Null Force Research Articles

Usage of Machine Learning Techniques to Classify and Predict the Performance of Force Sensing Resistors

Recently, there has been a huge increase in the different ways to manufacture polymer-based sensors. Methods like additive manufacturing, microfluidic preparation, and brush painting are just a few examples of new approaches designed to improve sensor features like self-healing, higher sensitivity, reduced drift over time, and lower hysteresis. That being said, we believe there is still a lot of potential to boost the performance of current sensors by applying modeling, classification, and machine learning techniques. With this approach, final sensor users may benefit from inexpensive computational methods instead of dealing with the already mentioned manufacturing routes. In this study, a total of 96 specimens of two commercial brands of Force Sensing Resistors (FSRs) were characterized under the error metrics of drift and hysteresis; the characterization was performed at multiple input voltages in a tailored test bench. It was found that the output voltage at null force (Vo_null) of a given specimen is inversely correlated with its drift error, and, consequently, it is possible to predict the sensor’s performance by performing inexpensive electrical measurements on the sensor before deploying it to the final application. Hysteresis error was also studied in regard to Vo_null readings; nonetheless, a relationship between Vo_null and hysteresis was not found. However, a classification rule base on k-means clustering method was implemented; the clustering allowed us to distinguish in advance between sensors with high and low hysteresis by relying solely on Vo_null readings; the method was successfully implemented on Peratech SP200 sensors, but it could be applied to Interlink FSR402 sensors. With the aim of providing a comprehensive insight of the experimental data, the theoretical foundations of FSRs are also presented and correlated with the introduced modeling/classification techniques.

Computation of the dynamic scalar response of large two-dimensional periodic and symmetric structures by the wave finite element method

In the past, the study of periodic media mainly focused on one-dimensional periodic structures (meaning periodic along one direction), on the one hand to determine the dispersion curves linking the frequencies to the wavenumbers and on the other hand to obtain the response of a structure to an external excitation, both for bounded or unbounded structures. In the latter case, effective approaches have been obtained, based on methods such as the Wave Finite Element (WFE). Two-dimensional periodic media are more complex to analyse but dispersion curves can be obtained rather easily as in the one-dimensional case. Obtaining the steady state response of two-dimensional periodic structures to time-harmonic excitations is much more difficult than for one-dimensional media and the results mainly concern infinite media. This work is about this last case of the steady state response of finite two-dimensional periodic structures to time-harmonic excitations by limiting oneself to structures described by a scalar variable (acoustic, thermal, membrane behaviour) and having symmetries compared to two orthogonal planes parallel to the edges of a substructure. Using the WFE for a rectangular substructure and imposing the wavenumber in one direction, we can numerically calculate the wavenumbers and mode shapes associated with propagation in the perpendicular direction. By building solutions with null forces on parallel boundaries, we can decouple the waves in the two directions parallel to the sides of the rectangle. The solution of each of these two problems is obtained by a fast Fourier transformation giving the amplitudes associated with the waves. By summing the contributions of all these waves we obtain the global solution for a two-dimensional periodic medium with a large number of substructures and a low computing time. Examples are given for the case of a two-dimensional membrane with many substructures and different types of heterogeneities.

Electronic and structural behavior of graphene and azulphene nanoflakes under the influence of two-point charges

We have studied the behavior of graphene and azulphene nanoflakes in the presence of two-point charges. The carbon systems geometry was optimized using the DFT method without symmetry constraint. We studied the coronene (7-ring), two azulphene-coronenes (7-ring) with different symmetries, the superbenzene (19-ring), and three azulphene-superbenzenes (19-ring) with also different symmetries and different combinations of five, six, and seven-member rings exposed to an electric field due to two-point charges. In addition, the induced electric dipole and quadrupole were studied as a function of the charge point magnitude and signs.The Stark-lo-Surdo effect in HOMO, LUMO, and total energies was analyzed. The positive (negative) charges decrease (increase) the HOMO, LUMO, and total electronic energies. The contraction and expansion of molecular systems and the induced charge in the molecular plane due to two identical charges were studied. Due to two identical charges, the null net force does not deform the molecular systems out-off the xy-plane at z = 0. Instead, the deformation occurs in the xy-plane at z = 0, and the positive (negative) identical charges expand (contract) the molecular systems. These systems suffer concavation under the presence of the electric field due to two-point charges with opposite signs. The central ring is closer to the positive charge, while the hydrogen atoms belonging to the edges are closer to the negative charge for curved graphene models. The concavation of azulene-based systems is irregular and very intricate.This work aims to generically describe the influence of a pair of ions on the energetic and structural (electronic and geometric) components of two-dimensional carbon nanosystems with five, six, and seven-member rings. Our studies allow understanding of the general behavior to extrapolate to other bidimensional systems with different charge exposition like ions. Despite the complexity of the performance of the electric field due to point charges to systems with many electrons, we can obtain some general behaviors, although difficult to interpret in some cases.

