Factors affecting minimum push and pull forces of manual carts.

The minimum forces needed to manually push or pull a 4-wheel cart of differing weights with similar wheel sizes from a stationary state were measured on four floor materials under different conditions of wheel width, diameter, and orientation. Cart load was increased from 0 to 181.4 kg in increments of 36.3 kg. The floor materials were smooth concrete, tile, asphalt, and industrial carpet. Two wheel widths were tested: 25 and 38 mm. Wheel diameters were 51, 102, and 153 mm. Wheel orientation was tested at four levels: F0R0 (all four wheels aligned in the forward direction), F0R90 (the two front wheels, the wheels furthest from the cart handle, aligned in the forward direction and the two rear wheels, the wheels closest to the cart handle, aligned at 90 degrees to the forward direction), F90R0 (the two front wheels aligned at 90 degrees to the forward direction and the two rear wheels aligned in the forward direction), and F90R90 (all four wheels aligned at 90 degrees to the forward direction). Wheel width did not have a significant effect on the minimum push/pull forces. The minimum push/pull forces were linearly proportional to cart weight, and inversely proportional to wheel diameter. The coefficients of rolling friction were estimated as 2.2, 2.4, 3.3, and 4.5 mm for hard rubber wheels rolling on smooth concrete, tile, asphalt, and industrial carpet floors, respectively. The effect of wheel orientation was not consistent over the tested conditions, but, in general, the smallest minimum push/pull forces were measured with all four wheels aligned in the forward direction, whereas the largest minimum push/pull forces were measured when all four wheels were aligned at 90 degrees to the forward direction. There was no significant difference between the push and pull forces when all four wheels were aligned in the forward direction.     

NEMS diaphragm sensors integrated with triple-nano-ring resonator

Two types of circular diaphragm, made by Si and Si/SiO₂, integrated with hexagonal photonic crystal (PhC) lattice with triple-nano-ring (TNR) resonator created at the centre are proposed as nano-scale force and pressure sensor. The optimized channel drop effect of the TNR resonator brings a strong forward drop resonant peak in both the cases and with Q-factor of 1602 and 1737, respectively. The resonant wavelength peak experience red shifts upon the applied load on the circular diaphragm along the normal direction, in terms of a 2nd-order polynomial relationship. The devices can detect a wide range of applied load. Si diaphragm based micro force sensor gives minimum detectable force of 0.847 μN in the region of applied force from 10 to 20 μN. Si/SiO₂ diaphragm based pressure sensor gives minimum detectable pressure of 4.17 MPa in the region of applied pressure from 20 to 40 MPa. From the derived wavelength shift versus a given centre displacement of the diaphragm, Si diaphragm based sensor shows higher sensitivity than Si/SiO₂ diaphragm sensor.     

A pseudo-waveform technique to assess forest structure using discrete lidar data

The use of airborne laser scanning systems (lidar) to describe forest structure has increased dramatically since height profiling experiments nearly 30 years ago. The analyses in most studies employ a suite of frequency-based metrics calculated from the lidar height data, which are systematically eliminated from a full model using stepwise multiple linear regression. The resulting models often include highly correlated predictors with little physical justification for model formulation. We propose a method to aggregate discrete lidar height and intensity measurements into larger footprints to create “pseudo-waves”. Specifically, the returns are first sorted into height bins, sliced into narrow discrete elements, and finally smoothed using a spline function. The resulting “pseudo-waves” have many of the same characteristics of traditional waveform lidar data. We compared our method to a traditional frequency-based method to estimate tree height, canopy structure, stem density, and stand biomass in coniferous and deciduous stands in northern Wisconsin (USA). We found that the pseudo-wave approach had strong correlations for nearly all tree measurements including height (cross validated adjusted R² (R²_cv) = 0.82, RMSE_cv = 2.09 m), mean stem diameter (R²_cv = 0.64, RMSE_cv = 6.15 cm), total aboveground biomass (R²_cv = 0.74, RMSE_cv = 74.03 kg ha^− 1), and canopy coverage (R²_cv = 0.79, RMSE_cv = 5%). Moreover, the type of wave (derived from height and intensity or from height alone) had little effect on model formulation and fit. When wave-based and frequency-based models were compared, fit and mean square error were comparable, leading us to conclude that the pseudo-wave approach is a viable alternative because it has 1) an increased breadth of available metrics; 2) the potential to establish new meaningful metrics that capture unique patterns within the waves; 3) the ability to explain metric selection based on the physical structure of forests; and 4) lower correlation among independent variables.     

