Shanks Method Research Articles

An easily applicable method to analyse the ankle-foot power absorption and production during walking

BackgroundPower and work at the ankle joint during gait are usually computed considering the foot as a rigid body [1–6] (Ankle Joint method, AJ). The foot is instead a deformable structure and can absorb and produce work by pronation/supination, foot arch deformation and other intrinsic movements. A different approach, named “the Distal Shank method (DS)” [7–12] considers all these aspects without increasing the complexity of the protocol, and thus it seems promising for clinical applications [12].Research questions: a) To characterize the differences in power and work computed using the two mentioned methods for a relatively large number of subjects walking at different velocities, barefoot and with different shoes; b) To assess the practical feasibility of the DS method for clinical applications. Materials and methodsEighteen healthy subjects were evaluated while walking barefoot at slow, natural and fast velocity. Shod walking was analysed at natural velocity. Four subjects were also analysed while walking in high-heel shoes. The power at the ankle joint was computed with both the AJ and the DS methods. We then compared the obtained results. ResultsThe DS method showed a consistent negative peak of power absorption during the load acceptance phase, barely visible with the AJ method. The maximum power production calculated with the DS method was significantly lower. The work at the end of the stride cycle was lower with the DS method, and in most conditions even negative, thus indicating higher energy dissipation. SignificanceWe confirmed on a large cohort of healthy subjects and in different walking conditions that neglecting foot deformations during gait leads to underestimate power absorption and overestimate power production. The DS method does not require a complex gait analysis protocol, nor additional time for the analysis, and can provide information of clinical interest, related to foot mechanical alterations.

Gait event detection in laboratory and real life settings: Accuracy of ankle and waist sensor based methods

Wearable sensors technology based on inertial measurement units (IMUs) is leading the transition from laboratory-based gait analysis, to daily life gait monitoring. However, the validity of IMU-based methods for the detection of gait events has only been tested in laboratory settings, which may not reproduce real life walking patterns. The aim of this study was to evaluate the accuracy of two algorithms for the detection of gait events and temporal parameters during free-living walking, one based on two shank-worn inertial sensors, and the other based on one waist-worn sensor. The algorithms were applied to gait data of ten healthy subjects walking both indoor and outdoor, and completing protocols that entailed both straight supervised and free walking in an urban environment. The values obtained from the inertial sensors were compared to pressure insoles data. The shank-based method showed very accurate initial contact, stride time and step time estimation (<14ms error). Accuracy of final contact timings and stance time was lower (28–51ms error range). The error of temporal parameter variability estimates was in the range 0.09–0.89%. The waist method failed to detect about 1% of the total steps and performed worse than the shank method, but the temporal parameter estimation was still satisfactory. Both methods showed negligible differences in their accuracy when the different experimental conditions were compared, which suggests their applicability in the analysis of free-living gait.

Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility

In the tool orientation planning for five-axis sculptured surface machining, the geometrical constraints are usually considered. Actually, the effect of nongeometrical constraints on tool orientation planning is also important. This paper studied one nongeometrical constraint which was cutting force induced static deflection under different tool orientations, and proposed a cutter deflection model based on that. In the study of the cutting force, the undeformed chip thickness in filleted end milling was modeled by geometrical analysis and coordinate transformation of points at the cutting edge. In study of static flexibility of multi-axis machine, static flexibility of the entire machining system was taken into consideration. The multi-axis machining system was divided into the transmission axes-handle (AH) end and the cutting tool end. The equivalent shank method was developed to calculate the static flexibility of the AH end. In this method, static flexibility anisotropy of the AH end was considered, and the equivalent lengths of the AH end were obtained from calibration experiments. In cutter deflection modeling, force manipulability ellipsoid (FME) was applied to analyze the static flexibility of the AH end in arbitrary directions. Based on the synthetic static flexibility and average cutting force, cutter deflections were derived and estimated through developing program realization. The predicted results were compared with the experimental data obtained by machining 300 M steel curved surface workpiece, and a good agreement was shown, which indicated the effectiveness of the cutter deflection model. Additional experiments of machining flat workpiece were performed, and the relationship of cutter deflections and tool orientations were revealed directly. This work could be further employed to optimize tool orientations for suppressing the surface errors due to cutter deflections and achieving higher machining accuracy.

A closed‐form solution for a confined flow into a tunnel during progressive drilling in a multi‐layer groundwater flow system

A mathematical model is developed to describe the groundwater inflow into a tunnel in a multi‐layer aquifer system. Based on the model, the closed‐form solution is derived to estimate the groundwater flow rate entering the multi‐layer tunnel during progressive drilling. The solution has an integrand not only consisting of the product and square of the Bessel functions but also having a singularity at the origin. A unified numerical approach is proposed to evaluate the solution with accuracy to five decimal places. This approach includes a singularity removal scheme, the Gaussian quadrature, and the Shanks method. For a multi‐layer formation, the results obtained from the solution based on the equivalent hydraulic conductivity and the newly derived solution differ significantly. This solution is capable of estimating the maximum flow rate inside the horizontal tunnel, and thus can be used as a tool for designing the drainage tunnel system in a multi‐layer formation.

