Apparent mass of the standing human body when using a whole-body vibration training machine: Effect of knee angle and input frequency

Several studies have investigated the transmission of vibration from the vibrating plate of a whole-body vibration training machine (WBVTM) to different locations on the human body. No known work has investigated the interface force between the vibrating plate of the machine and the human body. This paper investigates the effect of bending the knees and the vibration frequency on the interface force (presented as apparent mass (AM)) between the vibrating plate and the body. Twelve male subjects stood with four different knee angles (180, 165, 150 and 135°) and were exposed to sinusoidal vertical vibration at eight frequencies in the range of 17–42 Hz. The vertical acceleration and the interface force between the body and the vibrating plate were measured and used to calculate the AM. The acceleration and force depended on the frequency and were found to vary with both the adopted posture and subject. The AM generally decreased with increasing the frequency but showed a peak at 24 Hz which was clearer when the knees were bent. Bending the knees showed an effect similar to increasing the damping of a system with base excitation; increasing the damping reduced the AM in the resonance region but increased the AM at higher frequencies. Users of WBVTMs have to be careful when choosing the training posture: although, as shown in previous studies, bending the knees reduces the transmission of vibration to the spine, it increases the interface forces which might indicate increased stresses on the lower legs and joints.     

Dynamic forces over the interface between a seated human body and a rigid seat during vertical whole-body vibration

Biodynamic responses of the seated human body are usually measured and modelled assuming a single point of vibration excitation. With vertical vibration excitation, this study investigated how forces are distributed over the body-seat interface. Vertical and fore-and-aft forces were measured beneath the ischial tuberosities, middle thighs, and front thighs of 14 subjects sitting on a rigid flat seat in three postures with different thigh contact while exposed to random vertical vibration at three magnitudes. Measures of apparent mass were calculated from transfer functions between the vertical acceleration of the seat and the vertical or fore-and-aft forces measured at the three locations, and the sum of these forces. When sitting normally or sitting with a high footrest, vertical forces at the ischial tuberosities dominated the vertical apparent mass. With feet unsupported to give increased thigh contact, vertical forces at the front thighs were dominant around 8 Hz. Around 3–7 Hz, fore-and-aft forces at the middle thighs dominated the fore-and-aft cross-axis apparent mass. Around 8–10 Hz, fore-and-aft forces were dominant at the ischial tuberosities with feet supported but at the front thighs with feet unsupported. All apparent masses were nonlinear: as the vibration magnitude increased the resonance frequencies decreased. With feet unsupported, the nonlinearity in the apparent mass was greater at the front thighs than at the ischial tuberosities. It is concluded that when the thighs are supported on a seat it is not appropriate to assume the body has a single point of vibration excitation.     

Non-linearities in apparent mass and transmissibility during exposure to whole-body vertical vibration

The causes of low back pain associated with prolonged exposure to whole-body vibration are not understood. An understanding of non-linearities in the biomechanical responses is required to identify the mechanisms responsible for the dynamic characteristics of the body, to allow for the non-linearities when predicting the influence of seating dynamics, and to predict the adverse effects caused by various magnitudes of vibration. Twelve subjects were exposed to six magnitudes, 0.25-2.5ms(-2) rms, of vertical random vibration in the frequency range 0.2-20Hz. The apparent masses of the subjects were determined together with transmissibilities measured from the seat to various locations on the body surface: the upper and lower abdominal wall, at L3, over the posterior superior iliac spine and the iliac crest. There were significant reductions in resonance frequencies for both the apparent mass and the transmissibilities to the lower abdomen with increases in vibration magnitude. The apparent mass resonance frequency reduced from 5.4-4. 2Hz as the magnitude of the vibration increased from 0.25-2.5ms(-2) rms. Vertical motion of the lumbar spine and pelvis showed resonances at about 4Hz and between 8 and 10Hz. When exposed to vertical vibration, the human body shows appreciable non-linearities in its biodynamic responses. Biodynamic models should be developed to reflect the non-linearity.     

Artificial vestibular feedback in conditions of modified body scheme

Subjects standing in darkness on the rigid support, kept a vertical posture which was destabilized by vibration of the Achilles tendons. To create a feedback on the vestibular input, transmastoidal bipolar galvanic stimulation was used. Changes of current in the feedback contour looked as linear function considering amplitude and velocity of the subject's head displacements in reference to the vertical. To change the body scheme we used some posture configurations: turning of the head in relation to the trunk; turning of the trunk with the head fixed; joint turning of the head and trunk. As a result of these configurations, the head could be turned approximately at right angle in relation to the feet. In addition turning of one foot at right angle in relation to the other foot was used. Artificial feedback reduces body fluctuations caused by vibration only in the vertical plane which passes through interaural axis of the head. The authors assume that directional changes of vestibulo-motor responses and results of application of artificial feedback during changes of orientation of the head in relation to the feet can be connected to change of ensembles of vestibular hair cells, which signals dominate in responses of vestibulo-spinal neurones.     