The effect of handle height and cart load on the initial hand forces in cart pushing and pulling

The objective of this study was to measure the three-dimensional hand forces people exert to initiate a cart push or pull for two cart loads: 73 and 181 kg, and three handle heights: knuckle, elbow, and shoulder heights. The cart used was equipped with 15.24 cm (6 in) diameter wheels. The floor was covered with carpet tiles. The laboratory-measured hand force exertions were compared to the minimum forces needed to push/pull the cart under the same conditions and to the psychophysical initial push/pull force limits. For pushing and pulling, the measured anterior-posterior hand forces were 2–2.4 times the minimum required forces. For the heavier cart load, lower forces were applied as handle height increased. Pull forces were 7% higher than push forces. The smallest vertical forces were measured at elbow height. Strength capability and gender did not have an effect on the applied forces. The mean strength percentile for the male sample was 64%, while the mean strength percentile for the female sample was 13% as determined from the Adjusted Torso Lift Strength Test and population strength data for this test. The comparison with the psychophysical limits indicated that the tasks were well within the maximum acceptable initial forces for males, but not for females.     

Development and application of a multi-axis dynamometer for measuring grip force

Objective: This paper describes the development and application of a novel multi-axis hand dynamometer for quantifying 2D grip force magnitude and direction in the flexion-extension plane of the fingers. Methods: A three-beam reconfigurable form dynamometer, containing two active beams for measuring orthogonal forces and moments regardless of point of force application, was designed, fabricated and tested. Maximum grip exertions were evaluated for 16 subjects gripping cylindrical handles varying in diameter. Results: Mean grip force magnitudes were 231 N (SD = 67.7 N), 236 N (72.9 N), 208 N (72.5 N) and 158 N (45.7 N) for 3.81 cm, 5.08 cm, 6.35 cm and 7.62 cm diameter handles, respectively. Grip force direction rotated clockwise and the centre of pressure moved upward along the handle as handle diameter increased. Conclusions: Given that the multi-axis dynamometer simultaneously measures planar grip force magnitude and direction, and centre of pressure along the handle, this novel sensor design provides more grip force characteristics than current sensor designs that would improve evaluation of grip characteristics and model-driven calculations of musculoskeletal forces from dynamometer data.     

Grip force vectors for varying handle diameters and hand sizes

Grip force was measured along two orthogonal axes and vector summed. Sixty-one participants recruited from a manufacturing facility (29 men and 32 women) grasped instrumented cylinders (2.54, 3.81, 5.08, 6.35, and 7.62 cm diameter) using a maximal voluntary power grip. Two orthogonal force measurements relative to the third metacarpal were resolved into a magnitude and corresponding angle. On average, magnitude increased 34.8 N as handle diameter increased from 2.54 cm to 3.81 cm, and then monotonically declined 103.8 N as the handle diameter increased to 7.62 cm. The average direction monotonically decreased from 59.2 degrees to 37.7 degrees as handle diameter decreased from the largest to the smallest. When the diameter was smallest, the greatest force component, Fx (168.6 N), was in the direction where the fingertips opposed the palm. Conversely, when the diameter was largest, the smallest component, Fx (77.7 N), was in the same direction. These values are averaged for the left and right hand. The angle for the largest diameter increased with increasing hand size. These relationships should be useful for the design of handles that require gripping in specific directions, such as for hand tools and controls. Actual or potential applications of this research include the design of handles that require gripping in specific directions, such as for hand tools and controls, that reduce effort, and that prevent fatigue and overexertion.     

