Intermittent Forces Research Articles

Evaluation Of Lateral Root Resorption In Maxillary Teeth Among First Premolar Extraction Cases After Space Closure- A CBCT Study

Background: Orthodontic treatment usually involves usage of light continuous forces but when heavy forces are used it leads to apical root resorption. External apical root resorption refers to reduction in root structure involving the apices. This resorption is of transient inflammatory type. 2D images are commonly used for diagnostic purposes in orthodontics but it cannot detect root resorption on lingual or buccal surfaces thus cannot measure the volume of root loss. Cone beam computed tomography which can provide 3D images was introduced in late 1990s. Images provided by CBCT are more more accurate than panoramic and periapical radiographs . Therefore in this study , CBCT is used to evaluate lateral root resorption in maxillary teeth after after space closure among first premolar extraction cases . Materials and Methods: CBCTs of 20 patients fulfilling inclusion and exclusion criteria were taken before the start of orthodontic treatment and after space closure. Post treatment root width was substracted from the pre treatment root width at three levels from CEJ (3mm,6mm,9mm). The normality test (Shapiro-Wilk Test) was performed to analyze the data, and the results were expressed as frequency with percentage and mean with standard deviation. Difference between means were assessed using paired t test for before and after the procedure. All the statistical analyses were carried out at a 5% level of significance, and results with a P value < 0.05 were considered statistically significant. Results: Considering all the three levels the least tooth resorption was observed in the case of central incisor (0.1750 ± 0.0444, p <0.001) and highest in the canine tooth (5.900± 0.0000, p <0.001) . Conclusion: When root resorption is detected, it is recommended to pause the treatment for about 6 months to allow for root repair. Intermittent forces, which provide rest periods between applications, are more tissuefriendly and can help reduce the risk of further resorption

Intermittent mechanical loading on mouse tibia accelerates longitudinal bone growth by inducing PTHrP expression in the female tibial growth plate.

It is not clear as to whether weight bearing and ambulation may affect bone growth. Our goal was to study the role of mechanical loading (one of the components of ambulation) on endochondral ossification and longitudinal bone growth. Thus, we applied cyclical, biologically relevant strains for a prolonged time period (4 weeks) to one tibia of juvenile mice, while using the contralateral one as an internal control. By the end of the 4-week loading period, the mean tibial growth of the loaded tibiae was significantly greater than that of the unloaded tibiae. The mean height and the mean area of the loaded tibial growth plates were greater than those of the unloaded tibiae. In addition, in female mice we found a greater expression of PTHrP in the loaded tibial growth plates than in the unloaded ones. Lastly, microCT analysis revealed no difference between loaded and unloaded tibiae with respect to the fraction of bone volume relative to the total volume of the region of interest or the tibial trabecular bone volume. Thus, our findings suggest that intermittent compressive forces applied on tibiae at mild-moderate strain magnitude induce a significant and persistent longitudinal bone growth. PTHrP expressed in the growth plate appears to be one growth factor responsible for stimulating endochondral ossification and bone growth in female mice.

The effect of orthodontic Force Application and Tooth Movement on Dental Pulp

This systematic review aimed to conclusively investigate the effect of continuous intrusive force application on human pulpal blood flow (PBF). It is a well-established fact that applying a severe orthodontic force for an extended period can cause irreversible pulpitis and necrosis in the pulp by accelerating the inflammation process. In contrast, utilizing moderate and intermittent forces allows for ample tooth movement, limits pulp damage, and facilitates pulp healing. Materials and methods: A comprehensive search of published studies was conducted in several electronic databases such as MEDLINE, PubMed, EMBASE, Scopus, Web of Science, CINAHL, and the Cochrane Database of Systematic Reviews, as well as Google Scholar. The search was conducted without limitations to find published studies. The results showed that orthodontic forces can lead to a decrease in pulpal blood flow, which causes a reduction in tooth sensitivity. This reduction is indicated by an increase in response thresholds and more negative responses to tooth sensitivity tests. Conclusion: applying a severe orthodontic force over a prolonged period of time can lead to irreversible pulpitis and necrosis in the pulp due to an increase in the inflammation process. However, using moderate and intermittent forces can facilitate sufficient tooth movement while minimizing damage to the pulp. This highlights the importance of the endodontic-orthodontic interface and the need to consider dental pulp health during orthodontic treatment to avoid dental trauma.

