Q₂=αexp(-0.038t) where α is 38 or 311 according to the sample blood A or B drawn from two dogs. The tensile force (F) is assumed to have no relation with porosity (Q₂), thus enabling two-criterion decision making to be applied. The approaches of the three solution methods; ε-constraint approach, goal programming and surrogate worth trade-off method, have also been applied. Consequently, the most effective approach is goal programming. The same solution is obtained for different blood samples A and B.

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