Design and Optimization of an Omnidirectional Permanent-Magnetic Wheeled Wall-Climbing Microrobot with MEMS-Based Electromagnetic Micromotors

The paper presents a compact omnidirectional permanent-magnetic wheeled wall-climbing microrobot. A millimeter-sized axial flux electromagnetic micromotor based on MEMS technology has been specially fabricated for the microrobot and its size is 6.8 mm × 7.8 mm × 3.9 mm. A novel permanent-magnetic wheel is designed, which is directly integrated with the stators and rotor of the electromagnetic micromotor. The omnidirectional wall-climbing mechanism is realized by a set of steering gears and three standard permanent-magnetic wheels. By static and dynamic force analysis of the microrobot, the required magnetic force and the required torques for its translational and steering movements are derived. To reduce the unnecessary torque consumption of the microrobot, its structural parameters are optimized in combination with its design constraints by ANSOFT and Pro/Engineer simulation. A prototype of the proposed microrobot with the maximum designed load capacity of 3 g is developed, whose size is 26 mm in diameter and 16.4 mm in height. Experimental and simulation results demonstrate the feasibility of these concepts.     

The influence of flywheel weight and pedalling frequency on the biomechanics and physiological responses to bicycle exercise†

The physiological, subjective and biomechanical effects of altering flywheel weight and pedalling rate on a Quinton Model 870 bicycle ergometer were studied. Steel plates were added to the flywheel to increase its weight to 35·9 kg with a moment of inertia of 1·65 kg m². A 1·5 kg spoked wheel with a moment of inertia of 0·1 kg m² was used as the light flywheel. Eight subjects pedalled on two separate occasions for 6 min at 40, 50, 60, 70, 80 and 90 r.p.m. with workload levels representing 30 and 60% of their [Vdot]O₂max with each flywheel. Force plate pedals were used to measure the total resultant force on the pedals (F_R ) and the component perpendicular to the crank arm (F_T). A force effectiveness index (FEI) was denned as the average of F_T/F_R over a crank cycle. The result showed no statistically significant change (p<0·05) in [Vdot]O₂, heart rate and rating of perceived exertion of the FEI as a function of flywheel weight except for the [Vdot]O₂ at 50 r.p.m. for the light workload. As the r.p.m. increased from 40 to 90 r.p.m., the FEI decreased from 0·5 to 0·35 with the heavy load and from 0·36 to 0·22 with the light load. Measured physiological, subjective and biomechanical indices did not change significantly with flywheel weight. Increasing the pedalling rate caused a significantly less effective application of forces to the crank arm with only a small change in [Vdot]O₂.     

Effect of lifting height and load mass on low back loading

The objective of this study was to quantify the effect of lifting height and mass lifted on the peak low back load in terms of net moments, compression forces and anterior–posterior shear forces. Ten participants had to lift a box using four handle heights. Low back loading was quantified using a dynamic 3-D linked segment model and a detailed electromyographic driven model of the trunk musculature. The effects of lifting height and lifting mass were quantified using a regression technique (GEE) for correlated data. Results indicate that an increase in lifting height and a decrease in lifting mass were related to a decrease in low back load. It is argued that trunk flexion is a major contributor to low back load. For ergonomic interventions it can be advised to prioritise optimisation of the vertical location of the load to be lifted rather than decreasing the mass of the load for handle heights between 32 cm and 155 cm, and for load masses between 7.5 and 15 kg. Lifting height and load mass are important determinants of low back load during manual materials handling. This paper provides the quantitative effect of lifting height and mass lifted, the results of which can be used by ergonomists at the workplace to evaluate interventions regarding lifting height and load mass.     

Effect of lifting height and load mass on low back loading

The objective of this study was to quantify the effect of lifting height and mass lifted on the peak low back load in terms of net moments, compression forces and anterior-posterior shear forces. Ten participants had to lift a box using four handle heights. Low back loading was quantified using a dynamic 3-D linked segment model and a detailed electromyographic driven model of the trunk musculature. The effects of lifting height and lifting mass were quantified using a regression technique (GEE) for correlated data. Results indicate that an increase in lifting height and a decrease in lifting mass were related to a decrease in low back load. It is argued that trunk flexion is a major contributor to low back load. For ergonomic interventions it can be advised to prioritise optimisation of the vertical location of the load to be lifted rather than decreasing the mass of the load for handle heights between 32 cm and 155 cm, and for load masses between 7.5 and 15 kg. Lifting height and load mass are important determinants of low back load during manual materials handling. This paper provides the quantitative effect of lifting height and mass lifted, the results of which can be used by ergonomists at the workplace to evaluate interventions regarding lifting height and load mass.     