Randomized clinical trial on the effect of intermittent vibrational force application during orthodontic treatment with aligners on RANKL and OPG concentrations in crevicular fluid.

Application of intermittent forces by vibration is proposed as an easy-to-use accelerator of dental movement. The purpose of this study was to determine the effect of intermittent vibrational force application during orthodontic aligner treatment on receptor activator of nuclear factor-kappa B ligand (RANKL) and osteoprotegerin (OPG) concentrations in crevicular fluid as markers of bone remodeling. This three-arm parallel randomized clinical trial included 45 candidates for malocclusion treatment with aligners, randomly assigned to: Group A (vibrational forces from onset of treatment); Group B (vibrational forces at 6 weeks after treatment onset); or Group C (no vibration). The frequency of aligner adjustment also differed among groups. At different time points, a paper tip was used to draw crevicular fluid samples from a moving lower incisor for RANKL and OPG analysis using ELISA kits. Mixed-model ANOVA found no significant differences in RANKL (A: p=0.31, B: p=0.8, C: p=0.49) or OPG (A: p=0.24, B: p=0.58, C: p=0.59) over time in any group or as a function of the application/non-application of vibration or the frequency of aligner adjustments. Application of this accelerator device did not significantly affect bone remodeling in patients undergoing orthodontic treatment with aligners. However, a nonsignificant improvement in biomarker concentrations was observed when aligners were changed every 7 days and vibration was also applied. Further research is warranted to establish protocols for the application of vibration and the timing of aligner adjustments.

Levels of Pro-Inflammatory and Bone-Resorptive Mediators in Periodontally Compromised Patients under Orthodontic Treatment Involving Intermittent Forces of Low Intensities.

During orthodontic treatment, diverse cytokines, enzymes, and osteolytic mediators produced within the teeth surrounding periodontal tissues determine the rate of alveolar bone remodeling and consequent teeth movement. In patients with teeth presenting reduced periodontal support, periodontal stability should be ensured during orthodontic treatment. Thus, therapies based on the application of low-intensity intermittent orthodontic forces are recommended. To determine if this kind of treatment is periodontally well tolerated, this study aimed to analyze the production of receptor activator of nuclear factor kappa-B ligand (RANKL), osteoprotegerin (OPG), interleukin (IL)-6, IL-17A, and matrix metalloproteinase (MMP)-8 in periodontal tissues of protruded anterior teeth with reduced periodontal support and undergoing orthodontic treatment. Patients with periodontitis-associated anterior teeth migration received non-surgical periodontal therapy and a specific orthodontic treatment involving controlled low-intensity intermittent orthodontic forces. Samples were collected before periodontitis treatment, after periodontitis treatment, and at 1 week to 24 months of the orthodontic treatment. During the 2 years of orthodontic treatment, no significant differences were detected in the probing depth, clinical attachment level, supragingival bacterial plaque, and bleeding on probing. In line with this, the gingival crevicular levels of RANKL, OPG, IL-6, IL-17A, and MMP-8 did not vary between the different evaluation time-points of the orthodontic treatment. When compared with the levels detected during the periodontitis, the RANKL/OPG ratio was significantly lower at all the analyzed time-points of the orthodontic treatment. In conclusion, the patient-specific orthodontic treatment based on intermittent orthodontic forces of low intensities was well tolerated by periodontally compromised teeth with pathological migration.

Finite Element Study to Evaluate the Stress Around Mini-implant during Canine Retraction using Continuous and Interrupted Orthodontic Forces

Abstract:
 Objectives: This work aimed to determine the stress distribution around a mini-implant during dynamic canine retraction utilizing continuous and intermittent orthodontic forces and a three-dimensional finite element model.
 Materials and Methods: Establishing a three-dimensional finite element model of canine retraction. The model incorporates a mini-implant, alveolar bone, maxillary teeth, a closed coil spring, and an elastic chain. They were described as being homogeneous, isotropic, and linear elastic. Continuous and interrupted forces were approximated by a NiTi coil spring and an elastic chain, respectively. To retract the canine, a simulated orthodontic force of 1.5N, 2N, and 2.5N were loaded. ANSYS evaluated the value of the stress distribution around the mini-implant, canine, and bone interface (workbench 19).
 Results indicated that there was no significant difference between the values of maximum stress around the miniscrew, canine, and bone under different orthodontic loads when a closed coil spring and an elastic chain were evaluated.