Analytic Solution to Longitudinal Deformation of Suspension Bridges under Live Loads

Live load of moving vehicles has a very important effect on the fatigue life of suspension bridges, which causes not only vertical deformation but also longitudinal deformation. In this study, a general analytical formulation for analyzing the quasistatic longitudinal displacement of suspension bridges under vertical live loads is developed, and the underlying deformation mechanism is revealed. First, the analytical vertical and longitudinal deformation equations for the single main cable subjected to live loads are formulated considering the geometric nonlinearity. Then, the relation of longitudinal displacements between the stiffening girder and the main cable for a single-span suspension bridge is established through analyzing the geometric configuration of deformed deck-suspender segment and imposing the null longitudinal force condition. The relation is further modified to incorporate the effect of central buckles (CBs). Compared with the finite-element (FE) prediction, the proposed analytical solution is quite accurate for both concentrated and distributed loads. It is found that the coupling of vertical and longitudinal displacement of main cables and the longitudinal constraint between the cables and girder, are responsible for the longitudinal displacement of the girder. The effects of sag-to-span ratio, CB, and inclined suspenders are studied. The longitudinal displacement of the girder can be reduced by about 20% when the sag-to-span ratio is varied from 1/9 to 1/11, and the CB with proper stiffness is more effective in reducing the longitudinal displacements. The proposed formulation can be conveniently applied for parameter optimization in the preliminary design stage so as to avoid tedious repetitive FE analysis.

Upper Limb Sensory-Motor Control During Exposure to Different Mechanical Environments in Multiple Sclerosis Subjects With No Clinical Disability.

Multiple sclerosis (MS) is an autoimmune and neurodegenerative disease resulting in motor impairments associated with muscle weakness and lack of movement coordination. The goal of this work was to quantify upper limb motor deficits in asymptomatic MS subjects with a robot-based assessment including performance and muscle synergies analysis. A total of 7 subjects (MS: 3 M−4 F; 42 ± 10 years) with clinically definite MS according to McDonald criteria, but with no clinical disability, and 7 age- and sex-matched subjects without a history of neurological disorders participated in the study. All subjects controlled a cursor on the computer screen by moving their hand or applying forces in 8 coplanar directions at their self-selected speed. They grasped the handle of a robotic planar manipulandum that generated four different environments: null, assistive or resistive forces, and rigid constraint. Simultaneously, the activity of 15 upper body muscles was recorded. Asymptomatic MS subjects generated less smooth and less accurate cursor trajectories than control subjects in controlling a force profile, while the end-point error was significantly different also in the other environments. The EMG analysis revealed different muscle activation patterns in MS subjects when exerting isometric forces or when moving in presence of external forces generated by a robot. While the two populations had the same number and similar structure of muscle synergies, they had different activation profiles. These results suggested that a task requiring to control forces against a rigid environment allows better than movement tasks to detect early sensory-motor signs related to the onset of symptoms of multiple sclerosis and to differentiate between stages of the disease.

Enhancing Part-to-Part Repeatability of Force-Sensing Resistors Using a Lean Six Sigma Approach.

