Showing papers on "Angular displacement published in 2008"

Design of a robot joint with variable stiffness

Abstract: A robot joint with a variable stiffness unit is presented. The variable stiffness unit (VSU) is composed of a motor, two rings that consist of arc-shaped magnets separated by spacers, and a linear guide to change the cross-sectional area of the two rings. Angular displacement between two rings causes the magnets to generate torque, which acts as a nonlinear spring. The stiffness of the joint is varied via changing the overlapping area of the magnets. The VS J exhibits nearly zero stiffness, which enables robot manipulator to be harmless to humans at a wide range of operating speed. Connected to a joint motor in series, the stiffness by the VSU and the position of the joint are controlled independently by two motors. The torque generated by the magnets is analyzed. Using dynamics of the joint, feedback linearization method is adopted to control the VSJ. In addition to feedback linearization, an integral controller is augmented in order to reduce the effect of model uncertainty and disturbances.

Seismic Rotational Displacement of Gravity Walls by Pseudodynamic Method

Abstract: Prediction of the rotational displacements, induced by earthquake is a key aspect of the seismic design of retaining walls. In this paper, the pseudodynamic method is used to compute rotational displacements of the retaining wall supporting cohesionless backfill under seismic loading. The proposed method considers time, phase difference, and effect of amplification in shear and primary waves propagating through the backfill and the retaining wall. The influence of ground motion characteristics on rotational displacement of the wall is evaluated. Also the effects of variation of parameters like wall friction angle, soil friction angle, amplification factor, shear wave velocity, primary wave velocity, period of lateral shaking, horizontal, and vertical seismic accelerations on the rotational displacements are studied. Results are provided in graphical form with a comparison to the available pseudostatic result to validate the proposed theory. Present results give higher values of rotational displacements of...

Braking and positioning system for a wind turbine rotor

Abstract: A method of positioning a wind turbine rotor 160 comprises defining a predetermined angular position in a main rotation plane of the rotor 160 and controlling a rate of deceleration of the rotor, such as to stop the rotor at the predetermined angular position.

Optimization of the Trajectory of a General Free - Flying Manipulator During the Rendezvous Maneuver

Abstract: The paper is focused on the dynamics of a manipulator mounted on a free-flying satellite performing rendezvous and docking maneuver (RVD). The target satellite is assumed to be passive, without attitude control and telecommunication link. The servicing satellite performs, by means of thrusters, a fly - by maneuver, in which it approaches the target satellite on a non-collision path. In the last phase of the RVD maneuver, when the 6dof manipulator executes a predefined path towards the target, it can disturb the dynamics and, in consequence, the trajectory of the servicing satellite. The system (satellite + manipulator) is nonholonomic and its linear momentum and angular momentum are not conserved. The paper describes the algorithm of the manipulator trajectory planning, based on the calculus of variation, which can solve (n+6) dof problem. The cost functional trades off power use of the DC motor and additional conditions constraining the end-effector motion so that it reaches the final desired state expressed as the linear and angular position and velocity. The behavior of the system is described in the Lagrangian formulation and the collocation method is chosen to solve the boundary value problem. The initial trajectory is calculated using the Generalized Jacobian Matrix (GJM) approach that is extended to the system, in which linear and angular momentum is not conserved. An example is provided that shows the optimal trajectory of the LBR manipulator during the RVD maneuver to a tumbling satellite.

Classification of Aerial Acrobatics in Elite Half-Pipe Snowboarding Using Body Mounted Inertial Sensors

Abstract: We have previously presented data indicating that the two most important objective performance variables in elite half-pipe snowboarding competition are air-time and degree of rotation. Furthermore, we have documented that air-time can be accurately quantified by signal processing of tri-axial accelerometer data obtained from body mounted inertial sensors. This paper adds to our initial findings by describing how body mounted inertial sensors (specifically tri-axial rate gyroscopes) and basic signal processing can be used to automatically classify aerial acrobatic manoeuvres into four rotational groups (180, 360, 540 or 720 degree rotations). Classification of aerial acrobatics is achieved using integration by summation. Angular velocity (ω i, j, k ) quantified by tri-axial rate gyroscopes was integrated over time (t = 0.01s) to provide discrete angular displacements (θ i, j, k ). Absolute angular displacements for each orthogonal axes (i, j, k) were then accumulated over the duration of an aerial acrobatic manoeuvre to provide the total angular displacement achieved in each axis over that time period. The total angular displacements associated with each orthogonal axes were then summed to calculate a composite rotational parameter called Air Angle (AA). We observed a statistically significant difference between AA across four half-pipe snowboarding acrobatic groups which involved increasing levels of rotational complexity (P < 0.001, n = 216). The signal processing technique documented in this paper provides sensitive automatic classification of aerial acrobatics into terminology used by the snowboarding community and subsequently has the potential to allow coaches and judges to focus on the more subjective and stylistic aspects of half-pipe snowboarding during either training or elite-level competition.