Nonprehensile manipulation of a stick using impulsive forces

The problem of nonprehensile manipulation of a stick in three-dimensional space using intermittent impulsive forces is considered. The objective is to juggle the stick between a sequence of configurations that are rotationally symmetric about the vertical axis. The dynamics of the stick is described by five generalized coordinates and three control inputs. Between two consecutive configurations where impulsive inputs are applied, the dynamics is conveniently represented by a Poincaré map in the reference frame of the juggler. Stabilization of the orbit associated with a desired juggling motion is accomplished by stabilizing a fixed point on the Poincaré map. The Impulse Controlled Poincaré Map approach is used to stabilize the orbit, and numerical simulations are used to demonstrate convergence to the desired juggling motion from an arbitrary initial configuration. In the limiting case, where consecutive rotationally symmetric configurations are chosen arbitrarily close, it is shown that the dynamics reduces to that of steady precession of the stick on a hoop.

Intermittent attractive interactions lead to microphase separation in nonmotile active matter.

Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class. In particular, we confirm the presence of microphase separation by solving the kinetic equationsnumerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g., in populations of bacteria interacting via type IV pili.

Piezoelectric energy harvesting for powering a novel weigh-in-motion system

• Roadway piezoelectric energy harvester (PEH) developed to power weigh-in-motion system. • PEH was tested under sinusoidal and pulse forces in the laboratory. • An electromechanical model associates applied forces on PZT stacks to output voltage. • The developed PEH circuit includes a rectifier, a capacitor, and a flyback converter. • Traffic forces exceeding flyback input thresholds generate sufficient power for MCU. This paper describes the development and evaluation of a piezoelectric energy harvester (PEH) designed to power a novel system for weighing roadway vehicles in-motion. The PEH consists of four lead zirconate titanate piezoelectric (PZT) stacks connected in parallel. Each stack is made of six PZT elements of alternating polarity. The paper describes the electromechanical characterization of the PZT stacks, the design of the PEH electronic circuit and its power generation potential under realistic traffic conditions. An electromechanical model was fitted to laboratory data that allows relating PZT stacks voltage output to the applied forces, as a function of loading frequency (i.e., vehicle speed). The PEH circuitry consists of a rectifier, a flyback and a step-down converter to reduce voltage output to the 0–3.3 V range. The flyback input thresholds were 100 V and 300 mW. At highway speeds, these thresholds were exceeded for sinusoidal forces with amplitudes higher than 13 kN. Exceeding these thresholds generated over 200 mW of power, which is sufficient for supporting the low-power microprocessors considered. The amplitude of intermittent pulsating forces that can exceed these thresholds were estimated as a function of the rest period between pulses. For a rest period of 60 ms (i.e., typical rest period between tandem truck axles), the estimated amplitude was 33.4 kN. It was shown that this force is exceeded by roughly 35% of the typical truck tires.

Transitory R wave growth in the midst of ST-segment elevation myocardial infarction: A case of left septal fascicular block with atypical electrocardiographic presentation

We report the case of a patient who presented with angina and ST-segment elevation in the precordial leads owing to a proximal occlusion of the left anterior descending coronary artery. Serial electrocardiography (ECG) showed signs consistent with the left septal fascicular block (LSFB). The latter was observed in conjunction with a pre-existing left anterior fascicular block and presented atypical ECG features, such as intermittent prominent anterior QRS forces (prominent R wave) in V2 only and preserved septal q waves in I and aVL. In the discussion, we present an overview of the electrocardiographic criteria for the diagnosis of the LSFB together with reasons for which LSFB may present with an atypical ECG picture.

