Direction Of External Force Research Articles

Reactive molecular dynamics of the fracture behavior in geopolymer: Crack angle effect

Reactive molecular dynamics was applied in this study to construct the sodium aluminosilicate hydrate (N-A-S-H) and tensile fracture models with various crack angles. The impact of crack angle on the behavior of N-A-S-H fractures was explored while considering structural mechanical properties and energy evolution. Furthermore, the fracture toughness and brittleness index for various crack angle models were calculated. The findings indicated that the ultimate strength and elastic modulus of the fracture models grew linearly with the increase in crack angle. The fracture toughness value progressively grew while the model’s elastic energy efficiency and new surface energy efficiency decreased simultaneously. The 45° crack model possessed the largest oblique crack development surface in the fracture process due to the coupling effect of tensile and shear stress. Its elastic energy efficiency decreased as well the most, while the new surface energy efficiency increased and the fracture toughness value dropped sharply. It is crucial to place a stronger emphasis on spotting cracks both in the in-service structures or structures being demolished. This ensures optimal performance and safety by enabling more effective adjustments to the direction of external forces and energy input.

Magnetic Tactile Sensor with Bionic Hair Array for Sliding Sensing and Object Recognition.

Due to the high application value in intelligent robots, tactile sensors with large sensing area and multi-dimensional sensing ability have attracted the attention of researchers in recent years. Inspired by bionics of hairs on human skin, a flexible tactile sensor based on magnetic cilia array is developed, showing extremely high sensitivity and stability. The upper layers of the sensor are multiple magnetic cilia containing magnetic particles, while the lower layer is a serpentine flexible circuit board with a magnetic sensor array. When magnetic cilia are bent under force, the magnetic sensor array can detect changes in the magnetic field, thereby the magnitude and direction of external force can be obtained. The proposed sensor has a resolution of 0.2 mN with a working range of 0-19.5 mN and can distinguish the direction of external force. The large sensing area and short response time make this sensor suitable for sliding tactile detection, and experiments show that the sensor can be also applied in object recognition with a success accuracy of 97%. In addition to the shape of objects, the sensor can identify whether there is magnetism inside objects, making it of significant value in intelligent robots and modern medicine.

A Scientific Proposal for Surgical Decision-Making in Occult Intertrochanteric Fractures Based on Finite Element Analysis.

Background In the treatment of femoral intertrochanteric fractures, there is still a lack of consensus on the optimal approach for isolated greater trochanteric fractures and insufficient intertrochanteric fractures. The limited number of patients and restricted access to accurate assessment of fracture extension using magnetic resonance imaging contribute to the unclear treatment strategy. This study aims to utilize finite element (FE) analysis to analyze stress values at the fracture line and investigate their influence on intertrochanteric fracture extension under different loading conditions. The hypothesis is that fracture extension occurs following certain conditions, supporting the need for surgery based on scientific evidence. Methodology Osseous data from a computed tomography (CT) scan was used to create a proximal femur FE model using FEA software. CT scan data were converted to Digital Imaging and Communications in Medicine format and used to generate the FE model. Trabecular bone and cortex were meshed into tetrahedral elements. The model consisted of 1,592,642 elements and 282,530 nodes. Two models were created, namely, healthy proximal femur (HF) and femoral insufficient intertrochanteric fracture (FIF). Material properties were assigned based on CT values and conversion equations. The distal end of the femur was constrained. Stress analysis using the dynamic explicit approach was performed. Von Mises stresses were calculated for the proximal femur. The number of elements exceeding yield stress was counted to predict fracture risk by focusing on fracture line spots. In this study, the distribution of von Mises stress was compared between the HF and the FIF models. Six loading combinations were considered, namely, two weight-bearing conditions (3 W loading simulating for walking and 1/3 W for touch-down standing) and three hip flexion angles (0°, 15°, and 23°). Results Under 3 W loading, no significant stress elevations were observed in the HF model at any flexion angles. However, the FIF model exhibited increased stress at the site of the posterior fracture line extension. This stress-induced element destruction was observed in both cortical and cancellous bone. For the 1/3 W loading condition, only minimal stress elevation was observed in both HF and FIF models. To assess the influence on fracture extension, the number of yielded elements was evaluated along the fracture line edges (greater trochanter and middle of the intertrochanteric ridge). Under 3 W loading, the HF model had only one yielded element, indicating minimal fracture risk. In contrast, the FIF model exhibited a notable presence of yield elements in various regions (total/greater trochanter/shaft) at different flexion angles: 0° (115/16/28), 15° (265/158/23), and 23° (446/233/34). Under the 1/3 W loading condition, neither the HF nor the FIF models showed any yielding elements, regardless of the direction of external force. Conclusions The results demonstrated elevated stress levels at the fracture line in the FIF model, particularly during walking, indicating a higher risk of fracture extension at the flex position. However, under reduced weight-bearing conditions, the stress at the fracture site remained within the yield stress range, suggesting a relatively low risk of fracture extension. These findings hold significant clinical implications for developing surgical protocols that consider patients' compliance with weight-bearing restrictions.