Accelerated Computation of the Free Space Green's Function of Semi-Infinite Phased Arrays of Dipoles

In this Communication, we provide an efficient algorithm for the evaluation of the semi-infinite array Green's function (SAGF) for a semi-infinite planar periodic phased array of dipoles in free space. For observation points not too far from the array plane, the algorithm uses a hybrid spectral-spatial representation of the Green's function accelerated with the Levin T method, that we show to be faster than the Shanks method. For observation points sufficiently far away from the array plane, we show that the SAGF is efficiently evaluated by using asymptotic field expressions. Asymptotics is also used to explain the loss of accuracy of the Levin T accelerator in certain regions, and a correction procedure is proposed to overcome this problem

A new closed-form solution for a radial two-layer drawdown equation for groundwater under constant-flux pumping in a finite-radius well

A mathematical model is presented for describing the groundwater flow in a radial two-layer confined aquifer system with a constant-flux pumping well that has a wellbore skin and finite well radius. The Laplace-domain solution for the model is first derived by the Laplace transforms; and the time-domain solution in terms of the aquifer drawdown is then obtained form the Laplace inversion using the Bromwich integral method. When neglecting the well radius, our Laplace-domain solution is shown to reduce to a Laplace-domain solution given by Butler [J. Hydrol. 101 (1988) 15]. A unified numerical approach including a root search approach, the Gaussian quadrature, and the Shanks method is employed for evaluating this time-domain solution. The evaluated results of the solution agree well with those of the Laplace-domain solution estimated by the modified Crump algorithm. This new solution can be used either to predict the spatial and temporal drawdown distributions in both the skin and formation zones or to investigate the effects of the skin type, skin thickness and well radius on the drawdown distribution.

Three-dimensional simulation of charged particle beam trajectories in radio frequency electric field of a quadrupole mass spectrometer

A numerical simulation method for ion trajectory analysis in a three-dimensional radio frequency electric field is developed. The present method is based on the boundary element method (BEM) to calculate the electric field and the high-order Runge-Kutta method (Shanks method) to trace ion trajectories with high numerical accuracy. In order to reduce computational memory and time while maintaining computational accuracy, the interpolative functions of the BEM and the integration method of the equation of ion motion are discussed in detail. Ion trajectories at the entrance part of the quadrupole field are successfully simulated using the proposed method. The influence of the ion beam focusing position on the transmission efficiency at the entrance part is evaluated with the results.

On the stability of plane Poiseuille flow to finite-amplitude disturbances, considering the higher-order Landau coefficients

In this work a study has been made of the Stuart (1960)–Watson (1960) formalism as applied to plane Poiseuille flow. In particular, the higher-order Landau coefficients have been calculated for the Reynolds &amp; Potter (1967) method and for the Watson (1960) method. The results have been used to study the convergence of the Stuart–Landau series. A convergence curve in the (α, R)-plane has been obtained by using suitable Domb–Sykes plots. In the region of poor convergence of the series, and also in a part of the divergent region of the series, it has been found that the Shanks (1955) method, using the em1 transformation, serves as a very effective way of finding the proper sum of the series, or of finding the proper antilimit of the series. The results for the velocity calculations at R = 5000 are in very good agreement with Herbert's (1977) Fourier-truncation method using N = 4. The Watson method and the Reynolds &amp; Potter method have also been compared inthe subcritical and supercritical regions. It is found in the supercritical region that there is not much difference in the results by the ‘true problem’ of Watson and the ‘false problem’ of Reynolds &amp; Potter when the respective series in both methods are summed by the Shanks method. This fact could possibly be capitalized upon in the subcritical region, where the Watson method is difficult to apply.

Fumigants, rates, and application methods affecting Verticillium wilt incidence and potato yields

A three year comparison was made among fumigants, rates and placement for control ofVerticillium albo-atrum (microsclerotial type). Fumigants were placed in the soil by (i) row method [one shank with duck-foot tool attached to give two bands of fumigant 9 inches (22.8 cm) deep and 9 inches apart (4.5 inches = 11.4 cm from center of a 36-inch row = 91.44 cm)], (ii) deep shank method [one shank in center of a 36-inch row, 18–20 inches (45.7–50.8 cm) deep], (iii) and by the standard broadcast method (four shanks spaced 9 inches deep and 9 inches apart per 36-inch row). The row and deep shank methods were no more effective than the broadcast method when the fumigant rate was equal (calculated on an acre basis and not on the actual portion of the row treated by the method of application).