Automatic continuous distraction osteogenesis device for hand reconstruction applications

Distraction Osteogenesis (DO) is an emerging technique for reconstruction of bone tissue in different body zones including mandible, tibia, hand, and foot. The application of DO technique in reconstruction of bone tissue has shown promising results compared to conventional reconstruction techniques, including bone grafting, prosthetics, and the vascularized flap. Mechanical distractors, with intermittent manual activation by the user, have been widely used in different reconstruction applications. Recently, automatic devices have been developed and used for enabling reconstruction applications using continuous DO technique. These devices can generate a continuous force while continuously moving the bone segment with high movement accuracy and distraction rate. In the continuous DO technique, by using a continuous force, instead of applying intermittent manual forces generated by the operator, better results in a shorter treatment could be obtained. Previous studies have shown that current automatic devices could positively influence bone tissue regeneration while obtaining promising results in the reconstruction of mandible. In hand reconstruction applications (HRA), only manual and mechanical mechanisms, using discontinuous DO technique, have been developed and used. In this research, an automatic device for HRA, using continuous DO technique, has been designed and developed. The proposed system is capable of generating a continuous distraction force for moving the bone segment in a fully automatic DO process. This novel reconstruction approach can be used for lengthening and reconstruction of different hand bones, including distal, middle, proximal, metacarpal, and carpal bones. In HRA, by using the proposed automatic continuous distractor better results in a shorter treatment period, compared to manual DO solutions, can be achieved

Comparative evaluation of interrupted and intermittent forces on canine retraction: an in vivo study.

Various force systems are used in orthodontics to move teeth, such as continuous, intermittent and interrupted. Teeth responds differently to these orthodontic forces. The aim of the study is to compare the rate of canine retraction with intermittent and interrupted forces. A split mouth study was carried among eighteen participants. One side of maxillary arch randomly received interrupted force with elastomeric powerchain while other received intermittent force with elastics with magnitude of 150-170g for canine retraction on each side. For 15 weeks, participants were asked to wear the elastics 8 hours a day whereas the elastomeric powerchains were replaced by operator every 5 weeks. The outcomes were assessed using scanned images of study models collected at the beginning (T0) and 15 weeks later (T3) as well on OPG. Linear and angular measurements were used to measure the distal movement, rotation as well tipping of canines and the results were statistically analysed using Independent t-test. The distal movement of canine on the interrupted force side was 0.98mm/5weeks and on the intermittent force side was 1.06mm/5weeks. The distopalatal rotation on interrupted and intermittent force side was 8.38° and 5.72°. Tipping measured on OPG was 5.72° and 5.27° for interrupted and intermittent force. No statistically significant differences were found. The rate of canine retraction with interrupted force and intermittent force showed no statistically significant differences. Less canine rotation and tipping with intermittent force compared to interrupted force though not statistically significant.

Treatment of Class II malocclusion with the improved superelastic nickel-titanium alloy wire and long hooks for mandibular molar protraction

• Two patients were treated with extraction of the mandibular second premolars. • We used superelastic nickel-titanium alloy wires as working wires. • The use of nickel-titanium wires and long hooks worked to mesialize the molar bodily. The mandibular first molar must be carefully moved to prevent mesial tipping and extrusion in case extraction of the mandibular second premolar is required to achieve the desired goals. The nickel-titanium alloy has unique mechanical properties, including superelasticity and shape memory, leading to the generation of continuous light forces that may be more biologically compatible than intermittent strong forces. However, it provides poor root control because of its low stiffness. We herein have experienced the patients with Angle Class II malocclusion that uses the improved superelastic nickel-titanium wire (ISW) and long hooks to achieve bodily movement of the mandibular first molar. The 0.022 × 0.028-in slot preadjusted edgewise appliances and 0.020 × 0.025-in ISWs as the working archwire were used. We pinched the crimpable long hooks on the rectangular ISW and applied 100-150 g of contractile force between the fixed long hooks and bracket hooks of the mandibular first molars to activate the system with ligature wire lacing. The mandibular molars were uprighted and mesially moved; panoramic radiographs did not indicate severe root resorption. These experiences suggest that this method involving the combined use of the ISW and long hooks may be one of the useful methods for closing spaces by facilitating the uprighting and mesial movement of the molars in treating Class II malocclusion.

