Relative Angular Error Research Articles

Experimentally induced pain increases absolute but not relative errors and reduces variability in joint repositioning of the knee joint in healthy participants

BackgroundJoint position sense (JPS) plays an important role in knee joint function. Despite the possible influence of pain on the proprioceptive system, the effects of experimental muscle pain on knee JPS have not been studied. ObjectivesTo investigate if experimentally induced muscle pain affects knee JPS in healthy participants. MethodsMeasurements of knee JPS were conducted before and after the injection of 5.8% sterile hypertonic saline in the vastus medialis muscle of 26 healthy physically active adults. Knee JPS was assessed through a passive/active repositioning paradigm in target angles of 15°, 45° and 60° using an isokinetic dynamometer. Absolute and relative angular errors were calculated. The coefficient of variation analysis was used to assess differences in the angles’ variability during the repositioning task. ResultsAbsolute angular error increased in all three angles following experimentally induced pain. The difference was statistically significant at 45° (p = 0.003, d = 0.6) and 15° (p = 0.047, d = 0.4) but not at 60° (p = 0.064, d = 0.4). Relative error did not show directional bias at 45° (p = 0.272, d = 0.2), 15° (p = 0.483, d = 0.1) or 60° (p = 0.091, d = 0.3). The coefficient of variation analysis revealed a statistically significant reduction in variability at angles of 60° (p = 0.002, d = 0.7) and 15° (p = 0.031, d = 0.4) after the pain intervention. ConclusionThe presence of experimentally induced muscle pain affects the ability of healthy participants to accurately reposition the knee at two angles of knee flexion and reduces movement variability during the repositioning task. Further research is required to determine if these deficits also impact patients with clinical knee pain.

The effectiveness of fatigue on repositioning sense of lower extremities: systematic review and meta-analysis.

An injury can significantly harm both individual and team performance. One of the most important risk factors for sports-related injuries, especially non-collision injuries, is fatigue. It seems that poor proprioception may play an essential role to impose athletes to further injuries. This systematic review and meta-analysis aimed to examine the effectiveness of fatigue on the repositioning sense of the lower extremity joints. The electronic databases, including PubMed, Web of Science, Scopus, and Google Scholar were systematically searched from inception to 11January 2024. The obtained records were exported to the EndNote Software version 8. Then, two investigators examined the records independently to find eligible studies based on the inclusion/exclusion criteria. In the case of disagreements, a consequence method was utilized. The quality of the eligible studies was evaluated using the Downs and Black checklist. Comprehensive Meta-Analysis (CMA) software ver. 3 software was used for statistical analysis. Q-test and I2 were employed to examine the data homogeneity. In addition, considering the risk of bias, the Funnel Plot and trim-and-fill method were used. After reviewing the titles and abstracts of 3883 studies found in the selected databases, 43 articles were found to be eligible to include in meta-analyses. The results showed that fatigue led to a significant increase in the active absolute error of the knee (SDM = 0.524, 95% CI = 0.406-0.841), ankle in the horizontal plane (SDM = 0.541, 95% CI = 0.367-0.715), ankle in the sagittal plane (SDM = 0.443, 95% CI = 0.088-0.798), and hip (SDM = 0.988, 95% CI = 0.135-1.841). However, fatigue had no significant effects on the passive absolute error of the knee and ankle in horizontal plane and relative angular error of the knee. Fatigue can diminish the active joint position sense of the lower extremities and thus may increase the risk of injury by reducing proprioception. Therefore, future research could be conducted to investigate the potential impact of integrated fatigue-mitigating exercises into athletes' training programs, with the aim of reducing the incidence of sports-related injuries.

Angular Error Reduction of a Machine Vision System using a Trapezoidal Trajectory Velocity Profile

Nowadays laser scanners play an important role in technology and research, when it comes to measure 3D coordinates physically and in real time of any object under observation. Laser scanners have to measure the 3D coordinates of these objects in shortest time and with the smallest measuring error. A novel laser scanner called Technical Vision System (TVS), which uses Dynamic Triangulation and DC motors, was developed and proven to represent a fast and reliable scanning system. Previous research used the step response of the TVS mechanical actuators (DC motors), which can overshoot if certain controller parameters of the closed-loop control are selected. If the overshoot is undesirable, a trade-off must be made between speed and overshoot of the step response. Thereby, present paper describes a new approach to control the actual angular position of the TVS DC motors using a trapezoidal profile for the DC Motor velocity. The DC motors step response is replaced by a trajectory response, which allows the reduction of the relative angular error of the DC motors shaft to a value less than or equal to 0.1 percent. Also, the design of the control system, to implement the trapezoidal trajectory profile for the DC motor velocity in practice, is described in detail.

