Measuring average angular velocity with a smartphone magnetic field sensor

Introduction: Falling during walking is a common occurrence in people with Parkinson's disease and is closely associated with severe social and medical consequences. Recent evidence demonstrates that arm swing affects dynamic balance in healthy young adults; however, it remains unexamined what its effect is in people with Parkinson's disease, particularly when combined with a secondary dual task.Methods: Twenty people with Parkinson's disease (63.78 ± 8.97) walked with two arm swing conditions (absent and normal) with and without a secondary dual task. Data were collected on a split-belt treadmill CAREN Extended-System (Motek Medical, Amsterdam, NL). Average and standard deviations for trunk linear and angular velocity were calculated along with their instantaneous values (during foot strikes) in all three axes. Averages and coefficient of variations for step length, time, and width; margin of stability; and harmonic ratios were also calculated.Results: Compared with normal arm swing, absent arm swing reduced the least affected leg's average step length and increased its step length coefficient of variation while increasing step time coefficient of variation in the most affected leg. Further, absent arm swing reduced trunk anteroposterior instantaneous angular velocity (least affected leg) and reduced anteroposterior instantaneous linear velocity (bilaterally). For the vertical axis, absent arm swing increased the trunk's average angular velocity but reduced its instantaneous linear velocity and angular velocity standard deviation (least affected leg). Additionally, the margin of stability increased when the arms were absent (least affected leg). Alternatively, dual tasking reduced average step time (most affected leg) and increased the step width coefficient of variation (bilaterally). Additionally, dual tasking increased the mediolateral average angular velocity, instantaneous linear velocity standard deviation (bilaterally), and instantaneous angular velocity standard deviation (least affected leg). For the vertical axis, dual tasking increased average linear and angular velocity standard deviation as well as instantaneous angular velocity standard deviation (bilaterally).Conclusion: Findings suggest that participants attempted to control extraneous trunk movement (due to absent arm swing) through compensatory responses in both lower and upper extremities. However, participants appeared to predominately compensate on their least affected side. Contrastingly, modifying mediolateral foot placement appeared to be the main means of maintaining walking stability while dual tasking.