Steering angle sensor

Abstract: A steering angle sensor for determining absolute angular position of a steering wheel of a motor vehicle is disclosed. The steering angle sensor includes a steering angle sensor for determining absolute angular position of a steering wheel shaft of a motor vehicle, the steering angle sensor comprising a first rotational member coupled to the steering wheel shaft; the steering wheel shaft and the first rotational member being rotatable about a first rotational axis through a rotational range including a plurality of revolutions of the steering wheel shaft; a second rotational member rotatable about a second rotational axis, the second rotational member is operably coupled to the first rotational member; a first sensing device including a first sensing element, the first sensing device positioned adjacent to the second rotational member to generate a first signal used to determine rotational position of the second rotational member over a single turn of the second rotational member; a third rotational member rotatable about a third rotational axis, a reduction gear operably couples the second and third rotational members; at least four second sensors positions adjacent to the third rotational member; and the third rotational member includes a plurality of indexing elements disposed on the third rotational member and at least partially circumscribing the third rotational axis, the indexing members and the second sensors cooperatively positioned to generate a second signal used to determine the number of rotations of the steering wheel shaft.

Fabrication and analysis of a micro-machined tri-axis gyroscope

Abstract: This paper presents an innovative micro-gyroscope design. Solely by SOI (silicon on insulator) fabrication technology and wet etching, the proposed micro-gyroscope can be produced in batch and is capable of detecting three-axis angular rates. The induced motions of all individual seismic mass modules are designed to respond in the directions orthogonal to each other in order to decouple the obtained measurements. In our work, three pairs of high-resolution differential capacitors with signal processing circuits are employed to measure the angular velocity components in three axes. On the other hand, the drive electrode comb is used to constantly vibrate the outer-ring in the tangential direction by a sinusoidal voltage. The signal bandwidth is increased by distributed translational proof masses (DTPM), placed 90° apart orderly. Each individual proof mass of DTPM is designed with natural frequency discrepancy and constrained to move in the radial direction so that the superior mode matching can be easily, to some extent, achieved. The suspension flexures are particularly designed to resist planar displacements in the drive mode but increase the stroke of tilting angular displacement in the sense mode. By considering the complicated geometry of the suspension flexures, FEM (finite element method) is employed to examine the potential maximum induced mechanical stress. The dynamic equations of the proposed gyroscope are established so that the embedded gyroscopic effects are explicitly unveiled. More importantly, the efficacy of the drive and sense circuit modules are verified by commercial softwares Hspice and Multisim. By intensive computer simulations and preliminary experimental studies, the resolution, bandwidth and decoupling capability of the tri-axis gyroscope are expected to be fairly enhanced if a certain degree of trade-off is preset.Corrections were made to figure 5 in this article on 3 October 2008. The corrected electronic version is identical to the print version.

Systems and methods for fabricating displacement scales

Abstract: Methods and systems for forming a displacement scale comprising TIR prisms on a substrate are described. A system for forming the displacement scale includes one or more rollers having a pattern of total internal reflection (TIR) prism features in negative relief. As the rollers are rotated, the scale is formed on the substrate. The rollers may also include pattern features in negative relief. Rotation of the rollers simultaneously forms the displacement scale and the pattern features on the substrate. The TIR prism features of the displacement scale may be oriented to provide measurement of one or more of lateral displacement, longitudinal displacement and angular displacement.

Method and system for estimating rotor angular position and rotor angular velocity at low speeds or standstill

Abstract: A method and system for estimating an angular position and an angular velocity of a rotor in a dynamoelectric machine (12) measures an AC current (28) and a potential (26) for each of a plurality of windings coupled to a stator of the dynamoelectric machine, transforms the measured currents and potentials to a stationary frame (α-β) to produce transformed currents and transformed potentials, and processes the transformed currents and transformed potentials to produce a first intermediate signal and a second intermediate signal. The first intermediate signal and the second intermediate signal are cross-coupled and processed (Fig. 3) to obtain a first extended rotor flux value and a second extended rotor flux value. The first extended rotor flux value arid the second extended rotor flux value are applied to a phase lock loop (Fig. 4) to derive an estimated rotor angular position and an estimated rotor angular velocity for the dynamoelectric machine.