The effect of static stretching of agonist and antagonist muscles on knee joint position sense

Background/Aims Proprioception acuity is important in sports activities and stretching is widely used in warm-up programmes. The main objective of this study was to evaluate if a warm-up programme with and without stretching flexors and extensors muscles could affect knee joint position sense. Methods The effects of different stretching regimens on joint position sense were examined. A total of 12 semi-professional football players completed four warm-up sessions over 4 weeks: standard warm-up programme; standard warm-up programme with quadriceps stretching; standard warm-up programme with hamstring stretching; and standard warm-up programme with stretching of both quadriceps and hamstrings. Open kinetic chain knee joint position sense was estimated from the ability to reproduce the three target angles (20°, 45° and 60° knee flexion) in the dominant limb before and after the intervention. Results In the absolute angular error, there was a statistically significant three-way interaction between the warm-up programme, target angle and time (F (6, 54)=6.88, P=0.001). Findings of post-hoc analysis demonstrated that there was a statistically significant difference between the pre- and post-stretching of hamstrings for the target angles of 20° (4.70 vs 1.57, P=0.01), 45° (1.70 vs 4.50, P=0.02), and 60° (1.93 vs 4.20, P=0.02). In the relative angular error, interaction of time by the warm-up programme was significant (F (3, 27)=3.41, P=0.03). Conclusions The warm-up programme with static stretching of hamstrings had a negative effect on open kinetic chain knee joint position sense during the flexion to extension repositioning task, which may not only have a negative effect on performance of athletes as a part of warm-up exercises, but may also lead to further injuries.

Knee proprioceptive function and physical performance of patients with patellofemoral pain: A matched case-control study

BackgroundPatients with patellofemoral pain (PFP) present pain, functional limitation, and alteration in knee proprioception. PurposeTo compare the knee joint position sense and lower extremity functionality between patients with PFP and controls. Secondarily, investigate the relationship between proprioceptive acuity and physical performance. MethodsThis is a matched case-control study including 48 patients with PFP and 48 healthy individuals matched by age, sex, weight, height, and limb dominance. The proprioceptive evaluation was performed using the joint position sense test (absolute error and relative error) and functionality was assessed using the Single-Leg Triple-Hop test and the Y-Balance Test. The groups were compared using the independent student’s T-test. Proprioceptive acuity and physical performance correlations were determined by Pearson correlation coefficient. ResultsParticipants were on average 31 years old and 62.5% were men. There was no statistically difference for absolute and relative angular error between groups. Patients presented lower relative reached distance on the anterior direction of the Y-Balance Test than controls [patients=58.6 (6.6) % versus controls=61.7 (5.9) %, p=.020]. No differences between groups were found for other functional measures. Significant correlation was found between absolute angular error and anterior component at 60° (r=0.225, p=.028) and relative angular error at 60° with the posterolateral component of the Y- Balance Test (r=0.231, p=.024). ConclusionProprioceptive acuity of patients with PFP was not reduced. The anterior direction of the Y-Balance Test was impaired compared to matched controls. Proprioceptive sense is related to dynamic balance but not to jump ability.

Validity and Reliability of a Digital Inclinometer to Assess Knee Joint Position Sense in an Open Kinetic Chain.