Flow-induced forces on two circular cylinders in proximity

Flow-induced forces on two nearby circular cylinders of equal diameter immersed in the cross flow at Re = 100 were numerically studied. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. It turns out that significant changes in the characteristics of flow-induced forces are noticed depending on how the two circular cylinders are positioned, resulting in quantitative changes of force coefficients on both cylinders. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and rms values of force coefficient fluctuations for each of the two cylinders. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main flow direction.     

One-handed dynamic pulling strength with special application to lawn mowers

A laboratory study was conducted to determine one-handed dynamic and static pulling strengths of 50 males and 49 females from 14 to 71 years of age. The dynamic strength for a 11m pull was measured to simulate the act of starting a lawn mower engine for four different starting-rope handle locations: on the engine, in the middle, on the right and on the left side of the frame. The last three were located at the back of the lawn mower at a vertical height of 63 cm from the floor and the handle on the engine was located at 42 cm. Static strength was measured for the handle in the middle. Ratings of perceived exertion were recorded for different body parts.

Peak and average dynamic pulling strengths were 55% and 34% of static pulling strengths. Dynamic pulling strengths were highly correlated with peak velocity (r = 0·84). Men in the age group 21-34 years had the highest strength and women in the age group 51-71 years the least strength. Dynamic pulling strengths for women were 62% of strengths for men. Women took 10% longer to pull, had a lower peak velocity (16%), reached peak force faster (17%) and took a longer time (6%) to reach peak velocity than men.

The starting handle located on the engine resulted in the maximum pulling strength and on the left side in the minimum strength. However, two out of three subjects preferred the handle either on the right side or in the middle. Fifty-five percent of the subjects indicated they would prefer a height higher than 63 cm.

Maximum stresses were perceived on the shoulder and upper arm with a mean rating between fairly light and somewhat hard. Graphs of cumulative frequency distributions of average and peak dynamic pulling strengths are presented to aid in the determining forces required to start a lawn mower engine in order to satisfy a desired percentage of the population.     

Hamiltonian laceability of bubble-sort graphs with edge faults

It is known that the n-dimensional bubble-sort graph B_n is bipartite, (n − 1)-regular, and has n! vertices. We first show that, for any vertex v, B_n − v has a hamiltonian path between any two vertices in the same partite set without v. Let F be a subset of edges of B_n. We next show that B_n − F has a hamiltonian path between any two vertices of different partite sets if ∣F∣ is at most n − 3. Then we also prove that B_n − F has a path of length n! − 2 between any pair of vertices in the same partite set.     

DEPARTMENT OF SCIENTIFIC AND INDUSTRIAL RESEARCH: HUMAN SCIENCES COMMITTEE

Maximal power output during short term constant velocity cycling and vertical jumping from a force platform has been studied in five healthy young male subjects. From the measurements on the force platform the peak (instantaneous) power output (P), net impulse (I_N ), force (F₁ ). velocity of take-off(V_T ) and height of jump(h) were calculated. The corresponding values for power (H), force (F) and velocity (V) on the bicycle were obtained from analysis of the force-velocity relationship.

The results (mean ± S.D.) showed that on the force platform F₁ P, I_N, V_T and h were 1073± 167N, 2205±310W, 154±17Ns, 2·48+0·15ms^?1 and 31 +4cm. h was positively associated with both I_N (r= +0·77) and P (r = 0·67). The mean maximal power output for cycling was 854W(39%) greater than jumping and was achieved at a 271N (25%) increase in F and a reduction in V. Nevertheless they were closely related.

Platform P(W) = 717·6 + 0·483 bicycle H(W) r= +0·74

A comparison of linear and curvilinear (hyperbolic) analysis of the F/V bicycle data showed that the latter did not reduce the variance of observations and was not, therefore, statistically justifiable (Wilkie 1950). The mean intra-subject variations of P and H were 6·6%± 1·8 and 40%+1·2. The relative values of F and V at H were both found to be approximately 50% of their respective maximal values.

It was concluded that short term power output can be measured simply and accurately in man during the performance of two activities. Rotational movement of the legs as in cycling produces higher values of peak power output then vertically lifting body weight. For the achievement of peak power output in cycling, relative force and speed of movement must both correspond to approximately half of their respective maximal values.     