Spatial Periodic Adaptive Control for Rotary Machine Systems

Abstract: A spatial periodic adaptive control (SPAC) approach is developed to deal with rotary machine systems performing speed tracking tasks. Since the angular displacement is periodic when rotating by 2pi radians, most rotary machine systems present certain cyclic behaviors with a fixed periodicity which is either a fraction or multiple of 2pi . As a consequence, unknown system parameters and disturbances that characterize the system behaviors are also periodic in nature. By utilizing the spatial periodicity, the SPAC aims at improving the system performance. In the SPAC design, the dynamics of the rotary machine systems is first converted from the temporal to spatial coordinates in canonical form using the feedback linearization method. Then the new adaptive controller updates the parameters and the control signal periodically in a pointwise between two consecutive spatial cycles. Using a Lyapunov-Krasovskii functional, the convergence property of the SPAC can be analyzed for high order rotary systems and the periodic adaptation can be applied to rotary systems with pseudo-periodic parametric uncertainties. The effectiveness of the SPAC is verified through rigorous analysis and two numerical examples.

Angle measurement system

Abstract: An angular position measurement system including a continuous angular position sensor configured to provide a first signal representative of a continuous angular position of a rotating shaft, an incremental angular position sensor configured to provide a second signal representative of incremental angular positions of the rotating shaft, and a controller configured to calibrate the first signal based on the second signal to provide a third signal representative of a calibrated continuous angular position of the rotating shaft

Angular position sensor

Abstract: An angular position sensor (24) and method that relies on a stationary- circular array of Hall sensors (18) and a rotatable circular array of magnets (16) arranged about a common axis (22). A periodic and simultaneous reading of all of the Hall sensor outputs is used to determine angular velocity.

Ergometric training device

Abstract: A stationary ergometric exercise device, having a manually/foot operated drive with two drive elements (pedals) that can be alternately operated, and further having a measuring means for measuring the driving force applied by the drive or the torque force associated therewith, comprises a measuring arrangement (30) for measuring the angular position of the drive, having a pair of sensor means (31, 32), which are disposed in mutually opposed positions with respect to a wheel (19) connected to the drive such that the motions are synchronized, said positions each corresponding to a position of motion of a load change between the two drive elements (16). A computer device can receive the signals from the force measuring means and calculate therefrom the chronological sequence of the driving force, or the torque force, and variables that can be derived therefrom, and it can emit said signals alternately for a right or left extremity of an exercising person, as a function of the load changes reported by the measuring arrangement (30).

Design and dynamics of an innovative micro gyroscope against coupling effects

Abstract: This paper presents an innovative micro gyroscope design. The proposed tri-axis gyroscope possesses the capability of detecting three-dimensional angular motions. The motion of each sensing element is, by elaborate mechanical design, restricted to move in orthogonal direction to each other such that the measurements by high-resolution capacitors with signal processing circuits are decoupled and precisely represent, to some extent, angular velocity components in three axes. The drive electrode comb is used to constantly vibrate the proof mass in tangential direction by sinusoidal voltage. The signal bandwidth is increased by distributed translational proof masses, placed ninety degree apart from each other. Each individual proof mass is designed to move solely in radial direction so that superior mode matching can be achieved. In order to ensure better repeatability and more reliability, the suspension flexures and damping effects are studied such that stress of the proposed micro gyroscope is reduced but the span of angular displacements is increased. Owing to the complicated geometry of the suspension flexures, finite element method (FEM) is employed to obtain more exact stiffness values and compared with theoretical analysis. The dynamic model of the proposed gyroscope is established to include non-linear terms and embedded mechanical constraints. The entire micro device can be produced merely by surface fabrication such that the mass production cost can be considered at the design stage, while the resolution, bandwidth and decoupling capability of tri-axis detection are enhanced.