Background: In the field of biomechanical analysis of pedaling motion, researchers studied the relationship between cost energy and cycling technique for optimal use of the force applied to the pedals, to improve cycling velocity for minimal energy cost or to compute the joint powers according to the resistive load. For that, numerous measuring devices have been developed and investigated to evaluate resultant torque and/or power output. Recently, new pedal sensors I-Crankset (ICS) are sold to measure the forces applied to the pedals and to calculate the torque and/or power output produced during cycling. These pedals’ sensors were calibrated and certificated, but it was essential to check if these devices still measured accurately after their integration on an ergometer. Purpose: The aim of this study was to compare dynamically this new device for measuring crankset’s resultant torque, mechanical power and work outputs.  Methods: A subject (Male, 75 kg, 1.82 m, trained rider) took part to this study conducted ethically according to international standards. The rider adjusted the cycle ergometer according to its personal settings. Figure 1 described the test bench. It was composed of: a chainring (A) was used to connect the ergocycle to the bench through a chain and a flywheel (D) associated with a mechanical braking device (E) composed of a tray with additional masses. The evaluation protocol was implemented to achieve three pedaling conditions and so to cover the usual torque and power ranges (Table 1). For each condition, the subject produced a pedaling torque to overcome that resistive load during one trial of 90 seconds. Feedback of cadence was displayed on the Control SRM bicycle computer. The torque reference sensor (model 1641/1648, Lebow) named RTSL (C) was installed on the axis (B). The scientific version SRM sensor was mounted on the crankset of the ergocycle. The ICS sensors were fixed at each pedal. The relative pedal to crank and the crank to ergometer angles were measured using encoders.  Analyzed parameters: As all the signals are acquired at 200 Hz and synchronized, for each cycle and for each acquisition system, we had the same number of acquisitions samples. According to the sample rate and protocol used, more than 12 000 instantaneous measures will be available for the comparison of several devices. Three power outputs were computed through these equations: (1)  with , k is the reduction coefficient between SRM and bench chainrings, ratio of the two diameters. (2) SRM:,  is the average angular velocity of the crankset over the cycle. (3) ICS: ,  is instantaneous angular velocity of the crankset computed from encoders measures. The mechanical work outputs  were given by integration over the time of the power outputs. By design, the SRM only measures an average angular velocity, so we computed mechanical work firstly considering this constant angular velocity () and secondly considering instantaneous angular velocity provided by ICS encoders (). Statistical analysis: For each condition, the same analysis was performed on torque, power and work outputs obtained from the different sensors. These instantaneous parameters, once pedaling cycles normalized, were compared using a coefficient of multiple correlation inter-protocol (CMC ip ) to appreciate the similarity of the instantaneous measures waveforms given by various sensors in a single acquisition of the same parameter. For each condition (n=30 cycles) and for all conditions (n=90 cycles), the averaged torque and power output were computed over each cycle and then these values were compared pairwise of sensors (A Bland-Altman analysis). A global normalized averaged torque evolution over cycles was also computed for condition 1 and for each sensor using.  Results: Mechanical power output comparisons: Table 2 reports all the data for the comparison of the averaged power output measured by the three sensors, for the each condition and all conditions. Especially for condition 3, we note an increase for the power output of the mean bias and error range between SRM and RTSL against those computed for the torque [mean bias: -4.4 ±2.3% for the power vs -1.20 ±0.53% for the torque; error range: 29 W (9.2%) for the power and 0.79 Nm (1.9%) for the torque]. This is not the case for ICS. The figure 3 confirms these results with a 95% limits of agreement larger for the SRM than ICS [respectively -1.81; 7.37 W and -20.70; 9.48 W for ICS and SRM]. Mechanical work output comparisons: Table 3 shows the difference of cumulative output work over thirty cycles between ICS and RTSL then SRM and RTSL for each condition. The differences are also expressed as the percentage of the total cumulated work. To analyze the influence of the angular velocity, we integrated power output over time to compute the work output in using i) the torque and angular velocity measured by SRM (W SRM ) and ii) the SRM torque multiplied by ICS angular velocity (W SRM* ). These results are presented at the last lines of table 4. The relative error is under 2% whatever the conditions, excepted for condition 3 between SRM and RTSL (5.26%). This error can be reduced by using I‰ ICS provided by ICS to compute the W SRM* (1.44 %).  Discussion: Power output discussion. For the power output, we note high values of  between ICS and RTSL (Table 3). For the steady state condition (C1: 210 W), ICS power mean relative error (0.1 ±0.5%) is better than [1] when comparing Velotron cycle ergometer (-0.8% for constant 250 W trial) with a test bench. For condition 2 (150 – 250 W, 80 rpm), ICS results (1.8 ±0.5%, Table 2) are closed to power mean relative error reported by [4] when comparing Powertap (-1.5 ±0.6% for 50-1000 W at 100 rpm trial) with a test bench. As SRM is considered as a gold standard [5], we will try to position ICS against SRM. Before that, we check that SRM results are consistent with literature. The mean relative errors reported by [1] (0.18%) and [4] (0.1 ±1.1%) are lower than errors of the present study (respectively 0.8 ±1.2% for condition 1 and -0.8 ±2.1% for condition 2). These differences can be related to the possibility of the test bench used by [6] to maintain a constant pace along all the cycle unlike the protocol of this study (mean cadence: 8.3 ±0.2 rad/s for conditions 1 and 2). Indeed, it’s difficult for a rider to produce a constant crankset angular velocity like the motorised test bench used by [1] and [3]. [1] shows that a rapidly increasing angular velocity results in a more inaccurate power measurement (mean relative error: -3.3 %; CI = -8.1 to 1.5 %). This is closer to the results for condition 3 (-4.4 %; CI = -9 to 0.2 %). This condition accentuates the inability of the SRM to record, by design, instantaneous crankset angular velocity. For a similar pedaling cadence and power output, the relative mean error (1.2 %) between Powertap ergometer and SRM reported by [2] is comparable with the relative error between ICS and SRM computed for condition 1 (0.9%, Table 3). However, ICS seems to be more accurate than SRM when looking at the individual results obtained for SRM (-2.4%) and ICS (1.2%) against RTSL for all conditions. Consequently, as for the torque, ICS can be considered sufficiently accurate. Work output discussion: Table 3 show the requirement to precisely measure the instantaneous values of crankset angular velocity to calculate the work as part of an energy study of the pedaling motion. Thus, when pedaling with constant angular velocity, the power output computed by SRM () is enough accurate to calculate the work output (). For the conditions 1 and 2, the error respectively equal to 0.98% and 1.16% is acceptable. But when the angular velocity is variable, the error becomes equal to 5.26% for the SRM while it is still under 2% for ICS. This result confirms those obtained by [1] which indicates that a rapidly increasing angular velocity causes an inaccuracy in calculating the SRM power. This error is reduced to 1.44% when the torque measured by SRM () is multiplied by the instantaneous angular velocity measured by ICS (). So, ICS should be preferred for power and work outputs investigations.  Conclusions: The study showed that ICS sensor was an accurate powermeter comparable to a standard reference sensor and to SRM regardless the pedaling cadence (56 to 90 rpm) and the resistive load (18 to 42 Nm). However, ICS was more efficient than SRM for evaluating the work particularly when the pedaling angular velocity various significantly. This study showed that it was therefore essential to measure both instantaneous torque and angular velocity in order to conduct an energy analysis of the pedaling motion.