Polymer nanocomposites have found wide acceptance in research applications as pressure sensors under the designation of force-sensing resistors (FSRs). However, given the random dispersion of conductive nanoparticles in the polymer matrix, the sensitivity of FSRs notably differs from one specimen to another; this condition has precluded the use of FSRs in industrial applications that require large part-to-part repeatability. Six Sigma methodology provides a standard framework to reduce the process variability regarding a critical variable. The Six Sigma core is the DMAIC cycle (Define, Measure, Analyze, Improve, and Control). In this study, we have deployed the DMAIC cycle to reduce the process variability of sensor sensitivity, where sensitivity was defined by the rate of change in the output voltage in response to the applied force. It was found that sensor sensitivity could be trimmed by changing their input (driving) voltage. The whole process comprised: characterization of FSR sensitivity, followed by physical modeling that let us identify the underlying physics of FSR variability, and ultimately, a mechanism to reduce it; this process let us enhance the sensors’ part-to-part repeatability from an industrial standpoint. Two mechanisms were explored to reduce the variability in FSR sensitivity. (i) It was found that the output voltage at null force can be used to discard noncompliant sensors that exhibit either too high or too low sensitivity; this observation is a novel contribution from this research. (ii) An alternative method was also proposed and validated that let us trim the sensitivity of FSRs by means of changing the input voltage. This study was carried out from 64 specimens of Interlink FSR402 sensors.

Experimental and Numerical Mechanical Characterization of Unreinforced and Reinforced Masonry Elements with Weak Air Lime Mortar Joints

This paper deals with the results of an experimental and numerical campaign aimed at characterizing the mechanical response of masonry components and panels made of limestone units kept together by weak air lime mortar joints. The selected air lime mortar, typical of ancient masonry buildings but difficult to be built-up artificially, was specifically prepared for the experimental analyses, with the aim of obtaining a laboratory compression strength of 0.25–0.50 MPa. In the first part of the paper, the performed tests concerning the strength of the units (mean compression strength of 80 MPa) and of the mortar (mean compression strength after 28 days of 0.30 MPa), are described for different curing periods. Moreover, tests of masonry triplets in shear (shear strength of 0.11 MPa for null axial forces) are shown and used in order to establish the main parameters of the Mohr–Coulomb failure criterium. Then, the calibration of a continuous numerical micro-model implemented in Kratos Multiphysics is presented. The model is used for reproducing the behavior of an unreinforced panel in shear made of the studied masonry and to appraise the effectiveness of a FRCM- (Fiber Reinforced Cementitious Matrix) based reinforcement intervention applied. The obtained results proved that FRCM allows to increase the strength of the considered masonry type by about eight times and the ductility by about thirteen times.

Optical forces and directionality in one-dimensional PT -symmetric photonics

We discuss the optical forces exerted on parity-time $(\mathcal{PT})$ symmetric heterostructures under normal incidence of a single and two counterpropagating plane waves. The underlying strategy is through generalized parametric space, stemming from consideration of the $\mathcal{PT}$-symmetry condition and Lorentz reciprocity theorem. In such a generalized parametric space, we are able to not only exhaustively indicate various $\mathcal{PT}$ phases and extraordinary wave phenomena but also deduce the directionality and magnitudes of optical forces. We find that when the system is illuminated by a normally incident wave, it can exhibit the symmetric pushing effect in the exact symmetry phase, unidirectional null, and bidirectional null forces (BNF) at the exceptional point, and pulling-pushing flipped forces in the broken symmetry phase, with BNF found at the pushing-pulling turning point. In two counterpropagating plane wave interferences, the magnitudes as well as the directionality of the resultant optical force can be tuned by a relative phase of incident waves. More interestingly, we observe that a null force independent of the relative phase occurred in a specific region of the broken symmetry phase and exceptional point. In addition, we offer several $\mathcal{PT}$-symmetric heterostructures to support our findings. Our results may benefit applications in $\mathcal{PT}$ optomechanics and force rectifiers.

Pattern-Based Contractility Screening, a Reference-Free Alternative to Traction Force Microscopy Methodology.

The sensing and generation of cellular forces are essential aspects of life. Traction force microscopy (TFM) has emerged as a standard broadly applicable methodology to measure cell contractility and its role in cell behavior. While TFM platforms have enabled diverse discoveries, their implementation remains limited in part due to various constraints, such as time-consuming substrate fabrication techniques, the need to detach cells to measure null force images, followed by complex imaging and analysis, and the unavailability of cells for postprocessing. Here we introduce a reference-free technique to measure cell contractile work in real time, with commonly available substrate fabrication methodologies, simple imaging, and analysis with the availability of the cells for postprocessing. In this technique, we confine the cells on fluorescent adhesive protein micropatterns of a known area on compliant silicone substrates and use the cell deformed pattern area to calculate cell contractile work. We validated this approach by comparing this pattern-based contractility screening (PaCS) with conventional bead-displacement TFM and show quantitative agreement between the methodologies. Using this platform, we measure the contractile work of highly metastatic MDA-MB-231 breast cancer cells that is significantly higher than the contractile work of noninvasive MCF-7 cells. PaCS enables the broader implementation of contractile work measurements in diverse quantitative biology and biomedical applications.

