Μm In Translation Research Articles

Novel and Robust Forward Kinematic Algorithm for Real-Time Control of General Six-Degree-of-Freedom Parallel Robot for Tele-Manipulation and Tele-Navigation

Abstract The forward kinematics (FK) of a 6-6 universal-prismatic-spherical (UPS) structure of a parallel robot is highly nonlinear, coupled, and has a one-to-many nature of mapping. There exists no close form solution to a forward kinematic problem (FKP), and real-time kinematic control is extremely difficult. This paper presents the implementation of time efficient and robust solution for FKP using a trajectory modifier algorithm along with a Newton Raphson (NR) method. One micrometer in translation and 0.001 deg in orientation accuracy with an average pose computation time of 2.3 ms are achieved. The novel algorithm is elaborated and the detailed performance parameters are tabulated. The paper presents trajectory following experiments to show robust, real-time FK solution and efficient kinematic control on both standalone and master–slave modes to be used for robot-assisted neurosurgery. The neuro-registration using the FK solutions in real time in a tele-manipulation mode is demonstrated.

Simplifying the monoscopic deflectometric measurement by extra-facility-free workpiece positioning

Monoscopic deflectometry is a powerful and flexible measuring method for optical surfaces. Precise workpiece positioning is of significance because it directly determines the reliability of the measurement results. But unfortunately, the need for additional facilities severely limits the application of the monoscopic deflectometry. In this paper, a self-positioning method is proposed by combining the ray-tracing and Gaussian process regression. The phases retrieved from the captured images are parameterized using the Zernike polynomials. Then a training model is established for describing the relationship between the Zernike coefficients and the workpiece positions. Workpiece positioning is implemented by computing the associated joint Gaussian distribution. Experimental results show that the positioning accuracy of optical surfaces is comparable with that of a coordinate measuring machine, with a deviation less than 8 × 10−4° in tilt and 4 μm in translation. This greatly simplifies the sophisticated operation and improves the practicability and efficiency of deflectometric measurements.

Repeatability and sensitivity characterization of the far-field high-energy diffraction microscopy instrument at the Advanced Photon Source.

In the last two decades, far-field high-energy diffraction microscopy (FF-HEDM) and similar non-destructive techniques have been actively developed at synchrotron light sources around the world. As these techniques (and associated analysis tools) are becoming more available for the general users of these light sources, it is important and timely to characterize their performance and capabilities. In this work, the FF-HEDM instrument implemented at the 1-ID-E endstation of the Advanced Photon Source (APS) is summarized. The set of measurements conducted to characterize the instrument's repeatability and sensitivity to changes in grain orientation and position are also described. When an appropriate grain matching method is used, the FF-HEDM instrument's repeatability is approximately 5 µm in translation, 0.02° in rotation, and 2 × 10-4 in strain; the instrument sensitivity is approximately 5 µm in translation and 0.05° in rotation.

Alignment of sensor arrays in optical instruments using a geometric approach

Alignment of sensor arrays in optical instruments is critical to maximize the instrument's performance. While many commercial systems use standardized mounting threads for alignment, custom systems require specialized equipment and alignment procedures. These alignment procedures can be time-consuming, dependent on operator experience, and have low repeatability. Furthermore, each alignment solution must be considered on a case-by-case basis, leading to additional time and resource cost. Here I present a method to align a sensor array using geometric analysis. By imaging a grid pattern of dots, I show that it is possible to calculate the misalignment for a sensor in five degrees of freedom simultaneously. I first test the approach by simulating different cases of misalignment using Zemax before applying the method to experimentally acquired data of sensor misalignment for an echelle spectrograph. The results show that the algorithm effectively quantifies misalignment in five degrees of freedom for an F/5 imaging system, accurate to within ±0.87 deg in rotation and ±0.86 μm in translation. Furthermore, the results suggest that the method can also be applied to non-imaging systems with a small penalty to precision. This general approach can potentially improve the alignment of sensor arrays in custom instruments by offering an accurate, quantitative approach to calculating misalignment in five degrees of freedom simultaneously.