Investigation of the asteroid triple-drill anchoring force under complicated working conditions

The microgravity environment on asteroids necessitates the inclusion of anchoring devices on asteroid probes to facilitate in-situ landing detection. Complicated working conditions faced by asteroid probes significantly increase the difficulty of the anchoring device’s task. In this paper, based on the discrete element method (DEM), the anchorage performance of a triple-drill anchoring device under different external forces and drilling depth combinations is investigated. The forces on the probe and landing legs and the damaged area of the particle domains are analyzed to obtain the influence of the external force direction on the anchorage performance. Five drilling depth combinations are selected to represent the complicated working conditions asteroid probes face. Then the ultimate anchoring forces of the five drilling depth combinations under the different external force directions are calculated and analyzed. This work reveals the anchorage mechanism under complex working conditions and provides a reference for asteroid exploration missions.

Study the influence of anchoring parameters on asteroid drilling anchoring with discrete element simulation

Asteroid exploration has become a research hotspot, and anchoring probes to asteroids is essential for in situ scientific detections. The influence of ultrasonic drilling force-closure anchoring parameters on the anchoring performance and its influence mechanism are studied based on discrete element simulation. An anchoring simulation model is established after calibrating virtual asteroid soil, and its validity is verified by anchoring experiments. Discrete element simulations are performed to study the effect of cross-sectional shape and longitudinal cross-sectional shape of anchoring rods on anchoring force. The internal influence mechanism of anchor configurations on the anchoring force is analyzed by extracting the number of stressed particles in the simulation area. The anchoring force has a positive correlation with the cross-sectional area. The rotation of non-circular anchors causes fluctuations in the anchoring force. The effect of the anchored material strength on the anchoring force is studied with the calibrated virtual asteroid soil. The relationship between anchoring force and anchoring parameters is studied, and the optimal anchoring angle is 54° for anchored material strength of 100 kPa. Finally, the variation of the anchoring force with the direction of external force is studied. This work can guide the anchor configuration design and the anchoring condition parameter optimization.

An exact solution for vibration analysis of pipe coupled with conical-ring stiffened cylindrical shells with arbitrary boundary condition

In this paper, an analytical impedance synthesis method (ISM) is proposed to analyze the vibration characteristics of a pipe-hull coupled system, in which the hull of a submarine can be simplified to a combined conical-stiffened cylindrical-hemisphere shell. Wave solution and power series solution are used to describe the displacement of cylindrical and conical shell respectively. Rib stiffened and bulkhead are modeled as annular plate and circular plate. Based on exact general solutions, the impedance matrix of each segment is established separately and assembled in the global coordinate by displacement continuity and force balance boundary conditions. Natural frequency and forced responses are compared with open literature and FEM results to verify the correctness of the method. In the numerical examples, the effects of direction of external force and stiffness of support on the forced vibration characteristics are discussed, which can provide some guides for acoustic design of pipe in submarine.

Simulation and analysis of asteroid force closure anchoring performance based on discrete element method

Asteroid exploration is significant for studying the origin of the solar system, establishing planetary defenses, and alleviating the resource crisis of the Earth. Asteroid anchoring is the basis of in-situ exploration and resource development and utilization. Therefore, the performance of asteroid force-closure anchoring is investigated using the discrete element method. The micro parameters of the simulated materials are calibrated with angle of repose and uniaxial compression experiments, based on which the regional modeling method is adopted to establish the anchoring discrete element model. Asteroid anchoring experiments are conducted on a self-developed microgravity simulation platform to verify the accuracy of the simulation model. The asteroid anchoring simulations are performed to investigate the influence of external force on the anchoring performance. The analysis of anchoring force varying with time and the interaction between the anchor and regolith particles reveals the influence mechanism of external force direction on the anchoring performance. The external force direction affects the critical anchoring force by influencing the failure of the force-closure structure. The comprehensive analysis of simulation results clarifies the variation of the critical anchoring force with the external forces. Finally, a stable anchoring region is established, beneficial for asteroid anchoring device design.