Force Reconstruction at Mechanical Interfaces Using a Modal Filtering Decomposition Approach

Traditional approaches to analyzing nonlinear systems often involve assuming a specific model form and model order for the nonlinearity. These nonlinearities in a system could instead be modeled as a nonlinear force applied to an underlying linear system. Force reconstruction methods can be used to recreate this nonlinear force from measured data, allowing the system change to be quantified. A modal based force reconstruction technique has proven capable of recreating force inputs at unmeasured locations and has been successfully applied to nonlinear intermittent external contact forces in previous studies. To extend these findings, a two-beam system was designed such that intermittent contact occurs near the joint locations, resulting in correlated forces. Previous work with this methodology has not addressed correlated loading conditions, so this work extends these techniques to the localization of correlated forces beyond measured points. The methodology is first demonstrated using analytical case studies, then performed experimentally. Acceleration responses are obtained from a sparse measurement grid which does not include the contact points, so the forces are reconstructed at unmeasured locations. Estimates of the nonlinear contact forces are calculated using the force reconstruction process, which are then compared to the measured force values. Cases are presented which address intermittent contact, loosening of preloaded connections, and the reconstruction of multiple connections simultaneously. Reconstructing correlated forces beyond measured points allows for the ability to locate and estimate forces without needing to assume the locations of these forces prior to acquiring data, extending the range of applications for these techniques.

Common skin disease “corns” with effective homeopathic medicine Silicea

A corn (also termed clavus) is a thickening of the skin due to intermittent pressure and frictional forces. These forces result in hyperkeratosis, clinically and histologically. The word clavus has many synonyms and innumerable vernacular terms Silicea is a good homeopathic remedy of many skin issues one of from it corns. Silicea helps the body eliminate splinters, acne, eruptions, corns, and fungus issues. It also indicates in keloidal growth, felons, abscesses, boils, old ulcers. Silicea is key roll medicine in homoeopathic Materia medica in skin region. In India corns (clavus) are very commonly found. It will help to explore the scope and therapeutic effect of silicea in management of corns.

A self-calibration method for rotary tables’ five degrees-of-freedom error motions

The paper proposed a novel self-calibration method for five degrees-of-freedom error motions of rotary tables. Two encoders with multiple reading heads were installed on the spindle’s different positions to measure rotation angles. By analyzing indication differences between the reading heads, the two grid discs’ radial motions were obtained. After Fourier analysis, measurement errors caused by the installation errors of the grid discs were eliminated and two different positions’ error motions of the spindle were obtained. Therefore, the rotary table’s 5-DOF error motions, including angular positioning (ECC) error motions, radial (EXC, EYC) and tilt (EAC, EBC) error motions defined in ISO 230-7 and ANSI/AMSEB89.3.4, were self-calibrated. In order to verify the proposed self-calibration method, roundness errors of a cylinder were measured on a rotary table with a self-calibration system. During the measurement of the roundness errors, the error motions of the rotary table were measured simultaneously by the self-calibration system. After error compensations and eliminating influences of error motions of the rotary table, measurement data of the roundness errors were obtained. Compared with the calibration of three-point method for measuring roundness errors, the residual errors were less than ±0.5 μm. In order to verify dynamic measurement, external forces were loaded on the rotary table intentionally during the measurement process. The error motions of the rotary table changed with intermittent external forces, which were also detected accurately by the self-calibration system on line. After error compensations, the calibrations trend and magnitude with three-point method showed that error motions self-calibration of the rotary table are effectiveness and feasibility.

Comparison between two screws for maxillary expansion: a multicenter randomized controlled trial on patient's reported outcome measures.

The objective of this study was to compare an expansion screw of the maxilla that generates moderate and continuous forces versus a conventional screw for rapid maxillary expansion (RME) on patient-reported outcome measure during the first 12 weeks of treatment. This is a superiority, multicenter, two-arm parallel balanced randomization trial. Patients in the mixed dentition were included with a transverse discrepancy between the two arches of at least 3 mm. An expansion screw using moderate continuous forces (Leaf group, treated with an expansion screw with Ni-Ti springs) was compared to a conventional RME screw that generates intermittent heavy forces (RME group). The primary response variable was the visual analogue scale (VAS) on pain calculated in the first 12 weeks of therapy. The VAS on difficulty on speaking and oral hygiene, patient satisfaction, and complications were also evaluated. A computer-generated block randomization was used with allocation concealed in sequentially numbered opaque-sealed envelopes. Blinding was not applicable. Linear models were used for statistical analysis. Twenty-eight patients in the Leaf group and 28 patients in the RME group were randomized and included in the study. There were no dropouts. The mean of the VAS for pain was 0.3 ± 0.4 in the Leaf group and 0.6 ± 0.5 in the RME group. The difference was -0.3 (95 per cent CI from -0.5 to -0.0; P = 0.017) in favour of the Leaf group. The difference in pain was marked in the first week (Leaf group 2.2 ± 2.3; RME group 3.7 ± 2.6; difference -1.5; 95 per cent CI from -2.7 to -0.3; P = 0.019). Patients in the Leaf group experienced a lower degree of pain, especially during the first week following the application of the expander. For the other variables, no significant differences were reported between the two treatments. The study was registered in the ISRCTN register on 8 November 2016 with the number ISRCTN18263886.