Design of an Experimental Set-Up to Study the Behavior of a Flexible Surgical Instrument Inside an Endoscope

The success of flexible instruments in surgery requires high motion and force fidelity and controllability of the tip. However, the friction and the limited stiffness of such instruments limit the motion and force transmission of the instrument. In a previous study, we developed a flexible multibody model of a surgical instrument inside an endoscope in order to study the effect of the friction, bending and rotational stiffness of the instrument and clearance on the motion hysteresis and the force transmission. In this paper, we present the design and evaluation of an experimental setup for the validation of the flexible multibody model and the characterization of the instruments. A modular design was conceived based on three key functionalities: the actuation from the proximal end, the displacement measurement of the distal end, and the measurement of the interaction force. The exactly constrained actuation module achieves independent translation and rotation of the proximal end. The axial displacement and the rotation of the distal end are measured contactless via a specifically designed air bearing guided cam through laser displacement sensors. The errors in the static measurement are 15 μm in translation and 0.15 deg in rotation. Six 1-DOF load cell modules using flexures measure the interaction forces and moments with an error of 0.8% and 2.5%, respectively. The achieved specifications allow for the measurement of the characteristic behavior of the instrument inside a curved rigid tube and the validation of the flexible multibody model.

Kinematic modeling and calibration of a flexure based hexapod nanopositioner

Abstract This paper covers the kinematic modeling of a flexure-based, hexapod nanopositioner and a new method of calibration for this type of nanopositioner. This six degrees of freedom tri-stage nanopositioner can generate small displacement, high-resolution motions with high accuracy by actuating three inexpensive, high quality planar stages. Each stage is equipped with linear actuators. In this paper, we discuss the calibration of the nanopositioner and methods to improve its accuracy. First, we derive the kinematic model of the nanopositioner that is a Stewart platform with spherical joints. Based on this kinematic model, we then calculate the actuation data for a set of commands for decoupled and coupled motions. We use an interferometer and an autocollimator to measure the actual displacement and rotation of the platform. Finally, we obtain the Jacobian matrix of the moving platform for the controller. Experiments showed that with the calibration-corrected parameters, the maximum error is approximately 0.002° in rotations and 3.3 μm in translation for a workspace of ± 0.2° and ±200 μm in x, y and z direction.

Time-domain fixed-structure closed-loop model identification of an unstable multivariable maglev nanopositioning system

This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test model to verify the closed-loop system-identification method presented in this paper. A closed-loop identification technique employing a known controller structure is used for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a bandwidth in the frequency range of interest is used as a reference input. An order-reduction algorithm is developed to obtain TFs with predefined orders, which gives the closest match in the frequency range of interest without missing any significant plant dynamics. The entire analysis is performed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified TFs. Experimental results are presented in the time as well as frequency domains to verify the accuracy of the identified plant TFs. These results also demonstrate the effectiveness of the developed closed-loop identification method in meeting all of the three core objectives—(i) reduction in cross-axial coupling from 9.213 µm to 0.911 µm in translation and from 22.03 µrad to 1.353 µrad in rotation, (ii) large range motion capability with a travel range of ±2.9 mm, and (iii) improved robust stability.

A dual-purpose positioner-fixture for precision six-axis positioning and precision fixturing

The kinematics, stiffness, and repeatability of a moving groove, dual-purpose positioner-fixture were determined experimentally. A dual-purpose positioner-fixture is an alignment device that may be operated in a fixture mode or a six-axis nanopositioning mode. When operated in fixture mode, experiments show standard deviation in repeatability of 11, 11, and 38 nm in x, y, and z; and 0.7, 0.3, and 0.3 μrad in θx, θy, and θz. The stiffness characteristics were shown to match predictions within 5%. When operated in nanopositioner mode, the device demonstrated 4 nm resolution and a range, of 40 μm × 40 μm × 80 μm in translation and 800 μrad × 800 μrad × 400 μrad in rotation. The fixture possesses a load capacity of 450 N and a natural frequency of 200 Hz when the fixture is preloaded to 225 N.