Effect of three different attachment designs in the extrusive forces generated by thermoplastic aligners in the maxillary central incisor.

ABSTRACTIntroduction: Orthodontic aligners use have increased in dentistry. The resolution of complex movements such as extrusion demands the use of attachments to reach the aimed force, but just a few studies have been developed to evaluate the biomechanical performance of the aligners and their accessories. Objective: The objective of this study was to evaluate on the three axes (X, Y and Z) the forces generated by three different attachment designs for the extrusion of the maxillary central incisor using esthetic orthodontic aligners. Methods: Three prototypes of maxillary models were developed, each one with a specific attachment inserted in the central incisor. Three aligners were manufactured for each of the three attachment designs, with 0.33-mm activation in the direction of the extrusion. An analytical device was used to evaluate the forces applied to the three axes by each aligner/attachment. The data were assessed by one-way ANOVA and Tukey’s test (α = 0.05). Results: All of the studied attachment designs could satisfactorily perform the extrusion movement. However, force intensities were different in the three designs (design 1 = 2.5 N; design 2 = 2.2 N, and design 3 = 1.1 N). Furthermore, two of the three attachment designs (designs 1 and 2) eventually exerted significant forces on the X (mesiodistal) and Y (buccopalatal) axes. Conclusion: The attachment design 3 presents the best distribution of forces for extrusion movement, generating almost null forces on X and Y axes, and lower intensity of force on the Z axis.

The effective tensile and bending stiffness of nanotube fibers

We analyze the pure bending state, preliminarily considering the pure traction problem, for a fiber with circular cross-section composed by monodispersed Nano Tube (NT) segments, whose length is much lower than the length of the fiber, arranged in a cross-sectional square lattice, possibly inclined with respect to the bending plane. The proposed model accounts for the compliant shear coupling of the constituent NTs along their lateral contact surfaces, and considers that the position of each NT is offset with respect to the neighboring ones by a fixed distance. The shearing of the NTs permits their mobility in longitudinal direction, inducing an internal rearrangement, calculated through energy minimization, that affects the macroscopic response. With a micro-macro approach, the internal actions in the whole fiber are calculated. We find that uniform axial macroscopic strain is associated with constant tensile normal force in the fiber and null moment; correspondingly, constant macroscopic curvature provides a constant bending moment in the plane of bending and null axial force. It is then possible to consider the NT fiber as an equivalent homogeneous beam, whose effective tensile and bending stiffness can be calculated, finding a dependence upon the aspect ratio of the fiber, the aspect ratio of the individual NTs and, more important, the offset of the NTs. The model permits to interpret recent experimental results.

Mechanistic three-dimensional model to study centrosome positioning in the interphase cell.

During the interphase in mammalian cells, the position of the centrosome is actively maintained at a small but finite distance away from the nucleus. The perinuclear positioning of the centrosome is crucial for cellular trafficking and progression into mitosis. Although the literature suggests that the contributions of the microtubule-associated forces bring the centrosome to the center of the cell, the position of the centrosome was merely investigated in the absence of the nucleus. Upon performing a coarse-grained simulation study with mathematical analysis, we show that the combined effect of the forces due to the cell cortex and the nucleus facilitate the centrosome positioning. Our study also demonstrates that in the absence of nucleus-based forces, the centrosome collapses on the nucleus due to cortical forces. Depending upon the magnitudes of the cortical forces and the nucleus-based forces, the centrosome appears to stay at various distances away from the nucleus. Such null force regions are found to be stable as well as unstable fixed points. This study uncovers a set of redundant schemes that the cell may adopt to produce the required cortical and nucleus-based forces stabilizing the centrosome at a finite distance away from the nucleus.

Modeling musculoskeletal kinematic and dynamic redundancy using null space projection.

