The design and production system of the conical involute gear is developed. This system is composed of gear cutting method, gear grinding method, over-ball measurement for control of finishing dimensions, tooth surface measurement, tooth surface analysis, tooth action and normal allowable load between two mating gears, and the design of a pair of gears. As a result, the conical involute gears came to be used in a wide range of applications. This paper presents the research and development of the conical involute gears for more than 25 years, many applications, and a new possibility for tomorrow.

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Generally, the specifications of the actuator system robustness and the disturbance or noise are often provided in frequency domain. Traditional observer design method is based on a state space structure in time-domain approach of a linear system. In this paper, an observer designed using the transfer function in frequency domain is described. This method is composed of a diophantine equation and only three design steps are required to construct the observer. An estimation error was chosen for the evaluation of observer characteristics, and the simulation results show the effectiveness of the proposed method.

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This paper describes the current status and future works of micro robots factory. For the latest demand of micro production, the miniaturized mechanical system such micro-mechatronics and instruments is the one of key technologies for providing several micro parts with a higher accuracy. Although it is known that the new technology of molecular machine has the great benefit to change the industries as well as human lives, the micro mechanical system ranging a few milimeters is still important to realize the reliable productivity. For these years, an unique micro robots system which is organized many tiny robots with tools and sensors has been developed. In our group, the small robots that are composed of the piezo elements and the electromagnets for providing the accurate inch worm locomotion, are employed as the base motion mechanism and several unique micro tools have been implemented on them. In the experiments, several actual applications such micro machining, bio cell operating as well as surface defect detecting are demonstrated.

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Tribology has been recognized as key science to save energy, to save consumption and to realize reliable and durable machines. Solution of engineering problems is therefore the most important project of tribology research in U. K. On the other hand, the limit of the performance of modern high-tech machinery is often governed by characteristics of the contact interface. In such high specification machinery, tribology is increasingly essential as the key design input to achieve ultimate performance. A new concept of machine design from the viewpoint of tribology is therefore necessary : "Tribologically-based machine design, defined as design of the overall system based on to achieve ultimate tribological performance" in addition to the more conventional "design of a reliable mechanical element based on tribological understanding." Tribological research for tribologically-based machine design is believed as new direction of future tribology.

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A method for predicting gear noise produced by a gear system was developed. This method calculates the distribution of sound pressure around the gearbox and identifies the areas from which noise radiates intensely. According to the sound-power level calculated from this pressure distribution, a low-noise gearbox was designed by adding ribs. The appropriate adding points were then calculated from the viewpoint of mass variation. It was found that to decrease the noise, ribs should be added in two places : (i) along the line with maximum curvature through the antinode of the gearbox's vibration mode or (ii) the minimum-length line which crosses the most contour lines through the maximum point of the sound-pressure contour map. It was also found that in the case of a gearbox with a vibration mode in which the gearbox side faces vibrate in opposite directions, noise can be effectively reduced by connecting the ribs on both side faces.

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For further vibration reduction of a gear system, we discuss about availability of active vibration reduction gear system that has transverse and rotational PZT actuators. Because main vibration component is mesh frequency component, there is a possibility that gear vibration can be suppress rather easily than other types of machinery. As a foundation, the active vibration reduction gear system is operated changing the phase and amplitude of PZT actuator force and vibration behaviors are measured.

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Due to tooth surface deviations, various kinds of vibration occur depending on mutual geometry of mating gear. From the aspect of ensuring the vibrational behavior, however, it is essential to distinguish individual vibration cause from another, or tooth surface deviations which are the origin of the vibration. Especially, for frequencies other than mesh components, it is quite difficult to predict its existence. This paper proposes a technique to identify the vibrational characteristics inherent to each gear, driving and driven, from acceleration measurement by using a synchronous averaging triggered with once per revolution signal of individual shaft. The test was done using several gears at driving shaft, those are finished by different methods such as indexed generation, continuous generation, etc. The result suggest the measurement is applicable to gear surface inspection.

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This paper describes a simulation on the tooth stiffness of the helical gears, which is used to calculate the rotational vibration of helical gear pair. Theoretical stiffness curve of helical tooth pair has a turning point that depends on transverse contact ratio and overlap contact ratio. The stiffness curve for the start and end part of meshing has a different shape compared to that for the center part of meshing. In this paper, a new approximate equation, which considers the notable effect of turning point, is proposed. This new approximate equation can express the variable behavior of stiffness more precisely than the traditional Umezawa's equation.