Context: New methods are being validated to easily evaluate the knee joint position sense (JPS) due to its role in the sports movement and the risk of injury. However, no studies to date have considered the open kinetic chain (OKC) technique, despite the biomechanical differences compared with closed kinetic chain movements. Objective: To analyze the validity and reliability of a digital inclinometer to measure the knee JPS in the OKC movement. Design: The validity and intertester and intratester reliability of a digital inclinometer for measuring knee JPS were evaluated. Setting: Sports research laboratory. Participants: A total of 18 athletes (11 males and 7 females; 28.4 [6.6]y; 71.9 [14.0]kg; 1.77 [0.09]m; 22.8 [3.2]kg/m2) voluntary participated in this study. Main Outcomes Measures: Absolute angular error (AAE), relative angular error (RAE), and variable angular error (VAE) of knee JPS in an OKC. Results: Intraclass correlation coefficient (ICC) and standard error of the mean(SEM) were calculated to determine the validity and reliability of the inclinometer. Data showed excellent validity of the inclinometer to obtain proprioceptive errors compared with the video analysis in JPS tasks (AAE: ICC = .981, SEM = 0.08; RAE: ICC = .974, SEM = 0.12; VAE: ICC = .973, SEM = 0.07). Intertester reliability was also excellent for all the proprioceptive errors (AAE: ICC = .967, SEM = 0.04; RAE: ICC = .974, SEM = 0.03; VAE: ICC = .939, SEM = 0.08). Similar results were obtained for intratester reliability (AAE: ICC = .861, SEM = 0.1; RAE: ICC = .894, SEM = 0.1; VAE: ICC = .700, SEM = 0.2). Conclusions: The digital inclinometer is a valid and reliable method to assess the knee JPS in OKC. Sport professionals may evaluate the knee JPS to monitor its deterioration during training or improvements throughout the rehabilitation process.

The Validity and Reliability of Knee Proprioception Measurement Performed With Inclinometer in Different Positions.

Proprioception is the basic element of the spontaneous control of movement, balance and joint stability. Therefore, it is necessary for the execution of walking and daily and sport activities. Loss of proprioception of the knee, which may cause a new injury, is important to evaluate the position sense of the joint during the rehabilitation period. However, the evaluation methods that are used are very expensive, complicated and non-portable, or the measuring method is difficult to implement. We demonstrated the validity and reliability of knee proprioception measurements performed in the open kinetic chain position and closed kinetic chain position with a dual inclinometer. We assessed the validity and intra-tester reliability of a digital inclinometer for measuring the knee joint position sense in different positions. Clinical laboratory. We enrolled 22 participants (age = 21.8 ± 0.95 years, height = 172 ± 9.1 cm, weight = 64.9 ± 14 kg) into the study. The same investigator used an inclinometer to take knee proprioception measurements in open and closed kinetic chain positions. The relative angular error was calculated by taking the arithmetic average of the difference between the target angle and reproduced angle and was the main outcome measure. We found that the dynamometer-inclinometer had a moderate ICC value (ICC = 0.594, SEM = 1.60, p = 0.005), whereas inclinometer t1 vs inclinometer t2 (ICC = 0.778, SEM = 0.62, p < 0.001) and closed kinetic chain position t1 and closed kinetic chain position t2 (ICC = 0.888, SEM = 0.63, p < 0.001) had high ICC values. Knee proprioception measurements performed with a dual inclinometer were reliable in the closed kinetic chain position in healthy, sedentary individuals and were valid and reliable in the open kinetic chain position.

Relative Attitude Estimation for a Uniform Motion and Slowly Rotating Noncooperative Spacecraft

This paper presents a novel relative attitude estimation approach for a uniform motion and slowly rotating noncooperative spacecraft. It is assumed that the uniform motion and slowly rotating noncooperative chief spacecraft is in failure or out of control and there is no a priori rotation rate information. We utilize a very fast binary descriptor based on binary robust independent elementary features (BRIEF) to obtain the features of the target, which are rotational invariance and resistance to noise. And then, we propose a novel combination of single candidate random sample consensus (RANSAC) with extended Kalman filter (EKF) that makes use of the available prior probabilistic information from the EKF in the RANSAC model hypothesis stage. The advantage of this combination obviously reduces the sample size to only one, which results in large computational savings without the loss of accuracy. Experimental results from real image sequence of a real model target show that the relative angular error is about 3.5% and the mean angular velocity error is about 0.1 deg/s.

生体内コーンビーム CT 画像による三次元自動歯軸

The tooth axis is important as a morphological reference axis; however, a general definition of the tooth axis has not been established. This study presented a novel method of automatically calculating three-dimensional tooth axes on in vivo Cone-Beam Computed Tomography (CBCT) images. In this study, 36 teeth were obtained from 12 central and lateral incisors, and canines of 3 human subjects, respectively. Human in vivo images were obtained using a CBCT at a spatial resolution of 0.183 mm3 . The automatically tooth axis (PC-A) was calculated using principal component (PC) analysis of the segmented tooth and mandible. In experimental results using 36 teeth, the average relative angular errors between the tooth axes T-A manually specified by three dentists and the PC-A automatically calculated by the proposed method were 2.2 ± 1.4° for central incisors, 1.7 ± 1.0° for lateral incisors, 2.3 ± 1.4° for canines, respectively. The relative distance errors between the T-A and the PC-A were 0.39 ± 0.17 mm, 0.39 ± 0.21 mm and 0.63 ± 0.34 mm for central incisors, lateral incisors and canines, respectively. The experimental results of this study demonstrate that the proposed method of CBCT can accurately and automatically identify individual three-dimensional tooth axes.