HiVTac: A High-Speed Vision-Based Tactile Sensor for Precise and Real-Time Force Reconstruction with Fewer Markers.

Although they have been under development for years and are attracting a lot of attention, vision-based tactile sensors still have common defects—the use of such devices to infer the direction of external forces is poorly investigated, and the operating frequency is too low for them to be applied in practical scenarios. Moreover, discussion of the deformation of elastomers used in vision-based tactile sensors remains insufficient. This research focuses on analyzing the deformation of a thin elastic layer on a vision-based tactile sensor by establishing a simplified deformation model, which is cross-validated using the finite element method. Further, this model suggests a reduction in the number of markers required by a vision-based tactile sensor. In subsequent testing, a prototype HiVTac is fabricated, and it demonstrates superior accuracy to its vision-based tactile sensor counterparts in reconstructing an external force. The average error of inferring the direction of external force is 0.32, and the root mean squared error of inferring the magnitude of the external force is 0.0098 N. The prototype was capable of working at a sampling rate of 100 Hz and a processing frequency of 1.3 kHz, even on a general PC, allowing for real-time reconstructions of not only the direction but also the magnitude of an external force.

Effect of Continuous Working Fluid Flow Direction on Power Generation from Piezoelectric Sensors

This paper presents an experimental study to support the concept of generating energy by a continuous flow of water using piezoelectric sensors. This study is aimed to determine the effect of external force direction of continuous water flow, i.e., vertical and horizontal, on the output of the piezoelectric sensors. The piezoelectric type of ABT-441-RC is used and arranged in parallel. IC MAX471 as an amplifier and Arduino Uno R3 to read the flow rate, voltage, and current were employed. Flow rates with variations of 0.00011 up to 0.00030 m3/s are set to study the voltage and current of the output. The numbers of piezoelectric sensors used are 4, 6, 8, and 20. As a result, it is found that the pressure in the vertical direction differs up to 68% from the pressure in the horizontal one. The voltage and current in the vertical direction, compared to that of the horizontal direction, differ as much as 85% at a low flow rate and decrease down to 63% at a high flow rate for voltage and 86% to 34% at a low to high flow rate for current. In conclusion, the current generation by the present arrangement is within the micro-ampere range, and the voltage is in a volt range, respectively.

Tensile-Force-Resilient Biomedical Front-End Circuits Employing Auto-Calibrated Omni-Directional Thin-Film Transistors

Flexible electronics based on thin film transistors (TFTs) are expected to deliver important benefits in the mobile healthcare field. Nevertheless, the mechanical strain caused by the respiration or movement of organisms seriously affects the characteristics of the TFTs, and thus deteriorates the performance of TFT-based circuits and systems. Taking indium-gallium-zinc-oxide (IGZO) TFT as an example, this paper proposes a tensile-force-resilient biomedical front-end system based on omni-directional thin film transistors (OD TFTs). The proposed OD TFT is a combination of dual gate TFTs with optimized layout, whose force-insensitive axis can be adjusted by the biasing of top gate. Based on this, an auto calibration technique in front-end system is introduced, which can automatically adjust the top gate biasing of OD TFTs according to the Poisson's ratio of substrate and the direction of external force, so as to align the force-insensitive axis along the direction of external force. Employing the OD TFTs in circuits and the auto calibration technique, the force resilience of the flexible electronic system is significantly improved in practical applications. The simulations of front-end system on acquiring electrocardiogram (ECG) and electromyogram (EMG) signals are performed. The results show that the proposed front-end system with auto calibration provides an increase of SNR from initial -19.91 dB and -25.89 dB without calibration to 17.53 dB and 1.32 dB in two cases, respectively.