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In order to investigate the application of a damping alloy to gears, a damping alloy spur gear was compared with a thermally refined chromium molybdenum steel spur gear in term of their fatigue strength and dynamic performance. The fatigue test was performed using a power circulating type gear testing machine. The failure mode of the damping alloy gear was the tooth breakage at the tooth fillet and the plastic deformation on the tooth flank, and that of the steel gear was the pitting. The fatigue limit of the damping alloy gear was higher than that of the steel gear. In the wavelet maps of both the vibration acceleration of the gear box and the sound pressure near the gear box, the frequency range of high wavelet intensity of the damping alloy gear was smaller than that of the steel gear. Consequently, it was clear that the damping characteristic of the damping alloy gear was superior to that of the steel gear. Therefore, it coud be said that a damping alloy can be applied to gears under low load operating condition in this experimental range.

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The crossed axle traction drive developed by atuthors has been applied to the new mechanism of CVT. The input and output shafts attaching conical disks are parallel and a idler shaft having conical roller at the end is placed perpendicular to the input/output shafts. The relation between the movements of each axis to change a ratio is analyzed geometrically. Because the spin is generated during the speed change, the shape of curved disk was devised to decrease the amount of spin. The design procedure of shape of disk and roller are introduced and the effects of them are evaluated by the experiments using a prototype CVT.

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The jumping characteristics at the driven pulley of L type synchronous belt drives are experimentally and analytically discussed. The number of the driving and the driven pulley teeth is the same and the wrapping angle of the belt on both pulleys is radian. The jumping of synchronous belt occurs when the elongation of the free span of tight side belt is more than a certain value. In this paper, the experimental results of the belt winding condition on the pulleys are compared with FEM analysis "ABAQUS/Standard" is used for the simulation and analysis of the belt. The simulation of the FEM analysis of the wrapping angle of the belt on the driven pulley is almost the same with the experimental result. FEM analysis of the load distribution at just before jumping on the driven pulley compared with the experimental results.

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The use of silent chains for automotive cam drive systems spreads rapidly because of the excellent noise performance. However, it is still needed to develop a silent chain with lower noise. In this study, high frequency noise is analyzed experimentally. The generation mechanism of high frequency noise and its influence on noise level is revealed.

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The use of FEM is useful for analysis of meshing in synchronous belt. In this study, meshing of timing belt with round tooth analyzed. The influence of tooth ratio on the tooth load distribution and contact situation between belt and pulley is discussed. Comparison is carried out by changing the tooth ratio from 1 to 1/2.

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This paper presents a study on effects of carburized parts on residual stresses of case-hardened thin-rimmed spur gears with asymmetric web arrangements. A heat conduction analysis and an elastic-plastic stress analysis during the case-hardening process of thin-rimmed spur gears with asymmetric web arrangements were carried out of various case-hardening conditions by the three-dimensional finite-element method (3D-FEM), and then residual stresses were obtained. The effects of the case depth, the carburized parts (tooth surface, gear-side, rim, web surface), the web structure, the rim thickness on the residual stress were determined.

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This paper presents a study on bending fatigue crack propagation estimation of spur gear teeth. An analysis of bending fatigue crack propagation path of gear teeth on the basis of the fracture mechanics was carried out for various rim thicknesses by means of the FEM. Crack lengths and propagation paths in the bending fatigue process of spur gear teeth were measured for various tooth loads by the crack gauge. Calculated crack propagation paths were compared with measured ones, and the validity of this calculation method of crack propagation path was confirmed. On the basis of these calculated and measured results, an estimation method of bending fatigue crack propagation (path and length) of gear teeth was proposed.

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In order to develop the case-carburized gear for the high load-carrying capacity, the relation between the mechanical property of material and the surface durability of gear was studied. The experimental materials were the Cr-Mo-Si steel that the silicon was increased in chemical compositioin and the JIS Cr-Mo steel. First, the influence of temperature on the mechanical property of material was examined by means of a heating oil bath. Secondly, the effect of material on the surface durability of the gear was investigated by using a 2-roller-type contact fatigue tester. In the Cr-Mo-Si steel test rollers, the following results are obtained in comparison with the Cr-Mo steel test rollers : (1) The decrease value of hardness is low in the heat pattern with the high temperature. (2) The large pit and the spall do not occur under the rolling/sliding contact condition. (3) The endurance limit (the spalling life) is improved.