The ability to complete triple and quadruple jumps in figure skating is increasingly determining competitive outcomes. A closed arm position during rotating jumps increases the angular velocity and spin rate. Therefore, upper body strength may contribute to a successful jump. PURPOSE To examine the correlation between upper body strength, power and body size with off-ice vertical jump height (JH) and off-ice angular velocities. METHODS Seventeen competitive female figure skaters were tested for shoulder adduction/abduction and flexion/extension strength and power at speeds of 300, 400, and 450 degrees/second. Peak torque, torque as a percentage of body weight, and average power were measured for all of the isokinetic tests. Off-ice angular velocities were calculated using high-speed, three-dimensional cameras. Trials were filmed at 180 frames per second for 3 seconds. Subjects took a 2-step approach, jumped, and spun attempting to complete a maximal number of rotations. Measurements included: maximal angular velocity (MAV), (JH), time in the air (TIA), revolutions in the air (RIA), and average angular velocity (AAV). Correlations were examined by a Pearson Product correlation matrix. RESULTS No significant correlations were identified between the strength or power measurements and any of the angular velocities. However, off-ice MAV and AAV are only 78 and 80% of on-ice angular velocities. Both JH and TIA were correlated with RIA (P ≤.01). Age and BMI were also found to be inversely correlated with RIA respectively (P ≤.01); (P ≤ .05). CONCLUSION Although the results do not indicate a relationship between upper body strength and power and MAV or AAV, it is thought that the off—ice spin rates were too slow to adequately evaluate this relationship. Results do indicate a need to maintain a compact body shape, which may partially explain the success of younger, smaller female skaters. Results also indicate that body shape (> BMI) will change with age-related developmental changes, which will lead to increased torso inertia.

Numerical simulation of vortex flow evolution during droplet formation in T-inlet microchannel

Point-of-care ultrasound (POCUS) has become an important diagnostic tool in acute care medicine; however, little is known about the biomechanical differences between novice and expert practitioners. A low-cost ($50 CAD) gyroscope and accelerometer integrated sensor was assembled and affixed to an ultrasound probe. Seventeen participants, nine novices and eight experts, were recruited to perform three abdominal and four cardiac scans on a standardized patient. Participant demographics, time per scan, average acceleration, average angular velocity, decay in acceleration and angular velocity over time, and frequency of probe movements were analyzed. Video capture with blinded video review was scored. On video review, experts had higher image optimization and acquisition scores for both abdominal and cardiac scans. Experts had shorter scan times for abdominal (7s vs. 26s, p=0.003) and cardiac (11s vs. 26s, p<0.001) scans. There was no difference in average acceleration (g) between novices and experts performing abdominal (1.02 vs. 1.01, p=0.50) and cardiac (1.01 vs. 1.01, p=0.45) scans. Experts had lower angular velocity (°/s) for abdominal scans (10.00 vs. 18.73, p<0.001) and cardiac scans (15.61 vs. 20.33, p=0.02) There was a greater decay in acceleration over time for experts performing cardiac scans compared to novices (-0.194 vs. -0.050, p=0.03) but not for abdominal scans or when measuring angular velocity. The frequency of movements (Hz) was higher for novices compared to experts for abdominal (16.68 vs. 13.79, p<0.001) and cardiac (17.60 vs. 13.63, p=0.002) scans. This study supports the feasibility of a low-cost gyroscope and accelerometer integrated sensor to quantify the biomechanics of POCUS. It may also support the concept of "window shopping" as a method by which experts obtain abdominal and cardiac views, where sliding is used to find an acoustic window, then smaller rocking and tilting probe movements are used to refine the image.