Torque transmission device for motor vehicle, has arm with end supported on guiding surface, where distance from guiding surface to rotational axis varies with angular displacement of hub and disk to cause elastic deformation of arm

Abstract: The device has a connection unit ie pre-shock absorber (40), including an elastically deformable bent arm (44) with an end (46) connected to an inner washer (42) The arm has another end (48) cooperating with an annular disk (22) and slidingly supported on a circumferential guiding surface (50) The washer and the guiding surface are rotatably connected to a splined hub and the disk, respectively Distance from the guiding surface to a rotational axis (64) varies with angular displacement of the hub and the disk to cause elastic deformation of the arm, which varies with the displacement

Design and Analysis of a Tri-Axis Gyroscope Micromachined by Surface Fabrication

Abstract: This paper presents an innovative microgyroscope design. Solely by planar fabrication and wet etching, the proposed microgyroscope is capable to detect three-axis angular rates. The induced motion of individual seismic mass modules are designed to respond in the directions orthogonal to each other in order to decouple the obtained measures. In our work, three pairs of high-resolution differential capacitors with signal processing circuits are employed to measure the angular velocity components in three axes. On the other hand, the drive electrode comb is used to constantly vibrate the outer-ring in tangential direction by sinusoidal voltage. The signal bandwidth about the principle axis is increased by distributed translational proof masses, placed 90deg apart orderly around a circle. Each individual translational proof mass is designed to move in radial direction so that superior mode matching (i.e., resonance mode) can be easily, to some extent, achieved. The planar suspension flexures are particularly designed in geometry to resist acceleration in drive mode but increase the stroke of tilting angular displacement of the outer-ring such that the resolution of detected angular rate for the corresponding sense mode is upgraded. By considering the complicated geometry of the suspension flexures, finite-element method (FEM) is employed to examine the potential maximum induced mechanical stress. The dynamic equations of the proposed gyroscope are established are well so that the embedded gyroscopic effects are unveiled. More importantly, the efficacy of the drive and sense circuits modules is verified by commercial softwares Hspice and Multisim. By intensive computer simulations and preliminary experimental studies, the resolution, bandwidth and sensitivity of the tri-axis gyroscope are expected to be fairly enhanced if a certain degree of tradeoff is preset.

Tool face sensor method

Abstract: Exhaust pressure from at least one actuator (34,36) which can tilt joint (6) of a bottom hole assembly (4) can be utilized to determine the direction (26) tiltable joint (6) is pointing (e.g., orientation, angular displacement, and/or inclination and azimuth). In one embodiment, a known exhaust pressure can be correlated to a known orientation and/or angular displacement, and the measured exhaust pressure can be compared to the known exhaust pressure to determine the orientation and/or angular displacement. In another embodiment, the flow rate of fluid exhausted from an actuator (34,36) can be derived from the exhaust pressure. The exhaust flow rate can then be used to calculate the state of actuation, which can allow determination of the angular displacement of the tiltable joint (6). Orientation and/or angular displacement with respect to the bottom hole assembly (4) can be resolved into an inclination and azimuth with respect to a formation (14).

Image forming apparatus, belt unit, and belt driving control method

Abstract: An image forming apparatus for forming an image on a recording medium includes a belt configured to travel rotationally and looped around at least two rotary support members, a driven rotary member disposed facing at least one of the rotary support members via the belt and configured to rotate with the belt, and a controller. The controller is configured to minimize fluctuation in one of a travel velocity and a travel distance of the belt by controlling the travel of the belt based on one of a rotational angular displacement and a rotational angular velocity of each of the rotary support member and the driven rotary member.

Interferometric evaluation of angular displacements using phase retrieval.

Abstract: Phase retrieval is carried out using sequential intensity measurements of a volume speckle field and a wave propagation equation. Retrieved phases and phase subtraction facilitate the analysis of wavefronts before and after undergoing a small rotation. Angular displacement between incident planar wavefronts is determined from the unwrapped phase difference, phase diffuser aperture diameter, and the light source wavelength. Numerical simulations confirm the experimental results.

Electric instrument music control device with multi-axis position sensors

Abstract: An electric instrument music control device is provided having at least two multi-axis position sensors. One sensor is a reference multi-axis position sensor retained in a fixed position the reference multi-axis position sensor having at least one axis held in a fixed position. Another sensor is a moveable multi-axis position sensor rotatable about at least one axis corresponding to the at least one axis of the reference multi-axis position sensor, wherein the moveable multi-axis position sensor is in communication with the reference multi-axis position sensor. The device may include a processor that processes the differentiation between the angular position of the at least one axis of the reference multi-axis position sensor and the at least one axis of the moveable multi-axis position sensor, wherein the angular differentiation correlates to a music effect of an electric instrument.