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A compensation method for work setting errors in form grinding of gears is proposed. In the method, the setting errors of the gear work are measured and additional motions to cancel out the setting errors are calculated. In this paper, the usefulness of the proposed error compensation method is confirmed through the grinding tests under the eccentric error of the gear work. The method makes it possible to set the gear work to the worktable without cnetering and to realize automatic gear grinding.

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We developed and made involute-cycloid composite tooth profile gear to obtain high performance. The driving performance in involute-cycloid composite tooth profile gear is influenced by a variation in center distance because of the tooth profile based on cycloid tooth profile. In this study, we calculate transmission error and tooth root stress against center distance. Further, we measured tooth root stress and transmission error, and the driving performance for the involute-cycloid composite tooth profile gear was examined.

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Conical involute gears used for marine transmission are mostly helical conical involute gears. Besides these gears are not intersecting axis gears but also nonintersecting-nonparallel axis gears. In this case the contact between tooth surfaces of a pair of gears is point contact. Hence the tooth surface durability is generally small. In this research is aimed at the establishment of the design and production system of the Concave conical gears for marine transmissions. In this paper, first the gear tooth action of a pair of nonintersecting- nonparallel axis gears is analyzed. Secondly, test gears are made. Tooth bearing marks are in good agreement with the theoretical ones.

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The conical involute gear is the involute gear that external form is a cone. The strength design of the conical involute gear has not been established yet. The contact between tooth surfaces is a point contact. Therefore, in the design of the conical involute gear, the evaluation of tooth surface strength is more important than bending strength. A fatigue test is performed in order to evaluate the allowable contact stress of tooth surface. Since the material of the test gear is normalized steel, and tooth surface is worn out during this test. By this research, tooth surface form under examination is measured and it considers how wear of tooth surface. The final aim of this research is establishment of strength design of the conical involute gear.

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The contact between tooth surfaces of a pair of conical involute gears is point contact, so the load carrying capacity is generally small. The point of contact between tooth surfaces locates in the plane of contact. The contact ratio is obtained as a pair of gear mating in the plane of contact, and this is called the normal contact ratio. Concave conical gear is developed in order to overcome the weak point of the conical involute gear. The contact between tooth surface of Concave conical gears is point contact theoretically, but it becomes a line contact under the load. For this reason, in order to define an equivalent axial contact ratio, which is equivalent to the axial contact ratio of the helical gears, a curved plane of action was newly introduced. In this paper, the contact ratio of Concave conical gears is presented as the sum of the normal contact ratio and the equivalent axial contact ratio.

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The VGR rack & the pinion have the characteristic that the rack stroke changes according to the pinion rotation angle. It is used for a power steering in order to improve that stability of straight high speed running and steerage of turning. It is difficult to analyze the contact, because a tooth profile is complicated. In this research, the theoretical new calculation of the line of contact of the VGR rack & the pinion is shown.

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A new pedaling mechanism for bicycle was developed based on Z mechanism. First the most suitable mechanism was determined from the classifications of Z mechanism. Next the new pedaling mechanism was designed and made for trial. This new pedaling mechanism was compared with the conventional mechanism by experiments. Both input forces on pedals and output torque were measured in experiments. Experimental results prove possibility of this new mechanism for bicycle pedaling.

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The human body consists of skeleton, dermis and flexible muscle of spindle form. In this study, we aim to realize the artificial muscle that is comparable with natural muscle from the viewpoint of flexibility, power and response. It results to the serious problem such as the short circuit and intertwines together that bunches SMA coil springs like the natural muscle cells. We constructed a SMA artificial muscle actuator protected by "Rolled film tube" made of heat-resistant film as a mechanical element flexible in the axial direction, and experimented on characteristics of output force driven by PFM method as used in the natural muscle. Consequently, we found the possibility this actuator can be driven by natural nerve impulse.