Reproducibility of a knee and hip proprioception test in healthy older adults.

Proprioception can be assessed by measuring joint position sense (JPS). Most studies have focused on JPS of the knee joint while literature for other joints especially for hip JPS is scarce. Although some studies have evaluated proprioception of the knee joint, the reproducibility of methods has rarely been investigated. To estimate intrasession reliability and agreement of an active-active JPS test for hip flexion/abduction and knee flexion in healthy older adults. Nineteen healthy older adults participated in this study. The proprioception of the hip (flexion and abduction) and knee (flexion) were assessed in both legs using the "active-active" reproduction technique. Intraclass correlation coefficient (ICC), standard error of measurement (SEM), and limits of agreement (LOA) were estimated for relative angular error (RE), absolute angular error (AE), and variable angular error (VE). Reliability of our JPS test was substantial to almost perfect for the RE for both joints and legs (ICC values ranging from 0.75 to 0.93). We also found that the ICC values for AE were substantial for knee flexion and hip abduction of the left and right leg. The ICC results of VE showed poor reliability for hip and knee joints. SEM and LOA values for hip abduction were generally lower than for hip and knee flexion, indicating lower measurement error or more precise scores for the proprioception test of hip abduction. Proprioceptive acuity of the knee and hip joints in healthy older adults can be reliably assessed with an active-active procedure in a standing position with respect to relative and absolute error.

J0210204 三次元歯軸の自動決定法に関する研究([J021-02]診療技術と臨床バイオメカニクスセッション(2))

The tooth axis is an important as a morphological reference axis; however general definition of the tooth axis has not been established. This study presented a novel method of automatically calculating three-dimensional teeth axes in micro-CT images. In this study, 20 teeth specimens were obtained from five incisors, canines, premolars and molars, respectively. X-ray images were obtained using a micro-CT scanner at a spatial resolution of 33×33×33μm^3. The tooth axis was calculated using a principal component (PC) analysis on the segmented soft pulp and dentin. The teeth axes of PC-A_+ and PC-A__ were defined as the including of the pulp and not, respectively. No significant differences were noted in the experimental results between PC-A_+ and PC-A__. In experimental results using 20 teeth, the average relative angular errors between the teeth axes T-A manually specified by five dentists and automatically calculated PC-A_+ by the proposed method were 1.14±0.11 deg for incisor, 1.74±0.74 deg for canine, 3.51±0.43 deg for premolar and 2.90±0.57 deg for molar, respectively.

Reposition Acuity and Postural Control after Exercise in Anterior Cruciate Ligament Reconstructed Knees

This study aimed to compare the effects of 36 min of continuous exercise on postural control and joint reposition acuity in patients with anterior cruciate ligament reconstruction (ACL-R) and healthy controls. Twenty patients (10 women and 10 men; mean ± SD; age = 25.5 ± 5.5 yr, height = 1.75 ± 0.10 m, weight = 76.7 ± 14.4 kg) with a history of primary, uncomplicated ACL-R (5.0 ± 4.3 yr postsurgery) were matched to 20 healthy controls (10 women and 10 men, 24.6 ± 5.0 yr, 1.70 ± 0.09 m, 65.2 ± 12.1 kg). The center of pressure (COP) excursions in the medial-lateral (COP(ML-SD)) and anterior-posterior (COP(AP-SD)) directions and the velocity (COP(Vel)) and area (COP(Area)) were calculated during static, unipedal stance. Open-chain knee joint reposition acuity measures (absolute angular error [AAE] and relative angular error [RAE]) at 45° (AAE₄₅ and RAE₄₅) and 15° of knee flexion (AAE₁₅ and RAE₁₅) were recorded. Measures were recorded at baseline and after a 36-min exercise protocol. Exercise consisted of six repeating cycles of inclined treadmill walking (5 min) and jumping exercises (1 min). At baseline, the ACL-R group exhibited higher magnitude AAE₄₅ compared with controls. AAE₄₅ and COP(ML-SD) significantly increased after exercise in the control group; however, the ACL-R group did not experience a change in these measures. In a rested state, patients with a history of ACL-R have greater impairment in joint reposition acuity than healthy control. Exercise increased COP measurements and impaired joint reposition acuity. Healthy controls experienced impaired joint reposition acuity after exercise, whereas patients with a history of ACL-R did not.