High Wear Resistance and Mechanical Performance of NiAl Bronze Developed by Electron Beam Powder Bed Fusion

This work reports the additively manufactured NiAl bronze alloys via electron beam powder bed fusion (EB-PBF) that exhibit improved wear resistance without an increase of friction, exceeding those of conventional hot-rolled counterparts. High wear resistance is attributed to the formation of a Cu–O-rich transfer layer, and to exceptional mechanical strength induced by integrated effects including uniformly distributed precipitation, grain refinement, martensitic transformation around stacking faults, and a modulus mismatch between precipitates and the matrix. The simulation results indicate that the effect of the precipitate distribution on the internal stress field of the matrix is dependent on the external force direction. For the shear force, the uniformly distributed precipitates promote the overall stress concentration of the matrix, leading to its high work-hardening capability that plays a role in improving the wear resistance. This study reveals the potential of the EB-PBF technique to develop alloys with high wear resistance.

Recrystallization process of hot-extruded 6A02 aluminum alloy in solid and semi-solid temperature ranges

To provide the process parameters for preparing semi-solid billets, the impacts of heating temperature on recrystallization of a hot-extruded 6A02 aluminum alloy in solid and semi-solid temperature ranges were studied. The static recrystallization (SRX) even occurred at semi-solid temperature due to the low deformation ratio in the starting hot-extruded sample. Almost all elongated grains were transformed into equiaxed grains at immediate 630 °C. But not all grains with equiaxed shape were pure recrystallized grains, and small static recrystallized grain even emerged inside them. Bulk insoluble second particles including Fe, Mn, and Si were distributed at the grain boundaries. With the increasing of heating temperature, Vickers hardness increased firstly, then decreased and increased finally. And it was relevant with external force direction. According to the electron backscatter diffraction (EBSD) analysis, the fraction of the recrystallized, sub-structured and deformed grains changed little at 540 °C, but varied greatly at 600 °C and 630 °C. The contents of<111> and<100> fiber deformed textures as well as {100}<001> Cube texture showed analogical variation tendencies. The dislocation densities decreased roughly with temperature both from grain-based and kernel-based perspectives. Inhomogeneous deformation existed in an individual grain. Schmid factor had great relevance with external force direction and the gaps were narrowed by the equiaxed microstructure. In the isothermal deformation test, the liquid film was thickened and voids emerged in the shear-deformation region.

Stochastic stress-based topology optimization of structural frames based upon the second deviatoric stress invariant

This work pertains to the stochastic stress-based topology optimization of frame structures considering uncertainty. Specifically, this paper presents an investigation of the second deviatoric stress invariant, J2, as the measure of stress in the domain where the objective is to minimize the maximum of the expected values of the stress invariant. Analytical expressions for the expected value of the J2 invariant are developed employing the perturbation approach. The premise being that the J2 invariant eliminates the square root operator that would otherwise be present if using the von Mises stress, and by eliminating this operator, the nonlinearity in the functional mapping between the random input (magnitude and direction of external forces) and uncertain output (expected values of stress) is reduced. Hence, an improved accuracy can be achieved with an analytical approximation of a given order. The analytical expressions of the expected value of the J2 invariant to the second order are obtained based on a Taylor series expansion along with the associated sensitivities for gradient-based optimization. The analytical expressions are implemented in an optimization scheme and applied for the design of three ground structures considering different variability in the input random variables. For each example, the relative error between the maximum of the expected values of the J2 invariant obtained using the analytical expressions and corresponding values evaluated by performing stochastic finite element analysis, whereby the input distribution is sampled using Monte Carlo methods, finite element simulation performed for each sample realization, then computing the expected value of the stress measure using straightforward statistical expressions, and finally estimation of the maximum via the p-norm, were observed to be less than 2%, even for a coefficient of variation of 0.4. The optimized designs were again analyzed using the von Mises stress and the relative error again computed with respect to those obtained from Monte Carlo sampling and finite element simulation. In general, the relative error using the analytical expressions of the von Mises stress was greater than, except in a couple instances, those obtained using the J2 invariant.