Three-dimensional computer simulation of radiostereometric analysis (RSA) in distal radius fractures

Physical phantom models have conventionally been used to determine the accuracy and precision of radiostereometric analysis (RSA) in various orthopaedic applications. Using a phantom model of a fracture of the distal radius it has previously been shown that RSA is a highly accurate and precise method for measuring both translation and rotation in three-dimensions (3-D). The main shortcoming of a physical phantom model is its inability to mimic complex 3-D motion. The goal of this study was to create a realistic computer model for preoperative planning of RSA studies and to test the accuracy of RSA in measuring complex movements in fractures of the distal radius using this new model. The 3-D computer model was created from a set of tomographic scans. The simulation of the radiographic imaging was performed using ray-tracing software (POV-Ray). RSA measurements were performed according to standard protocol. Using a two-part fracture model (AO/ASIF type A2), it was found that for simple movements in one axis, translations in the range of 25 μm–2 mm could be measured with an accuracy of ±2 μm. Rotations ranging from 1 6 ° to 2° could be measured with an accuracy of ±0.015°. Using a three-part fracture model the corresponding values of accuracy were found to be ±4 μm and ±0.031° for translation and rotation, respectively. For complex 3-D motion in a three-part fracture model (AO/ASIF type C1) the accuracy was ±6 μm for translation and ±0.120° for rotation. The use of 3-D computer modelling can provide a method for preoperative planning of RSA studies in complex fractures of the distal radius and in other clinical situations in which the RSA method is applicable.

An optical sensor for the ATLAS muon spectrometer: The reference alignment system

The muon spectrometer of the ATLAS detector at the LHC has been designed to provide a precise track momentum measurement for muons up to 1 TeV. It is composed of several hundred monitored drift tube chambers. Their positions must be known with an accuracy of 20 μm in translation and 200 μrad in rotation. For this purpose, a precise alignment system is required. This system is based on several subsystems using optical sensors measuring the deformations, and the relative and absolute positions of muon chambers. In this article we will focus on one of them: the reference system.

Technical feasibility and precision of radiostereometric analysis as an outcome measure in canine cemented total hip replacement

Radiostereometric analysis (RSA) is an analytical technique in which biplanar radiographs are used to quantify the migration of implants in vivo. RSA is now considered the benchmark for quantifying implant migration in clinical studies of total joint replacement, yet its use in preclinical animal models has not been widely reported. The same attributes that make RSA appealing as an analytical method in humans (i.e., high precision and accuracy, noninvasiveness, objectivity) also make it a promising option for animal studies. The specific aims of this study were to determine the technical feasibility and analytical precision of RSA in a canine model of cemented total hip replacement. The precision of RSA was assessed in (1) a Plexiglas phantom, (2) a canine Sawbone model, and (3) a pilot series of dogs implanted with cemented canine THR implants. In vitro precision values, calculated as the 95% confidence limits for the error between duplicate RSA examinations, ranged from 4.3 to 17.9μm for translation and from 0.01° to 0.22° for rotation. In vivo precision values ranged from 16.2 to 41.1μm for translation and 0.17° to 0.44° for rotation. As is the case in humans, RSA appears to provide an order-of-magnitude improvement in technical precision as compared to plain film X-ray. RSA can therefore be considered a practical and potentially valuable noninvasive outcome measure for assessing implant function in canine cemented THR.

Design methods for six-degree-of-freedom displacement measurement systems using cooperative targets

Six-degree-of-freedom displacement measurement systems generally employ various kinds of cooperative targets, and calculate displacement from the coordinate values of reflective rays. To improve the performance of measurement systems, a new design methodology is required, which considers the relationship between each axial output and the coordinate values, Jacobian matrix. Several performance indices are derived from Jacobian matrix and the design parameter values are determined through the optimization process. In a design example, the improvement of performance is verified by evaluating resolution, accuracy and crosstalk. The newly designed measurement system shows a maximum error of ± 0.5 μm for translation and ± 2 arcsec for rotation.

Multidimensional motion measurement of a bimorph-type piezoelectric actuator using a diffraction grating target

Precision actuators, such as pick-up actuators for HDDs or CD-ROMs, mostly show multidimensional motion. So, to evaluate them more completely, multidimensional measurement is required. Through structural variation and optimization of the design index, the performance of a measurement system can be improved to satisfy the requirement of this application, and so the resolution of each axis is higher than 0.1 μm for translation and 0.5 arcsec for rotation. Using this measurement system, the multidimensional motion and frequency transfer functions of a bimorph-type piezoelectric actuator are obtained.