Pennation Angle Dependency in Skeletal Muscle Tissue Doppler Strain in Dynamic Contractions

Tissue velocity imaging (TVI) is a Doppler based ultrasound technique that can be used to study regional deformation in skeletal muscle tissue. The aim of this study was to develop a biomechanical model to describe the TVI strain’s dependency on the pennation angle. We demonstrate its impact as the subsequent strain measurement error using dynamic elbow contractions from the medial and the lateral part of biceps brachii at two different loadings; 5% and 25% of maximum voluntary contraction (MVC). The estimated pennation angles were on average about 4° in extended position and increased to a maximal of 13° in flexed elbow position. The corresponding relative angular error spread from around 7% up to around 40%. To accurately apply TVI on skeletal muscles, the error due to angle changes should be compensated for. As a suggestion, this could be done according to the presented model.

Warming-up before sporting activity improves knee position sense

Objective To evaluate the effects of a warm-up program on knee joint position sense in karatekas. Design Repeated measures design. Setting Research laboratory. Participants: Ten young amateur karatekas (17.6 ± 4.0 years of age). Main Outcome Measures Knee joint position sense evaluated before and immediately after a warm-up program through active repositioning in open kinetic chain (OKC) and closed kinetic chain (CKC). Results At baseline testing no differences were observed between OKC and CKC in absolute (4.1 ± 1.6° vs. 3.4 ± 2.0°) and relative angular errors (2.4 ± 3.4° vs. 2.1 ± 3.5°). After the warm-up program, a significant decrease in absolute angular error was observed only in CKC (from 3.4 ± 2.0° to 1.8 ± 0.5, p < 0.05). Additionally, in CKC the subjects reduced the relative angular error to approximately zero (from 2.1 ± 3.5° to −0.01 ± 1.6°) and decreased the variability of the responses, expressed by the decrease in standard deviation of the relative errors. Conclusions The warm-up program enhanced knee joint position sense only in CKC. Since no effects were detected in OKC, the evaluation of the effects of warm-up on knee joint position sense using merely an OKC technique would underestimate the valuable role of warm-up.

Cryotherapy Impairs Knee Joint Position Sense

The effects of cryotherapy on joint position sense are not clearly established; however it is paramount to understand its impact on peripheral feedback to ascertain the safety of using ice therapy before resuming exercise on sports or rehabilitation settings. Thus, the aim of the present study was to determine the effects of cryotherapy, when applied over the quadriceps and over the knee joint, on knee position sense. This within-subjects repeated-measures study encompassed fifteen subjects. Knee position sense was measured by open kinetic chain technique and active positioning at baseline and after cryotherapy application. Knee angles were determined by computer analysis of the videotape images. Twenty-minute ice bag application was applied randomly, in two sessions 48 h apart, over the quadriceps and the knee joint. The main effect for cryotherapy application was significant (F (1.14)=7.7, p=0.015) indicating an increase in both absolute and relative angular errors after the application. There was no significant main effect for the location of cryotherapy application, indicating no differences between the application over the quadriceps and the knee joint. In conclusion, cryotherapy impairs knee joint position sense in normal knees. This deleterious effect is similar when cryotherapy is applied over the quadriceps or the knee joint.

Effect of physical exercise and age on knee joint position sense

This study aimed to test the hypotheses that knee position sense declines with age and that regular exercise can attenuate that decline. This cross-sectional study encompassed 69 older and 60 young adults divided in four groups (exercised-old, N = 31; non-exercised-old, N = 38; exercised-young, N = 35; non-exercised-young, N = 25) according to chronological age and exercise practice in the past year. Knee position sense was measured by open kinetic chain technique and active positioning and is reported as the absolute and relative angular error. Knee angles were determined by computer analysis of videotape images using the Ariel Performance Analysis System. Compared to their non-exercised counterparts, exercised-young and -old showed lower absolute and relative angular errors. The absolute (1.62 ± 0.71°) and relative errors (0.02 ± 1.65°) for exercised-young were lower than all other groups ( p < 0.001). The absolute and relative errors of exercised-old (4.27 ± 2.49° and 5.51 ± 3.42°) were similar to non-exercised-young (4.74 ± 2.67° and 4.18 ± 3.40°). The non-exercised-old exhibited higher absolute (9.35 ± 4.34°) and relative errors (9.73 ± 5.15°) than all other groups ( p < 0.001). The present data indicates that age has deleterious effects on knee position sense although regular exercise can attenuate that age-related decline.