We demonstrate the control of vortical motion of neutral classical particles in driven superlattices. Our superlattice consists of a superposition of individual lattices whose potential depths are modulated periodically in time but with different phases. This driving scheme breaks the spatial reflection symmetries and allows an ensemble of particles to rotate with an average angular velocity. An analysis of the underlying dynamical attractors provides an efficient method to control the angular velocities of the particles by changing the driving amplitude. As a result, spatially periodic patterns of particles showing different vortical motion can be created. Possible experimental realizations include holographic optical lattice based setups for colloids or cold atoms.

After sustained stepping in-place on a rotating disc, healthy subjects will inadvertently turn in circles when asked to step in-place on a stationary surface with eyes closed. We asked whether the cerebellum is important for this adaptive phenomenon, called podokinetic after-rotation (PKAR). Subjects with cerebellar degeneration and age-matched control subjects performed 15 min of stepping in-place with eyes open on a rotating disc, then 30 min of attempting to step in-place with eyes closed on a stationary surface. Rotational velocity of PKAR was measured during this 30-min period. All control subjects demonstrated PKAR; average initial rotational velocity for control subjects was 16.4+/-3.5 degrees /s. Five of the eight cerebellar subjects demonstrated impaired PK adaptation, defined as PKAR with an initial velocity more than two standard deviations below the control mean initial velocity. Average initial rotational velocity for cerebellar subjects was 7.8+/-0.2 degrees /s. Impaired PK adaptation was not associated with impaired time constants of decay and was not correlated with variability of PKAR velocity. Our results suggest that the cerebellum is important for regulation of the amplitude of PK adaptation and that reduced PKAR amplitude is not likely the result of dyscoordination or variability of movement in the subjects tested.

We employ Gaia DR2 proper motions for 151 Milky Way globular clusters (GCs) from Vasiliev in tandem with distances and line-of-sight velocities to derive their kinematical properties. To assign clusters to the Milky Way thick disk, bulge, and halo, we follow the approach of Posti et al., who distinguished among different Galactic stellar components using stars’ orbits. In particular, we use the ratio L z /e, the Z projection of the angular momentum to the eccentricity, as a population tracer, which we complement with chemical abundances extracted from the literature and Monte Carlo simulations. We find that 20 GCs belong to the bar/bulge of the Milky Way, 35 exhibit disk properties, and 96 are members of the halo. Moreover, we find that halo GCs have close to zero rotational velocity with an average value km s−1. On the other hand, the sample of clusters that belong to the thick disk possess a significant rotation with average rotational velocity 179 ± 6 km s−1. The 20 GCs orbiting within the bar/bulge region of the Milky Way have an average rotational velocity of 49 ± 11 km s−1.