Force-responsive Zyxin modulation in periodontal ligament cells is regulated by YAP rather than TAZ

In the context of mechanically induced force transmission, the modification of the actin cytoskeleton through involvement of zyxin is an established concept. However, in cells of the periodontal ligament (PDL), which is physiologically subjected to intermittent mechanical forces, the force-responsive modulation of zyxin and the molecular key players, which orchestrate its cellular regulation, have not yet been elucidated. By employing indirect immunofluorescence and western blotting with different subcellular fractions, we show here in stretch force-exposed human PDL fibroblasts (hPDLFs) that (i) the zyxin protein is modulated, and (ii) its subcellular localization is altered. More importantly, using a pharmacological intervention approach, to inhibit the nuclear presence of the co-transcriptional activator yes-associated protein (YAP), we evidence for the first time that on the molecular level, the cellular abundance of zyxin, among the Thyrotrophic Embryonic Factor (TEF)-binding proteins, is regulated by YAP rather than TAZ. Our findings provide novel insights into the topic how cells of the periodontium and the periodontal ligament in particular respond and may adapt to mechanical forces, and first time identify YAP as the key player of the intracellular regulation of the mechano-sensor and mechano-transducer zyxin in hPDLFs. Moreover, the findings broaden the current knowledge on YAP, since so far, currently only very few YAP-regulated genes have been identified.

Review of the biological aspects in the periodontal ligament and alveolar bone associated with compression

Background: Tissue remodeling requires protein degradation through a process directly dependent on metalloproteinases — enzymes capable of degrading the majority of proteins in this system. This process is regulated by some enzyme inhibitors, and balance between enzyme and inhibitor activity is fundamental to tissue integrity and health. Bone resorption and formation, and the molecules involved in these processes, raise questions on possible differences in tissue behavior in the system. Histological studies of tissues surrounding teeth that have been subjected to such forces show the presence of tension (associated with bone formation) and compression, which induce bone resorption. The duration of load application is an important parameterin osteoclastogenesis. The present study aimed to analyze the biological aspects associated with in vitro compression of the PL and alveolar bone. To this end, we reviewed articles describing the biological events that occur in the PL and alveolar bone during load application on this system and the possible influence of culture medium on the expression of molecules involved in response to such an event.
 Methods: This literature review included articles published between March 2008 and January 2018 describing in vitro laboratory tests and data on load application and its associated biological events in the human PL and alveolar bone, including studies on molecular-expression events and pathways involved in the process.
 Conclusions: Intermittent compressive forces stimulate bone resorption in orthodontic treatment, while cyclical forces induce cellular apoptosis at lighter loads than do compressive forces. Both 2D and 3D cell-culture systems seem to reproduce the physiology of evaluated tissues and are reliable analytical models for research purposes.

An Embedded Sensor System for Real-Time Detecting 5-DOF Error Motions of Rotary Stages.

The geometric error motions of rotary stages greatly affect the accuracy of constructed machines such as machine tools, measuring instruments, and robots. In this paper, an embedded sensor system for real-time measurement of two radial and three angular error motions of a rotary stage is proposed, which makes use of a rotary encoder with multiple scanning heads to measure the rotational angle and two radial error motions and a miniature autocollimator to measure two tilt angular errors of the axis of rotation. The assembly errors of the grid disc of the encoder and the mirror for autocollimator are also evaluated and compensated. The developed measuring device can be fixed inside the rotary stage. In the experiments, radial error motions of two points on the axis (h = 5 mm and 60 mm) were measured and calibrated with LVDTs, and the data showed that the radial error motions of the axis were less than 20 μm, and the calibration residual errors were less than 2 μm. When intermittent external forces were applied to the stage, the change of the stage’s error motion could also be monitored accurately.