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We have been developing a resonantly-driven piezoelectric micropump using active-type check valves in place of conventional passive-type. It actively controls open/close motion of check valves using piezoelectric actuator installed into inlet and outlet. In the previous paper, frequency characteristics of the flow rate without load pressure were investigated using a prototype micropump fabricated with the effective size of 17×8×11(mm)^3. In this paper, load characteristics and bi-directional flow characteristics are experimentally investigated using an adequate timing control for valve closing motion. Maximum flow rate of 65(mm)^3/s and maximum pressure of 0.2MPa are obtained at the driving frequency of 2.8kHz. Besides, it is ascertained that optimal values of phase shift against voltage for driving pump chamber are 15° for inlet check valve and 195° for outlet. Based on the obtained results, a sheet-type active shuttle valve that has a unified valve-body for inlet and outlet check valves is proposed and a novel micropump with the effective size of 10×10×10(mm)^3 using the shuttle valve is fabricated and tested.

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MR (Magneto-Rheological) fluid is a functional fluid whose apparent viscosity is controlled by the applied magnetic field intensity. A valve using MR fluid called the MR valve features simple structure without moving parts. This paper improves the response of the micro MR vale that applies magnetic field to the MR fluid through a thermo-control magnetic circuit composed of a permanent magnet, a thermosensitive ferrite and a Peltier element. First, a thermo-control magnetic circuit that concentrates the thermal input to the thermosensitive ferrite is proposed. The characteristics of the magnetic circuit between magnetic field intensity and temperature of the thermosensitive ferrite are experimentally investigated and the improvement of the response is confirmed. Second, a 3-port micro MR valve is designed and fubricated. The characteristics of the 3-port micro MR valve among load pressure, flow rate and temperature are experimentally clarified.

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Electro-Conjugate Fluid (ECF) is a kind of dielectric fluids and a kind of functional fluids, which produces jet-flow (ECF-jet) by applying high voltage between electrodes. The ECF-jet generated between needle-type electrodes and ring-type electrodes is called ECF-jet with needle-type electrodes. In this study, novel microactuators using ECF-Jet with needle-type electrodes is proposed. In this paper, firstly, the characteristics of ECF-jet with needle-type electrodes are experimentally investigated. It is ascertained that the pressure due to ECF-jet with needle-type electrodes is increased by miniaturizing each dimension of the electrodes. The characteristics are suitable for microactuator. Secondly, a novel microactuator using ECF-jet with needle-type electrodes which is actuated by the same principle as well-known Bourdon tubes is proposed and fabricated. Next, another type microactuator which has two-degree-of-freedom is proposed and fabricated. Future works are fabrication of the tube with lower elasticity for improvement of characteristics of actuators.

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This paper reports the development of micro motors using Electro-Conjugate Fluids (ECFs). ECF is a kind of dielectrc fluids, which produces jet-flow by applying high DC voltage between electrodes inserted in the fluid. By applying this phenomena of ECFs to motor principle, simple structure and lightweight micro motors can be realized. We call these motors ECF micro motors. In this study, effect to the output characteristics of DP-RE-type ECF micro motors for increasing the electrodes thickness is investigated by using 2-layered DP-RE-type ECF micro motors with inner diameter φ9mm and inner height 1.9mm, and also 8-layered DP-RE-type ECF micro motor with inner diameter φ9mm and inner height 1.0mm is designed and fabricated in order to realize more poweful multi-layered DP-RE-type ECF micro motors. In conclusion, it is confirmed it is effective to increase electrodes thickness for realization of more powerful DP-RE-type ECF micro motors, and obtained max. output torque is 55μNm at 6kV for fabricated 8-layered DP-RE-type ECF micro motor.

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This paper describes the capability of a pin-typed tactile display to present virtual striped textures. Each pin of the tactile display was driven by a bimorph PZT ceramic actuator; the stroke of the pin was about 1 mm. The size of the pin-array was 8-by-8; the pin-array typed tactile display was mounted on a mouse. Two display pads were produced; one's pitch of tactile pins was 1 mm; the other's was 1.8 mm. In order to evaluate presentation capabilities of the tactile display, the authors conducted a series of psychophysical experiments. In the experiments seven human subjects adjusted a crossing angle of a comparison texture to be equivalent to a standard texture. From the experimental results, it was found that the pitch of 1.8 mm was enough to present the striped textures, and that the pin stroke being larger than 250 μm at least was need to present them.

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The stick/slip distribution in the contact area between the finger and grasped object is important information for precision grip of human. The deformation of finger in precision grip depends on the stick/slip distribution. Therefore the device displaying sensation of local slip makes it easy to grasp objects using remote controlled mechanical hand. The purpose of this paper is to design the device displaying sensation of local slip using finite element analysis. As a result of analysis, it is confirmed that there is possibility of displayng sensation of local slip using the tactile display device which stimulates finger through the deformation of an elastic body.