Comparison and Analysis of Radial and Tangential Bending of Softwood and Hardwood at Static and Dynamic Loading

This paper should primarily lead to a targeted expansion of the database dealing with bending characteristics, and thus help to understand the static and dynamic bending strength depending on the direction of external forces. Wood is very often used in the structural elements of buildings and wood products (e.g., furniture), in which there is both a static load, and in many cases a dynamic load, whilst the direction of loading is usually not considered. Specifically, the paper focuses on determining the bending strength and impact strength of seven economically-important wood species in the Czech Republic. The research includes not only the above-mentioned strength characteristics, but also the elastic characteristics, i.e., the static modulus of elasticity, and the dynamic modules of elasticity determined using the ultrasound and resonance methods. The procedure was methodologically in accordance with the valid harmonized standards or the usual methodological regulations. The most significant finding can be considered that the largest difference of the mean values of impact strength in the radial direction to the tangential direction was recorded for spruce wood, namely 50.3%. Slightly smaller differences were observed for larch wood, i.e., 41.2%. Minor differences of around 20% were recorded for beech, ash and oak wood. A difference with the opposite trend was recorded for birch wood rather than for the above-mentioned woods, namely −9.5%. Linden wood showed almost no difference (−0.8%). With regard to static bending strength, it was found that the largest difference (radial/tangential) was recorded for oak wood, i.e., 7.9%, while smaller differences were found for linden wood amounting to 6.6% and birch 4.7%. For spruce, larch, beech and ash wood, these differences are negligible. Another finding is that the dynamic modules of elasticity are greatly overestimated compared to static modules of elasticity. In the case of the examined wood of coniferous trees, these differences were up to a maximum of 20%. For wood of wood species with a diffuse-porous structure of wood, the differences were more pronounced, i.e., the range of 36% to 68%, and for wood species with a ring-porous structure in the range of 21% to 43%.

Stability and free vibration analysis of compound column with piezoelectric rod

This paper deals with the divergence and flutter instability of a slender geometrically nonlinear two-member column under eccentric partially follower load. The external force direction is governed by follower parameter η, which changes over the interval 0 ≤ η ≤ 1, hence both the conservative (η = 0) and nonconservative load may be taken into account. To eliminate the static column deflection, the host aluminium member is associated with an auxiliary piezoceramic rod subjected to an electric field. The governing equations of motion and boundary conditions are derived using extended variational Hamilton’s principle. Constitutive equations expressing the piezoelectric coupling between the electric and elastic fields, the von Kármán theory of moderately large rotations but small strains and the Euler–Bernoulli beam theory are used in the formulation. Due to the nonlinearity of the governing equations, their solutions are attempted by a regular perturbation technique leading to asymptotic expansions of displacements, internal forces and the natural vibration frequency. The stability analysis of the column is investigated by using the kinetic criterion, i.e. by studying the evolution of the eigenfrequencies for an increasing external load. Both the divergence and flutter instability phenomena are detected and the latter exists only for the pure tangential load.It has been found that the courses of frequency curves, which are strictly dependent on the load eccentricity and follower parameter, may be modified by the piezoelectric actuation. As a result, both the divergence and flutter forces of the column are affected by the electric field. When η ≤ 0.5, the tensile piezoelectric force increases the vibration frequency, whereas the compressive force acts in the opposite way. For such η, the limit points of column instability are manifested, which are reflected by the additional branches of the eigenfrequency curves existing over a narrow range of the external load.For the pure follower load, the piezoelectric force may increase or decrease the frequency, which depends on both the external force level and its eccentricity. On the other hand, the piezoelectric actuation may be efficiently used to increase the flutter force. Specific mode shapes of the column are observed, which are characterized by an uneven number of nodes for particular members. Additionally, it is observed that the sequence of vibration modes with the growing values of the external load is reorganized. Finally, the present analysis reveals that the piezoelectric actuation not only counteracts the column bending, but also modifies the transversal vibration frequency of the system and enhances its critical forces for the conservative or nonconservative external load.

DEM numerical studies on the design and efficiency of the continuous operating triboelectric separator

Triboelectric separation has gained importance as a dry separator for mineral and coal beneficiation. The different grade components of coal powder can be classified, beneficiated, and segregated with the help of the triboelectric separator. A batch-mode triboelectric separator is being used in CSIR-Institute of Minerals & Materials Technology for separating pure coal particles from gangue quartz and kaolinite particles. The sticking of particles on the electrode plates forces the separator to be paused for cleaning the electrode plates. A moving belt over an electrode plate can prevent its direct contact with particles and also carries the particle down towards collection bins. The feasibility study of installing moving belts along with the optimum conditions for design and operating parameters were studied with the help of DEM simulations. The bi-modal frequency distributions of coal and quartz in collection bins ware observed. The rationale for observation of bi-modal distribution is attributed to the varying initial angles and velocities of the particles entering the active electric field region. The non-uniform probabilistic opportunities of the particles to attach with the respective belts resulted in two groups of particles; (a) particles attached to belt followed by their collection in the expected bins (b) particles with initial inclination opposite to the direction of external force and their collection in the bins on the other side. The second group of particles followed trajectories governed by external forces and got collected into the bins on the other side. The phenomena resulted in the bi-modal distribution of mass distribution.