Age-related Differences In Knee Joint Position Sense

Proprioception has been found to deteriorate due to aging. Impaired proprioception has been linked to balance problems and degenerative joint disease. Age-related decline in joint position sense has been found at the elbow, fingers and ankle. However, few studies reporting incongruent results addressed this issue in the major joints (hip and knee) of the lower limb. PURPOSE: To investigate age-related differences in knee joint position sense. METHODS: The technique of open-kinetic chain and active knee positioning was used to evaluate knee joint position sense of 34 male subjects, 18 young (23.7 ± 2.5 years) and 16 older (69.81 ± 3.92 years). Subjects were seated, with the legs hanging freely, and blindfolded. One test position in middle range was investigated. Each subject had performed five trials trying to reproduce the target position. The target and the response positions were recorded with a video camera. The Ariel Performance Analysis System software was used to measure the angle of the knee from videotape records. Joint position sense was evaluated by measuring the following parameters: the absolute angular error (AAE), defined as the absolute difference between the target position and the response position; the relative angular error (RAE), defined as the signed arithmetic difference between a test and response position; and, the variable angular error (VAE) determined as the standard deviation from the mean of the relative errors. RESULTS: The mean AAE score (5.62 ± 4.21 vs. 2.48 ± 1.13; p=0.005) and the RAE score (5.13 ± 4.83° vs. −0.16 ± 2.59°; p<0.001) was higher in older subjects. Being the start position at 90° of flexion and the desired movement the knee extension, old age subjects showed a clear tendency to reproduce lower knee flexion angles than the pre- selected flexion angle determined by the examiner. The young subjects showed a trend to undershot the target. The VAE showed that young subjects had almost two times better reliability and accuracy in estimating knee angles than old age subjects. CONCLUSIONS: Aging lead to a significant decrease of the knee joint position sense. The age-related decline in joint position sense lead to a significant deviation from the target angle into the extension movement.

Experimental approach and RSM procedure on the examination of springback in wiping-die bending processes

Abstract In this work, springback has been investigated using experimental and theoretical approaches. Hence, the springback evolution with different die radius and stroke values was obtained on wiping-die bending process. In addition, the relative angular error was measured at the end of several bent tests for different clearance values and graphics were plotted. The experimental results have been also plotted for different cut directions of specimens in order to display the anisotropic effect on springback. Measurements were also carried out for concave and convex bending cases referring to the strip curvature. RSM methods, using three die radii and seven clearance values, were constructed for cubic interpolation functions and two cut specimen directions. The effects of each investigated parameter on springback and convenience of the obtained graphics were discussed in details.

Vestibular and vestibulo-proprioceptive perception of motion in the horizontal plane in blindfolded man—II. Estimations of rotations about the earth-vertical axis

Perception of angular displacement in the horizontal plane was studied in blindfolded human subjects. Subjects sitting on a rotating chair were turned and turned themselves about the earth-vertical axis. Magnitudes of left- and rightward directed rotations were in steps of 30° and overlapped an entire circle. The averaged relative angular error in estimation of passive turns was 0.19±0.014 (M±m), that of active turns 0.16±0.011. Passively rotated subjects tended to overestimate turns with an increase in the rotation magnitude. Estimations of passive turns were linearly related to the turn magnitude ( Y=−0.357+1.065 X; R 2=0.864). When turning themselves, subjects tended to overestimate rotations of lower magnitudes and underestimate those of higher magnitudes. Linearity was observed between estimations of active turns and their magnitude ( Y=26.456+0.862 X; R 2=0.857). Turn estimation is regarded as a geometrical task, which associates subjectively defined angular and linear parameters of circular motion. It is proposed that during rotation blindfolded subjects perceive the horizontal plane as a heterometric space, the extent of which depends on the estimation of a turn.