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This paper describes a development of an ultrasonic clutch as a new passive element for a haptic device using passive force feedback. The ultrasonic clutch can solve conventional problems of passive elements such as time delay, instability, and large size by using unique characteristics of ultrasonic motor such as high response, silent motion, and nonmagnetic feature. It is also designed to be smaller than conventional ones by cogitating its structure. The clutch fixes or unfixes the rotor by use of ultrasonic levitation phenomenon. First, we designed the structure of the ultrasonic clutch using an equation of ultrasonic levitation phenomenon, and results of both structural analysis and frequency analysis of the stator. Then we manufactured the ultrasonic clutch and conducted a driving experiment. Finally, we successfully verified that the maximum value of the levitation force was around 20N and the static friction torque of the ultrasonic clutch was up to 0.14Nm.

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Energy circulation efficiency of surface acoustic wave motor was investigated by changing the electrodes design. At basic design, the circulation power was about 30W when the driving power was 10W. When we used 24% wide aperture one direction IDTs for circulation electrodes, the circulation power was about 37W against 10W driving power. By using grating reflector for one directional IDT, the circulation power was improved up to 50W.

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The driving performance of a surface acoustic wave (SAW) motor using a silicon slider is influenced by the diameter and number of projections arranged on the contact surface of the slider. In order to improve the performance, it is necessary to clarify the influence of the these projection parameters. In this paper, the simulation model which confirmed validity in previous research is applied to the SAW motor using the silicon slider, and the new simulation model considering the influence of the projection parameters is proposed. Moreover, the validity of the proposed simulation model is evaluated from the comparison with experimental results.

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This paper describes a new configuration of SAW (surface acoustic wave) fluidic device. The SAW device using LiNbO_3 was fabricated to transport and atomize liquid. This device interacts with liquid on IDT electrodes, whereas conventional SWA device interacts on wave propagation lane. We tested six types of liquid; purified water, tap water, ethanol, and fluorinert (FC40,FC70,FC77). Ability of liquid transportation was evaluated by observing spout flow. Among those six liquids, fluorinerts, ethanol, and purified water were successfully transported, whereas tap water was not. By coating electrodes with urethane resin, every liquid including tap water was successfully transported. Also, atomizing ability of the fabricated device was tested. Every liquid was successfully atomized, both on coated and non-coated devices.

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To drive a motor in vacuum condition, many factors must be considered, such as friction and heat generation. Therefore it is difficult to use typical motors in vacuum condition. Besides, in some vacuum applications like EB lithography, SEM, and TEM, electromagnetic motors are unlikely to be used since existence of electromagnetic field is a fatal problem. This paper proposes the application of non-contact levitation electrostatic motor using Dual Excitation Multiphase Electrostatic Drive (DEMED) system. Electrostatic motor is driven with high voltage and low current that generate a very small magnetic field. In this paper non-contact levitation and driving control systems for DEMED are proposed. A non-contact levitation motor using DEMED utilizes the same electrodes for non-contact levitation and driving. For controlling attractive force, bias voltage is superposed onto driving voltage. Levitation and driving were realized with levitation gap of 200μm and the maximum driving speed of 20mm/s.

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A laser tracking system useful for measuring machines, robots and large structures with high accuracy is required. Previously we developed spherical motors, which have two or three axes. To meet this requirement, we have made two axes actuator, which gives the mirror of the tracking system three-dimensional motion. In this report, we introduce design criteria, process of design and experimental results.

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Coordinate measuring machines (CMM) and robots in industry require accurate and easy calibration over a wide measuring-range. The new calibration instrument (laser tracking interferometer) we produced makes use of a spherical surface motor for laser tracking mechanism. This enabled wide-range measurement for middle size CMM because the movable angle of the spherical surface motor is so wide. In this paper, we refer to the accuracy of the new laser tracking interferometer based on our experiment.

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Bilayered molecular film PFPE (perfluoropolyether), namely, ultrathin lubricant film consisting of bonded molecular layer and mobile molecular layer was dip-coated on DLC surface and the experiments for the tribological characteristics of the bilayered molecular film were carried out. Friction reduced with either layer average thickness but was more dependent on the average thickness of bonded layer. It was found that the lubricant film of bi-monolayer structure showed lowest friction and highest durability.