Three-machine flowshop with two operations per job to minimize makespan

This work studies three variants of a three-machine flowshop problem with two operations per job to minimize makespan (F3/o = 2/C_max). A set of n jobs are classified into three mutually exclusive families A, B and C. The families A, B and C are defined as the set of jobs that is scheduled in machine sequence (M₁, M₂), (M₁, M₃) and (M₁, M₃), respectively, where (M_x, M_y) specifies the machine sequence for the job that is processed first on M_x, and then on M_y. Specifically, jobs with the same route (machine sequence) are classified into the same family. Three variants of F3/o = 2/C_max are studied. First, F3/GT, no-idle, o = 2/C_max, in which both machine no-idle and GT restrictions are considered. The GT assumption requires that all jobs in the same family are processed contiguously on the machine and the machine no-idle assumption requires that all machines work continuously without idle time. Second, the problem F3/GT, o = 2/C_max, in which the machine no-idle restriction in the first variant is relaxed, is considered. Third, the problem F3/no-idle, o = 2/C_max with the GT assumption in the first variant relaxed is considered. Based on the dominance conditions developed, the optimal solution is polynomially derived for each variant. These results may narrow down the gap between easy and hard cases of the general problem.     

Spectroscopic determination of leaf water content using continuous wavelet analysis

The gravimetric water content (GWC, %), a commonly used measure of leaf water content, describes the ratio of water to dry matter for each individual leaf. To date, the relationship between spectral reflectance and GWC in leaves is poorly understood due to the confounding effects of unpredictably varying water and dry matter ratios on spectral response. Few studies have attempted to estimate GWC from leaf reflectance spectra, particularly for a variety of species. This paper investigates the spectroscopic estimation of leaf GWC using continuous wavelet analysis applied to the reflectance spectra (350-2500 nm) of 265 leaf samples from 47 species observed in tropical forests of Panama. A continuous wavelet transform was performed on each of the reflectance spectra to generate a wavelet power scalogram compiled as a function of wavelength and scale. Linear relationships were built between wavelet power and GWC expressed as a function of dry mass (LWC_D) and fresh mass (LWC_F) in order to identify wavelet features (coefficients) that are most sensitive to changes in GWC. The derived wavelet features were then compared to three established spectral indices used to estimate GWC across a wide range of species.Eight wavelet features observed between 1300 and 2500 nm provided strong correlations with LWC_D, though correlations between spectral indices and leaf GWC were poor. In particular, two features captured amplitude variations in the broad shape of the reflectance spectra and three features captured variations in the shape and depth of dry matter (e.g., protein, lignin, cellulose) absorptions centered near 1730 and 2100 nm. The eight wavelet features used to predict LWC_D and LWC_F were not significantly different; however, predictive models used to determine LWC_D and LWC_F differed. The most accurate estimates of LWC_D and LWC_F obtained from a single wavelet feature showed root mean square errors (RMSEs) of 28.34% (R² = 0.62) and 4.86% (R² = 0.69), respectively. Models using a combination of features resulted in a noticeable improvement predicting LWC_D and LWC_F with RMSEs of 26.04% (R² = 0.71) and 4.34% (R² = 0.75), respectively. These results provide new insights into the role of dry matter absorption features in the shortwave infrared (SWIR) spectral region for the accurate spectral estimation of LWC_D and LWC_F. This emerging spectral analytical approach can be applied to other complex datasets including a broad range of species, and may be adapted to estimate basic leaf biochemical elements such as nitrogen, chlorophyll, cellulose, and lignin.     

Analysis of applied forces and electromyography of back and shoulders muscles when performing a simulated hand scaling task

Hand scaling is a physically demanding task responsible for numerous overexertion injuries in underground mining. Scaling requires the miner to use a long pry bar to remove loose rock, reducing the likelihood of rock fall injuries. The experiments described in this article simulated “rib” scaling (scaling a mine wall) from an elevated bucket to examine force generation and electromyographic responses using two types of scaling bars (steel and fiberglass-reinforced aluminum) at five target heights ranging from floor level to 176 cm. Ten male and six female subjects were tested in separate experiments. Peak and average force applied at the scaling bar tip and normalized electromyography (EMG) of the left and right pairs of the deltoid and erectores spinae muscles were obtained. Work height significantly affected peak prying force during scaling activities with highest force capacity at the lower levels. Bar type did not affect force generation. However, use of the lighter fiberglass bar required significantly more muscle activity to achieve the same force. Results of these studies suggest that miners scale points on the rock face that are below their knees, and reposition the bucket as often as necessary to do so.     