The coordination of the human musculoskeletal system is deeply influenced by its redundant structure, in both kinematic and dynamic terms. Noticing a lack of a relevant, thorough treatment in the literature, we formally address the issue in order to understand and quantify factors affecting the motor coordination. We employed well-established techniques from linear algebra and projection operators to extend the underlying kinematic and dynamic relations by modeling the redundancy effects in null space. We distinguish three types of operational spaces, namely task, joint and muscle space, which are directly associated with the physiological factors of the system. A method for consistently quantifying the redundancy on multiple levels in the entire space of feasible solutions is also presented. We evaluate the proposed muscle space projection on segmental level reflexes and the computation of the feasible muscle forces for arbitrary movements. The former proves to be a convenient representation for interfacing with segmental level models or implementing controllers for tendon driven robots, while the latter enables the identification of force variability and correlations between muscle groups, attributed to the system’s redundancy. Furthermore, the usefulness of the proposed framework is demonstrated in the context of estimating the bounds of the joint reaction loads, where we show that misinterpretation of the results is possible if the null space forces are ignored. This work presents a theoretical analysis of the redundancy problem, facilitating application in a broad range of fields related to motor coordination, as it provides the groundwork for null space characterization. The proposed framework rigorously accounts for the effects of kinematic and dynamic redundancy, incorporating it directly into the underlying equations using the notion of null space projection, leading to a complete description of the system.

Thrust actuator with passive restoration force for wide gap magnetic bearings

Abstract Active thrust magnetic bearings provide an axial force to balance the moving parts of machines. However, most devices produce null or unbalancing passive forces. Furthermore, reported designs usually feature very small axial and radial gaps. This paper presents a thrust actuator for wide axial gaps that produces both passive and active restoring axial forces. It features a long biconical rotor and a stator housing a single winding and two permanent magnets. Simulations are done using finite-element-analysis (FEA) and compared to magnetic circuit analysis and experimental results from a prototype with a diameter of 48 mm and 20 mm axial displacement.

Quantum Interference of Force

We show that a quantum particle subjected to a positive force in one path of a Mach-Zehnder interferometer and a null force in the other path may receive a negative average momentum transfer when it leaves the interferometer by a particular exit. In this scenario, an ensemble of particles may receive an average momentum in the opposite direction of the applied force due to quantum interference, a behavior with no classical analogue. We discuss some experimental schemes that could verify the effect with current technology, with electrons or neutrons in Mach-Zehnder interferometers in free space and with atoms from a Bose-Einstein condensate.

Learning to shape virtual patient locomotor patterns: internal representations adapt to exploit interactive dynamics.

This work aimed to understand the sensorimotor processes used by humans when learning how to manipulate a virtual model of locomotor dynamics. Prior research shows that when interacting with novel dynamics humans develop internal models that map neural commands to limb motion and vice versa. Whether this can be extrapolated to locomotor rehabilitation, a continuous and rhythmic activity that involves dynamically complex interactions, is unknown. In this case, humans could default to model-free strategies. These competing hypotheses were tested with a novel interactive locomotor simulator that reproduced the dynamics of hemiparetic gait. A group of 16 healthy subjects practiced using a small robotic manipulandum to alter the gait of a virtual patient (VP) that had an asymmetric locomotor pattern modeled after stroke survivors. The point of interaction was the ankle of the VP’s affected leg, and the goal was to make the VP’s gait symmetric. Internal model formation was probed with unexpected force channels and null force fields. Generalization was assessed by changing the target locomotor pattern and comparing outcomes with a second group of 10 naive subjects who did not practice the initial symmetric target pattern. Results supported the internal model hypothesis with aftereffects and generalization of manipulation skill. Internal models demonstrated refinements that capitalized on the natural pendular dynamics of human locomotion. This work shows that despite the complex interactive dynamics involved in shaping locomotor patterns, humans nevertheless develop and use internal models that are refined with experience.NEW & NOTEWORTHY This study aimed to understand how humans manipulate the physics of locomotion, a common task for physical therapists during locomotor rehabilitation. To achieve this aim, a novel locomotor simulator was developed that allowed participants to feel like they were manipulating the leg of a miniature virtual stroke survivor walking on a treadmill. As participants practiced improving the simulated patient’s gait, they developed generalizable internal models that capitalized on the natural pendular dynamics of locomotion.