Constrained Slews for Single-Axis Pointing

Abstract: T HERE is a significant interest in the determination of maneuver strategies for underactuated satellites, where the availability of only two torque components prevents the spacecraft from performing arbitrary slews. The problem is representative of those situations in which an actuator failure [1,2] or inherent physical constraints (e.g., use of magnetic torquers only as attitude effectors that deliver a command torque along directions perpendicular to the externalmagneticfield [3,4]) result in constraints onto the admissible rotations and full three-axis control is not attainable. In these cases, the available torque is constrained on a plane, perpendicular to the direction b about which it is not possible to rotate the spacecraft, where b is prescribed in either the body-fixed frame (for actuator failure) or in the fixed target frame (as for the direction of the magnetic field). In the present note it is shown that, regardless of the direction of b, there always exists an eigenaxis rotation [5] that provides for the exact pointing of a given body-fixed axis toward a prescribed target direction, identified by the unit vectors
and , respectively. The direction of the admissible rotation eigenaxis and the amplitude of the resulting rotation are analytically determined for any possible combination of the unit vectors
, , and b. In [6], a similar problem is dealt with, and its solution proposed as a means for planning feasible maneuvers for underactuated spacecraft, where the overall angular displacement " from a specified target frame is minimized by rotating the body frame about a nonnominal Euler axis ĝ. The analytical solution of Giulietti and Tortora [6] provides a reorientation strategy in which the final misalignment error grows with the angle between e and ĝ, where e is the nominal eigenaxis. Thus, the optimal nonnominal eigenaxis ĝ lies along the projection of e onto the plane of the admissible rotation axes, perpendicular to the direction of b, where the angle between e and the admissible ĝ is minimum [6]. The resulting final pointing error grows linearly with the desired nominal rotation about e, when is small, reaching a limit value " cos 1 ĝ e for a desired rotation . As a consequence, the misalignment error may attain rather large values when the angle between ĝ and e and the required reorientation angle are both large. The actual limits for the maximum tolerable attitude error will strongly depend on accuracy requirements for the considered application, but the exact acquisition of a prescribed attitude may not be mandatory, especially in the presence of failures, when a deterioration of system performance is expected and may be tolerated. Conversely, accurate pointing of a single direction
, such as the boresight of a sensor payload or a directional antenna, may be vital for the mission or, at least, sufficient for a minimal level of operations in those critical situations where arbitrary attitude maneuvers cannot be accomplished. As an example, orbit maneuvers require pointing of the thruster nozzle with an accuracy within a fraction of a degree from the desired v direction, whereas the roll angle of the spacecraft around the thrust vector line has no effect on the outcome of the thrust pulse. By application of an approach similar to that discussed in [6], based on the identification of a suitable eigenaxis ĝ and corresponding rotation
, this paper demonstrates that it is possible to analytically define a rotation which exactly aims a body-fixed axis toward a prescribed (yet arbitrary) target direction. The approach is initially derived by choosing an ad hoc body reference frame FB, where the first axis of FB is parallel to the unit vector
, which must be pointed along the target direction . This choice makes the derivation of the pointing strategy simpler from the mathematical standpoint. It will then be generalized for arbitrary sensor and target directions by use of a suitable coordinate transformation matrix. The derivation of the eigenaxis rotation that allows for the desired alignmentwill be discussed in the next section. Some examples of the resulting rotation strategies will then be given in the Results section, where a comparison with the minimum misalignment provided by the solution proposed in [6] is also presented. The Conclusions section ends the note.

Device and method for controlling a satellite tracking antenna

Abstract: The invention relates to A device for controlling a satellite tracking antenna (10) comprising an azimuth drive means (MAz) configured to impart an azimuthal rotational motion to the antenna about an azimuth axis (Z), an elevation axis drive means (MEι) configured to impart a rotational motion to the antenna about an elevation axis (Y) orthogonal to the azimuth axis and a tilt axis drive means (Mτ; MT1, MT2) configured to impart a rotational motion to the antenna about a tilt axis (T), the tilt axis being connected to the elevation axis in such a way that the rotational freedom of motion of the antenna (19) about the tilt axis (T) is dependent on the elevation angle such that: at an elevation angle of 0° the rotational freedom of motion of the antenna (10) about the tilt axis (T) corresponds to the azimuthal rotational motion; at an increasing elevation angle the rotational freedom of motion about the antenna (10) successively transcends into a roll rotation; and at an elevation angle of 90° the rotational freedom of motion of the antenna about the tilt axis (T) corresponds to a roll rotation about a roll axis (X) orthogonal to said azimuth axis (Z) and to said elevation axis (Y), control means being provided for controlling the operation of the azimuth axis drive means, the elevation axis drive means, and the tilt axis drive means, said control means comprising means, preferably including a true north seeking gyro, for tracking position, orientation, direction and speed of movement of the device, wherein said control means further comprises an additional gyro (G) comprising an elevation gyro axis (GEI) arranged to sense the elevation movement and a tilt gyro axis (GT) arranged to sense the tilt movement, so as to minimize the angular velocity of the antenna pointing vector. The invention further relates to a method for controlling a satellite tracking antenna, and a vessel comprising said device.