一种可越过管内凹形障碍的双驱动多轮移动载体的研究

本文在轮式和履带式管内行走机构的基础上，提出了一种新的管内行走机构，它利用两个电机分别驱动均布在机架上的与管内壁用弹簧力封闭的两组６个行进轮，从周向来看，３组驱动轮分别均布在３组平行四边形机构上，巧妙的把轮式和履带式管内行走机构结合在一起，使机构具有很好的越障能力．该机构紧凑，驱动效率高，工作可靠，尤其适用于管内壁有内凹障碍的管内环境．     

Assessment of the impacts of surface topography, off-nadir pointing and vegetation structure on vegetation lidar waveforms using an extended geometric optical and radiative transfer model

In order to prioritize the measurement requirements and accuracies of the two new lidar missions, a physical model is required for a fundamental understanding of the impact of surface topography, footprint size and off-nadir pointing on vegetation lidar waveforms and vegetation height retrieval. In this study, we extended a well developed Geometric Optical and Radiative Transfer (GORT) vegetation lidar model to take into account for the impacts of surface topography and off-nadir pointing on vegetation lidar waveforms and vegetation height retrieval and applied this extended model to assess the aforementioned impacts on vegetation lidar waveforms and height retrieval.Model simulation shows that surface topography and off-nadir pointing angle stretch waveforms and the stretching effect magnifies with footprint size, slope and off-nadir pointing angle. For an off-nadir pointing laser penetrating vegetation over a slope terrain, the waveform is either stretched or compressed based on the relative angle. The stretching effect also results in a disappearing ground peak return when slope or off-nadir pointing angle is larger than the “critical slope angle”, which is closely related to various vegetation structures and footprint size. Model simulation indicates that waveform shapes are affected by surface topography, off-nadir pointing angle and vegetation structure and it is difficult to remove topography effects from waveform extent based only on the shapes of waveform without knowing any surface topography information.Height error without correction of surface topography and off-nadir pointing angle is the smallest when the laser beams at the toward-slope direction and the largest from the opposite direction. Further simulation reveals within 20° of slope and off-nadir pointing angle, given the canopy height as roughly 25 m and the footprint size as 25 m, the error for vegetation height (RH100) ranges from − 2 m to greater than 12 m, and the error for the height at the medium energy return (RH50) from − 1 m to 4 m. The RH100 error caused by unknown surface topography and without correction of off-nadir pointing effect can be explained by an analytical formula as a function of vegetation height, surface topography, off-nadir pointing angle and footprint size as a first order approximation. RH50 is not much affected by topography, off-nadir pointing and footprint size. This forward model simulation can provide scientific guidance on prioritizing future lidar mission measurement requirements and accuracies.     

Force direction and physical load in dynamic pushing and pulling

In pushing and pulling wheeled carts, the direction of force exertion may, beside the force magnitude, considerably affect musculoskeletal loading. This paper describes how force direction changes as handle height and force level change, and the effects this has on the loads on the shoulder and low back. Eight subjects pushed against or pulled on a stationary bar or movable cart at various handle heights and horizontal force levels while walking on a treadmill. The forces at the hands in the vertical and horizontal direction were measured by a forcetransducer. The forces, body movements and anthropometric data were used to calculate the net joint torques in the sagittal plane in the shoulder and the lumbosacral joint. The magnitudes and directions of forces did not differ between the cart and the bar pushing and pulling. Force direction was affected by the horizontal force level and handle height. As handle height and horizontal force level increased, the pushing force direction changed from 45° (SD 3.3°) downward to near horizontal, while the pulling force direction changed from pulling upward by 14° (SD 15.3°) to near horizontal. As a result, it was found that across conditions the changes in force exertion were frequently reflected in changes in shoulder torque and low back torque although of a much smaller magnitude. Therefore, an accurate evaluation of musculoskeletal loads in pushing and pulling requires, besides a knowledge of the force magnitude, knowledge of the direction of force exertion with respect to the body.