Full-Pose Tracking Control for Aerial Robotic Systems With Laterally Bounded Input Force

In this paper, we define a general class of abstract aerial robotic systems named Laterally Bounded Force (LBF) vehicles, in which most of the control authority is expressed along a principal thrust direction, while in the lateral directions a (smaller and possibly null) force may be exploited to achieve full-pose tracking. This class approximates well platforms endowed with non-coplanar/non-collinear rotors that can use the tilted propellers to slightly change the orientation of the total thrust w.r.t. the body frame. For this broad class of systems, we introduce a new geometric control strategy in SE(3) to achieve, whenever made possible by the force constraints, the independent tracking of position-plus-orientation trajectories. The exponential tracking of a feasible full-pose reference trajectory is proven using a Lyapunov technique in SE(3). The method can deal seamlessly with both under- and fully-actuated LBF platforms. The controller guarantees the tracking of at least the positional part in the case that an unfeasible full-pose reference trajectory is provided. The paper provides several experimental tests clearly showing the practicability of the approach and the sharp improvement with respect to state of-the-art approaches.

Sliding Dynamics of Parallel Graphene Sheets: Effect of Geometry and Van Der Waals Interactions on Nano-Spring Behavior

Graphene and carbon nanotubes are promising materials for nanoelectromechanical systems. Among other aspects, a proper understanding of the sliding dynamics of parallel graphene sheets or concentric nanotubes is of crucial importance for the design of nano-springs. Here, we analytically investigate the sliding dynamics between two parallel, rigid graphene sheets. In particular, the analysis focuses on configurations in which the distance between the sheets is kept constant and lower than the equilibrium interlayer spacing of graphite (unstable configurations). The aim is to understand how the interlayer force due to van der Waals interactions along the sliding direction changes with the geometrical characteristics of the configuration, namely size and interlayer spacing. Results show metastable equilibrium positions with completely faced sheets, namely a null force along the sliding direction, whereas net negative/positive forces arise when the sheets are approaching/leaving each other. This behavior resembles a molecular spring, being able to convert kinetic into potential energy (van der Waals potential), and viceversa. The amplitude of both storable energy and entrance/exit forces is found to be proportional to the sheet size, and inversely proportional to their interlayer spacing. This model could also be generalized to describe the behavior of configurations made of concentric carbon nanotubes, therefore allowing a rational design of some elements of carbon-based nanoelectromechanical systems.

Framework for a Calibration-Less Operation of Force Sensing Resistors at Different Temperatures

Force sensing resistors (FSRs) typically exhibit noticeably different responses from one device to another, and thus, an individual time-consuming calibration is required for each device. With the aim of speeding-up the development process of applications involving FSRs, a framework for a calibration-less operation of FSRs is presented. The method is based on performing periodic updates on the output voltage at null force and on employing a unique sensitivity value. Dynamic forces were applied at different temperatures to 96 FlexiForce sensors manufactured by Tekscan, Inc. The sensors exhibited rather constant sensitivity values at the temperatures spanning between 24 °C–60 °C. Conversely, the output voltage at null force showed a non-deterministic behavior when the temperature changed. The proposed method showed higher accuracy than the manufacturer method when measuring small forces, whereas the manufacturer method exhibited higher accuracy when working with large forces. Statistical tools were employed to fit the univariate sensitivity data to probability density functions and to assess the relationship between the FSR parameters and temperature. Finally, the effects of temperature changes over sensors’ hysteresis are discussed.

High-Frequency Intermuscular Coherence between Arm Muscles during Robot-Mediated Motor Adaptation.

Adaptation of arm reaching in a novel force field involves co-contraction of upper limb muscles, but it is not known how the co-ordination of multiple muscle activation is orchestrated. We have used intermuscular coherence (IMC) to test whether a coherent intermuscular coupling between muscle pairs is responsible for novel patterns of activation during adaptation of reaching in a force field. Subjects (N = 16) performed reaching trials during a null force field, then during a velocity-dependent force field and then again during a null force field. Reaching trajectory error increased during early adaptation to the force-field and subsequently decreased during later adaptation. Co-contraction in the majority of all possible muscle pairs also increased during early adaptation and decreased during later adaptation. In contrast, IMC increased during later adaptation and only in a subset of muscle pairs. IMC consistently occurred in frequencies between ~40–100 Hz and during the period of arm movement, suggesting that a coherent intermuscular coupling between those muscles contributing to adaptation enable a reduction in wasteful co-contraction and energetic cost during reaching.