A Sensorless Hand Guiding Scheme Based on Model Identification and Control for Industrial Robot

Most industrial robots are not capable of teaching by hand and require path points to be specified by teaching pendants. To enable the teaching of industrial robots by hand without any force sensors, this paper proposes a scheme to minimize the external force estimation error and reduce disturbance in the guiding task by using the virtual mass and virtual friction model. In this case, the maximum velocity and acceleration of the robot end effector shall be limited to ensure safety. Thus, the operator is allowed to guide the robot by hand. The joint torque is obtained from the motor current. The inertial force and friction of the links and driving systems are analyzed. The nonlinear dynamic model of the industrial robot is built and its parameters are calibrated by a nonlinear method. The force estimation is referenced to set the virtual friction and to design the force-following controller. Hence the end effector can follow the direction of external force compliantly and suppress jitters. Finally, several experiments on a six degrees of freedom industrial robot demonstrate the validity of the proposed control scheme.

Monitoring the failure forms of a composite laminate system by using panda polarization maintaining fiber Bragg gratings.

In this paper, the property of panda polarization maintaining fiber Bragg gratings (PPM-FBGs) embedded in a composite laminate system (CLS) under a transversal force from 1 × 105 Pa to 5 × 105 Pa is explored. Both the wavelengths shift and the rotation angle of the principal axes of the PPM-FBGs are surveyed theoretically. We investigate the corresponding relation between the direction of external force and the rotation angle of principal axes of the PPM-FBGs and prove that the magnitude and direction of the strain distribution in the CLS can be monitored simultaneously, which can realize the detection of interlaminar damage of the CLS. We find that the strain, which corresponds to the shift of wavelengths of the PPM-FBGs, has a different angular dependence, and therefore the potential failure forms of the CLS can be differentiated.

Shape changes of two-dimensional atomic islands and vacancy clusters diffusing on epitaxial (1 1 1) interfaces under the impact of an external force

Surface nanostructures migrate as a consequence of atomic diffusion. Under the effect of a force, arising for instance from an electric current or a thermal gradient (electromigration or thermomigration phenomena), the atomic diffusion is preferential in specific directions and affects the nanostructures making them move and change shape. In this work, based on Kinetic Monte Carlo simulations, we show the impact of an external force on the shapes of 2D atomic islands and vacancy clusters located on homoepitaxial (1 1 1) surfaces. At different temperatures, we identify critical values of the strength of the external force applied to the edge atoms, that lead to a series of transitions of the morphology of both islands and vacancy clusters from hexagonal to triangular-like shape. The shape variation is strongly dependent on the external force direction and on the step edge anisotropy.

Towards Subject-Specific Strength Training Design through Predictive Use of Musculoskeletal Models.

Lower extremity dysfunction is often associated with hip muscle strength deficiencies. Detailed knowledge of the muscle forces generated in the hip under specific external loading conditions enables specific structures to be trained. The aim of this study was to find the most effective movement type and loading direction to enable the training of specific parts of the hip muscles using a standing posture and a pulley system. In a novel approach to release the predictive power of musculoskeletal modelling techniques based on inverse dynamics, flexion/extension and ab-/adduction movements were virtually created. To demonstrate the effectiveness of this approach, three hip orientations and an external loading force that was systematically rotated around the body were simulated using a state-of-the art OpenSim model in order to establish ideal designs for training of the anterior and posterior parts of the M. gluteus medius (GM). The external force direction as well as the hip orientation greatly influenced the muscle forces in the different parts of the GM. No setting was found for simultaneous training of the anterior and posterior parts with a muscle force higher than 50% of the maximum. Importantly, this study has demonstrated the use of musculoskeletal models as an approach to predict muscle force variations for different strength and rehabilitation exercise variations.