Switch reluctance machine rotor angular position and rotation speed detection device and method

Abstract: The invention relates to a device for detecting the angular position and the speed of the switch magnetic resistance motor and method, comprising a rotary encoder and a signal processing circuit mounted in the motor and fixed on a support plate, wherein the rotary encoder is connected with the main axis of the motor. The rotary encoder collects and transfers the angular position signals of the rotator to the encoder signal pretreating unit of the signal processing circuit. The encoder signal pretreating unit converts the output signal of the encoder into the signal capable for being received by the microprocessor unit. The microprocessor unit processes the angular position signals and calculates the speed of the motor. The communication unit sends the angular position signals and speed signals by serial communication bus. The connection line of the said device with the outside is simple and the antijamming capability is strong. The device device for detecting the angular position and the speed of the switch magnetic resistance motor is suitable for long distance transmission with high resolution, easy operation, small error and no zero setting by manpower.

Method and apparatus for determining the angular position of the rotor on a wind turbine

Abstract: The present invention relates to a method and apparatus for determining an angular position of a rotor of a wind turbine. The method comprises the steps of rotating at least three acceleration sensors (16), which are situated at a distance from the rotor centre axis, around the rotation axis (4) of the rotor (2) in accordance with the rotation (5) of said rotor (2), and measuring the acceleration, said at least three acceleration sensors (16) are mounted tangentially or radially or in any intermediate tilted position between tangentially and radially on the rotor in equidistant angular positions, converting the measured accelerations to input signals for computing the relationship between said inputs from said at least three acceleration sensors to determine the direction of gravity as a reference position of the rotor (2), and on basis of the measured accelerations from said acceleration sensors and said computed relationship calculating the angular position of the rotor.

Novel approach for lower limb segment orientation in gait analysis using triaxial accelerometers

Abstract: This paper presents a novel approach only based on triaxial accelerometers for three-dimensional (3D) orientation of lower limb segment during real-time motion. With two coaxially placed triaxial accelerometers, the actual resultant acceleration signals containing the acceleration of gravity and lineal movement along each axis were obtained. The angle displacements for orientation of each segment were calculated based on low-pass filtered accelerometer signals without integration. To evaluate accuracy, two calculated angular displacements around z, y axes during different rotational conditions were obtained and compared with the result from a high-accuracy camera system. Only based on one kind of inertial sensor, triaxial accelerometers, the approach can be used to assess spatio-temporal gait parameters and evaluate movements of each segment of the lower limbs, and thus to objectively monitor gait function of patients in a clinical setting.

Multi-axial linear and rotational displacement sensor

Abstract: A MEMS multiaxial inertial sensor of angular and linear displacements, velocities, or accelerations has four comb drive capacitive sensing elements integrated on a planar substrate, each sensing element having an output responsive to displacement along a Z axis, and responsive to a displacement along X or Y axes. The sensing elements are located at different parts of the substrate on both sides of the X axis and the Y axis, the outputs being suitable for subsequently deriving linear and angular displacements about any of the X, Y or Z axes. Linear or angular movement is determined from combinations of the sensor signals.

Accuracy analysis of parallel plate interferometer for angular displacement measurement

Abstract: The measurement accuracy of a parallel-plate interferometer for angular displacement measurement is analyzed. The measurement accuracy of angular displacement is not only related to the accuracy of phase extraction, but also related to initial incident angle, refraction index and thickness of plane-parallel plate as well as wavelength's stability of laser diode, etc. Theoretical analysis and computer simulation show that the measurement error of the angular displacement bears a minimum value when choosing an optimal initial incident angle in a large range. These analytical results serve as a guide in practical measurement. In this interferometer, reducing the refraction index or increasing the thickness of the parallel plate can improve the measurement accuracy; and the relative error of the phase measurement is 3.0 x 10(-4) corresponding to 1 degrees C temperature variation. Based on these theoretical and experimental results, the measurement accuracy of the parallel-plate interferometer is up to an order of 10(-8) rad. (c) 2007 Elsevier Ltd. All rights reserved.