Multi-degree-of-freedom displacement measurement system formilli-structures

A new multi-degree-of-freedom measurement system formilli-structures is presented. This methodology is based on optical beamdeflection method and triangulation. It employs a diffraction grating as areflective object, which reflects an incident laser beam into severaldirections. To obtain the pose information of a measured object, the detectingpositions of zeroth- and first-order diffracted rays are measured using threetwo-dimensional detectors. From these values, we can calculatesix-degree-of-freedom displacement through a kinematic analysis. Theperformance was evaluated with resolution, measurement errors and crosstalk.The results show that measurement errors and maximum crosstalk are within ±0.5 µm in translation and ±2''in rotation. As an application, we measuredthe multi-DOF motion of a bimorph type PZT actuator and obtained its frequencyresponse function.

Two transparent optical sensors for the positioning of detectors using a reference laser beam

We have developed two different optical systems in order to position detectors with respect to a reference laser beam. The first system, a telescope, permits the absolute positioning of an element with respect to a reference laser beam. The resolution is of the order of 10 μm in translation and 50 μrad in rotation. It is highly transparent (∼90%) permitting several elements to be aligned. A calibration procedure has also been studied and is currently being tested in order to obtain an absolute alignment information. The second system is a highly transparent (95%) two-dimensional position sensor which allows the accurate positioning (below 20 μm ) of several (up to 10) elements to which each sensor is attached, transversally to a laser beam used as a reference straight line. The present useful area of the first sensor is 20×20 mm 2 and is 15×15 mm 2 for the second. In both cases it can be further increased to meet the experiment's requirement.

上顎第一小臼歯の運動の６自由度測定と解析

Soundness of stomatognathic system can be achieved with a functionally adequate occlusal contact. A study on this occlusal morphology requires the analysis of micro tooth movement as well as analysis of jaw movement. The purpose of this study was to investigate micro upper first premolar movement under several occlusalloading conditions. Our jaw tracking device was modified to develop the new motion analyzer in six-degree-of-freedom that can perform simultaneous measurement of tooth and jaw movements.The results were as follows:1. The resolution of the recording system was improved up to 1.3 μm for translation and 0.00017° for rotation.2. Three male adult volunteers were selected as the subjects. Movements of right upper first premolars against left upper first premolarsof these subjects were measured with this device. Occlusal load was provided perpendicularly on buccal cusp, central fossa, palatal cusp and canine cusp. Directions of tooth movements of these subjects were almost the same under the same loading conditions.3. In some loading conditions, the rotation centers of tooth movement were found.

高分解能６自由度運動測定器の開発

The pursuit of ideal occlusal contact is one of the fundamental objectives of the dental prosthesis. To attain this objective, the study on micro tooth movement is significant as well as the study on jaw movement. The purpose of this study was to evaluate a newly-developed extraordinary accurate motion detector that measures tooth movement in six-degree-of-freedom. The principle of the measurement is to detect magnetic field changes induced by Helmholtz coils. A right maxillary first premolar of an adult male volunteer was selected for the measurement. The tooth movement during buccal and palatal cusps loading was measured as the relative position changes to the opposite side maxillary first premolar. The results were as follows:1. An extraordinary accurate motion detector that can evaluate tooth movement in six-degree-offreedom was developed. The resolution of the measuring system is 4 μm for translation and 0.0004°for rotation.2. Under 23 kgf buccal cusp loading, the tooth was moved in the buccomedioapical direction. This movement ranged from 143 to 366 μm. Under palatal cusp loading, the tooth was moved in the palatoapical direction, ranging from 71 to 231 μm.

平面3自由度インパクト駆動機構の開発 (第2報)

Piezoelectric XYγ positioning device using impulsive force has capabilities of simple construction, no limitation of traverse length and high resolution. The force that maintains the device to be stationary is only static friction force. Furthermore the motion characteristic is extremely influenced by the conditions of sliding surface. In this paper, the friction control devices were manufactured to improve the motion characteristic of the XYγ positioning device and mounted on the positioning device with three feet of steel ball. These were designed to control the friction force between the each foot and sliding surface individually. As a result, the ratio of movement with three friction control devices to that without one was 1.6 in any directions. The experimental results agreed well with the estimated factor of 1.64. It was demonstrated that the positioning device had capability of a fine positioning less than 0.05μm in translation and 0.6'' in rotation. It was able to rotate around any foot by increasing the friction between the sliding surface and one foot that was to be the rotation axis and removing the friction of the others.