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DLC films show the excellent tribological properties under the lubrication with humid air or water. However, lubricity of industrial oils for DLC films is not so good compared with conventional tribo-materials. It is considered that the lubricant additives do not act on the DLC surface, because of chemical stabilities of carbon. Recently, metal elements doped DLC films were developed in order to improve the adhesion property and the lubricity. In this paper, lubrication mechanism of Ti doped DLC films were discussed with the results of friction test and surface analysis. The sliding surfaces were analyzed by using the TOF-SIMS.

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This paper describes the investigation of the sliding wear characteristics of chain materials and sliding bearing in the industrial furnace at high temperature. The experimental results show the wear rate relative to combination of materials, surface treatment and surface finish.

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Oiliness is very important characteristics to make reduction of friction and wear in mild frictional condition. Also in severe frictional conditions such as cutting or milling, it has been reported that lubricant possessing oiliness indicates large effect upon reduction of friction. However, the mechanism on lower friction can not be revealed clearly in that situation. In this study, friction and wear characteristics of aluminum alloy against steel are experimentally investigated in reciprocating friction with small amplitude under relatively severe condition. Measurements of a variation in friction coefficient with time and wear amount, and observations of wear scar are carried out for several kinds of lubricant. Measured and observed results shows that the higher the concentration of oleic acid or oleyl alcohol, the larger the wear amount but the smoother the wear surface.

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It is known that electricity appears when two bodies contact or cause friction. Although tribology has been slightly discussed about the electricity due to friction. This study deals with generation of static electricity while a metallic ball slides on a lubricated metal. The experiment was conducted at various sliding velocities under the lubricated conditions by using modified pin-on-disc machine. The static electricity, which was accumulated on the insulated pin and ball assembly, was measured. Within the range of the experiment, it was found that both the potential of the static electricity and the frequency of its discharges would increase in proportion to the sliding velocity and decrease with surface roughness.

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The triple arm mechanism is simple and basic spatial parallel mechanism with three degree of freedom, which consists of a base link, a coupler link and three two-link-chains having the actuated prismatic joint. In previous paper, we reported the method of the displacement and sensitivity analyses with respect to the length of the sides of the movable platform. Measuring the fluctuation of output angle caused by external force experimentally, we found the practical workspace of the movable platform is different with the one obtained from the analysis because of the closeness of the solution of the input and output function. In this paper, we improve the experimental device to let the operating range be large and we analyze the sensitivities with respect to the kinematic constants which indicate the orientation of the rotational axes of the revolute pairs to consider the clearance of the revolute pair. We investigate the range of the operation theoretically and experimentally.

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A new surface mount system with a parallel arrangement of miniature manipulators was proposed for use in system down sizing. The miniature manipulator consists of a molded pantograph mechanism, which is composed of large-deflective hinges and links. The purpose in this study is to investigate the static and dynamic characteristics of the pantograph mechanism. The static characteristic is clarified to analyze the nonlinear torque at the hinges and the displacement error of the output point. The dynamic characteristic deals with the dynamic displacement error of the output point when the miniature manipulator, the pantograph mechanism, is driven at 20Hz, and the output point is moved on a U-shape for picking and placing works. We consider forced vibrations corresponding to natural frequencies and mode shapes of the pantograph mechanism. These investigations apply the Finite Element Method (FEM; ANSYS) and Multi-Body-Simulation approach (MBS; SIMPACK).

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Conventional machine tools or coordinate measuring machines consisting of XYZ mechanism have difficulty to satisfy the Abbe's principle which is the basis of the precision mechanism. In other words, there are some offsets between the scale unit axes and the machining point or the measuring point. However, the machining point of machines based on the parallel kinematics can be located in the extension lines of the axes. In this study, the effects of the joint errors on the motion error of Hexapod mechanism has been analyzed by using a singular value decomposition. In this paper, it is proved that the point don't have to be located in the lines in the Hexapod. Because six actuating struts are employed, not only positions but also attitudes of the moving platform are able to be measured and actuated. In other word, the Hexapod can control the whole positions and attitudes of the platform. Thus, even if any offset exists between the machining point and the extensional lines, the point can be positioned precisely. Consequently, Hexapod enables to realize accurate machining and measurement regardless of Abbe's principle.

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