From deer antlers to crab claws, weapons are some of the most elaborate and enormous structures in the animal kingdom. Within a species, weapon size generally increases with the size and condition of an individual, and those with larger weapons are usually better at fending off more diminutive competitors. Although it may seem desirable for all individuals to have large weapons, size varies greatly within a species. The ‘handicap principle’ proposes that the cost of bearing a weapon dictates the variation in weapon size. Smaller or less fit individuals pay more for weapons than larger or fitter animals, so smaller individuals tend to grow smaller weapons. Although popular, only a handful of studies have demonstrated experimental evidence that supports this theory. To test the handicap principle, Dinh and Patek studied a group of crustaceans known as snapping shrimp. Each shrimp has one enlarged claw that it uses as a weapon to fire imploding vapor bubbles at opponents during fights. Larger snapping shrimp have bigger enlarged claws and tend to win more contests. Males also have larger weapons than females, and this sex difference is amplified during the breeding season. Dinh and Patek studied weapon size in several species of snapping shrimp. Measurements showed that after controlling for body size, individuals with larger weapons had smaller abdomens, suggesting there is a tradeoff between weapon size and abdomen size. Furthermore, small males exhibited the steepest tradeoff, in line with the handicap principle. Snapping shrimp also showed sex-specific costs and benefits. After controlling for body size, females with larger weapons produced fewer and smaller eggs, while males with larger weapons were more likely to be paired with females and generally paired with larger females. This suggests that weapons are particularly burdensome to female shrimp and particularly beneficial to males, especially during the breeding season. These findings provide elusive evidence for the handicap principle and extend the theory to explain sex and seasonal differences in the size of snapping shrimp weapons. More broadly, the findings highlight the value of studying both male and female animal weapons when, historically, the focus has been on male weaponry.

In preceding papers of this series (Kopal, 1968; 1969) the Eulerian equations have been set up which govern the precession and nutation of self-gravitating fluid globes of arbitrary structures in inertial coordinates (space-axes) as well as with respect to the rotating body axes; with due account being taken of the effects arising from equilibrium as well as dynamical tides. In Section 1 of the present paper, the explicit form of these equations is recapitulated for subsequent solations. Section 2 contains then a detailed discussion of the coplanar case (in which the equation of the rotating configuration and the plane of its orbit coincide with the invariable plane of the system); and small fluctuations in the angular velocity of axial rotation arising from the ‘tidal breathing’ in eccentric binary systems are investigated. In Section 3, we consider the angular velocity of rotation about theZ′-axis to be constant, but allow for finite inclination of the equator to the orbital plane. The differential equations governing such a problem are set up exactly in terms of the time-dependent Eulerian angles θ and ϕ, and their coefficients averaged over a cycle. In Section 4, these equations are linearized by the assumption that the inclinations of the equator and the orbit to the invariable plane of the system are small enough for their squares to be negligible; and the equations of motion reduced to their canonical form. The solution of these equations — giving the periods of precession and nutation of rotating components of close binary systems, as well as the rate of nodal regression which is synchronised with precession — are expressed in terms of the physical properties of the respective system and of its constituent components; while the concluding Section 6 contains a discussion of the results, in which the differences between the precession and nutation of rigid and fluid bodies are pointed out.

PURPOSE: To compare the youth pitching biomechanics with that of elite adult pitchers and to identify differences that might explain common injuries seen in youth pitcher populations. METHODS: Twenty-five professional and 14 youth baseball pitchers were filmed at 120 Hz using two high-speed video cameras. The locations of 21 body landmarks were digitized and their three-dimensional locations were calculated using the DLT method (Abdel-Aziz & Karara, 1971). Three-dimensional position data were filtered using a fourth order Butterworth filter with a cutoff frequency of 13 Hz. From the marker coordinates, the kinematics of the pitching elbow and shoulder were calculated using a standard technique (Fleisig et al., 1996; Werner et al., 1993). Kinematic data were normalized in time to facilitate comparisons and so group mean values could be calculated. RESULTS: The peak shoulder internal rotation and elbow extension angular velocities of the youth pitchers were greater than those of the professional pitchers. Peak shoulder external rotation in youth pitchers was 166 +/− 9 degrees, compared with 182 +/− 13 degrees in professionals (p<0.001). The most striking difference between the groups was in trunk motion. The peak rotational velocities of both the upper trunk and pelvis were greater in youth baseball pitchers than in professional pitchers. Peak upper trunk rotational velocity was 2102+/− 324 deg/s in youth pitchers and 1193 +/− 176 deg/s in professional pitchers (p<0.001). CONCLUSIONS: The data support the observation that youth baseball pitchers control their trunk motion in a less efficient way than elite pitchers (Ireland & Hutchinson, 1995). Peak pelvis rotation velocity occurred near the time of stride foot contact in the professionals, while it occurred much later in the youth pitchers. Proper timing of pelvis and upper trunk rotation are necessary to effectively transfer energy from the trunk to the throwing arm (Fleisig et al., 1996). Therefore, increased trunk rotational velocity may be a compensation for improper timing of segment rotations or insufficient muscle strength in youth pitchers. Improper energy transfer from the trunk to the upper extremity may lead to the increased shoulder internal rotation and elbow extension velocities in youth pitchers compared to the professionals.

A Detailed Motion Analysis of the Angular Velocity Between the Vocal Folds During Throat Clearing Using High-speed Digital Imaging

A new boundary-integral algorithm for the motion of a particle between two parallel plane walls in Poiseuille flow at low Reynolds number was developed to study the translational and rotational velocities for a broad range of particle sizes and depths in the channel. Instead of the free-space Green’s function more commonly employed in boundary-integral equations, we used the Green’s function for the domain between two infinite plane walls [Liron and Mochon, J. Eng. Math. 10, 287 (1976)]. This formulation allows us to directly incorporate the effects of the wall interactions into the stress tensor, without discretizing the bounding walls, and use well-established iterative methods. Our results are in good agreement with previous computations [Ganatos et al., J. Fluid Mech. 99, 755 (1980)] and limiting cases, over their range of application, with additional results obtained for very small particle–wall separations of less than 1% of the particle radius. In addition to the boundary-integral solution in the mobility formulation, we used the resistance formulation to derive the near-field asymptotic forms for the translational and rotational velocities, extending the results to even smaller particle–wall separations. The decrease in translational velocity from the unperturbed fluid velocity increases with particle size and proximity of the particle to one or both of the walls. The rotational velocity exhibits a maximum magnitude between the centerline and either wall, due to the competing influences of wall retardation and the greater fluid velocity gradient near the walls. The average particle velocity for a uniform distribution of particles was generally found to exceed the average fluid velocity, due in large part to exclusion of the particle centers from the region of slowest fluid near the walls. The maximum average particle velocity is 18% greater than the average fluid velocity and occurs for particle diameters that are 42% of the channel height; particles with diameters greater than 82% of the channel height have smaller average velocities than does the fluid, due to the retarding effects of the nearby walls. Additionally, the translational and rotational velocities of oblate and prolate ellipsoids were calculated using the boundary-integral algorithm. The proximity of the walls to the ellipsoids was found to have a strong effect on particle velocity, so that a prolate spheroid aligned on the channel centerline moves faster than an oblate spheroid of the same volume, because the edge of the latter spheroid is closer to the channel walls. For off-centerline locations for a prolate spheroid with its major axis at an angle to the walls, a second translational velocity component normal to the walls is present. For each lower-wall gap examined, the maximum normal translational velocity occurs for smaller gaps from the upper wall (i.e., larger angle). The direction of this velocity component changes sign for mid-range angles studied, due to increased interactions with the lower wall that prevent the ellipsoid from rotating upward and, hence, yield a negative velocity perpendicular to the walls. The rotational velocity changes direction for particles at the smallest angles studied, due to the competition between the Poiseuille fluid velocity profile, which pushes the particle clockwise, and the lubrication forces, which impede this rotation.

The average radial and angular velocity components are obtained for a rotating two-dimensional self-gravitating system near an equilibrium state. First-order perturbation configurations of flaring straight bars emanating from the center provide examples of such systems. In these systems the average velocity field to first order is incompressible and irrotational. The second-order effects on the product of the average velocity components with the spatial density are essentially independent of the angular coordinate.

In introductory physics laboratories, spring constants are traditionally measured using the static method. The dynamic method, via vertical spring-mass oscillator, that uses a stopwatch in order to measure the period of oscillations is also commonly employed. However, this time-measuring technique is prone to human errors and in this paper we present a similar setup, except for the motion timer being the B-field sensor of a smartphone, in order to measure the period of oscillations and thus the spring constant. The smartphone device as an introductory physics experimental tool is quite well established. For instance, the smartphone-based acceleration sensor has been employed in a rather quick measurement of the acceleration due to gravity and in analyzing simple pendulum phenomena. In addition, the magnetic field sensor of the smartphone device has been effectively used as well in measuring average angular velocity and the acceleration due to gravity.