Non-linear characteristics in the dynamic responses of seated subjects exposed to vertical whole-body vibration

The effect of the magnitude of vertical vibration on the dynamic response of the seated human body has been investigated. Eight male subjects were exposed to random vibration in the 0.5 to 20 Hz frequency range at five magnitudes: 0.125, 0.25, 0.5, 1.0 and 2.0 ms(-2) r.m.s. The dynamic responses of the body were measured at eight locations: at the first, fifth, and tenth thoracic vertebrae (T1, T5, T10), at the first, third, and fifth lumbar vertebrae (L1, L3, L5) and at the pelvis (the posterior-superior iliac spine). At each location, the motions on the body surface were measured in the three orthogonal axes within the sagittal plane (i.e., the vertical, fore-and-aft, and pitch axes). The force at the seat surface was also measured. Frequency response functions (i.e., transmissibilities and apparent mass) were used to represent the responses of the body. Non-linear characteristics were observed in the apparent mass and in the transmissibilities to most measurement locations. Resonance frequencies in the frequency response functions decreased with increases in the vibration magnitude (e.g. for the vertical transmissibility to L3, a reduction from 6.25 to 4.75 Hz when the vibration magnitude increased from 0.125 to 2.0 ms(-2) r.m.s.). The transmission of vibration within the spine also showed some evidence of a non-linear characteristic. It can be concluded from this study that the dynamic responses of seated subjects are clearly non-linear with respect to vibration magnitude, whereas previous studies have reported inconsistent conclusions. More understanding of the dependence on vibration magnitude of both the dynamic responses of the soft tissues of the body and the muscle activity (voluntary and involuntary) is required to identify the causes of the non-linear characteristics observed in this study.     

The apparent mass of the seated human exposed to single-axis and multi-axis whole-body vibration

Most workplaces where workers are exposed to whole-body vibration involves simultaneous motion in the fore-and-aft (x-), lateral (y-) and vertical (z-) directions. Previous studies reporting the biomechanical response of people exposed to vibration have almost always used single-axis vibration stimuli. This paper reports a study where apparent masses of 15 subjects were measured whilst exposed to single-axis and tri-axial whole-body vibration. Each subject was exposed to 28 vibration conditions comprising every combination of single-axis and tri-axial vibration with magnitudes of 0.4 and 0.8 ms(-2) r.m.s. in each direction, once with backrest contact and once without backrest contact. Results show that increasing the magnitude of vibration in directions orthogonal to that being measured affects the apparent mass, causing a reduction in the resonance frequency as the total magnitude of vibration increases. It is demonstrated that the apparent mass resonance frequency is a function of the total vibration magnitude in all axes rather than a function of the vibration magnitude in the direction being measured. It is also shown that, for individuals, the frequency of the peak in the apparent mass in one direction is not related to the frequency of the peak in another direction. It is concluded that more complex biomechanical models are required in order to simulate human response to multi-axis vibration.     

Measurement and modelling of x-direction apparent mass of the seated human body-cushioned seat system

For modelling purposes and for evaluation of driver's seat performance in the vertical direction various mechano-mathematical models of the seated human body have been developed and standardized by the ISO. No such models exist hitherto for human body sitting in an upright position in a cushioned seat upper part, used in industrial environment, where the fore-and-aft vibrations play an important role. The interaction with the steering wheel has to be taken into consideration, as well as, the position of the human body upper torso with respect to the cushioned seat back as observed in real driving conditions. This complex problem has to be simplified first to arrive at manageable simpler models, which still reflect the main problem features. In a laboratory study accelerations and forces in x-direction were measured at the seat base during whole-body vibration in the fore-and-aft direction (random signal in the frequency range between 0.3 and 30 Hz, vibration magnitudes 0.28, 0.96, and 2.03 ms(-2) unweighted rms). Thirteen male subjects with body masses between 62.2 and 103.6 kg were chosen for the tests. They sat on a cushioned driver seat with hands on a support and backrest contact in the lumbar region only. Based on these laboratory measurements a linear model of the system-seated human body and cushioned seat in the fore-and-aft direction has been developed. The model accounts for the reaction from the steering wheel. Model parameters have been identified for each subject-measured apparent mass values (modulus and phase). The developed model structure and the averaged parameters can be used for further bio-dynamical research in this field.     

The apparent mass of the seated human body: vertical vibration

Apparent mass frequency response functions of the seated human body have been measured with random vibration in the vertical direction at frequencies up to 20 Hz. A group of eight subjects was used to investigate some factors (footrest, backrest, posture, muscle tension, vibration magnitude) that may affect the apparent mass of a person; a group of 60 subjects (24 men, 24 women and 12 children) was used to investigate variability between people. Relative movement between the feet and the seat was found to affect the apparent mass at frequencies below resonance, particularly near zero-frequency. The resonance frequency generally increased with the use of a back rest, an erect posture and, in particular, increased muscle tension; but there was considerable intersubject variability in the changes. The magnitude of the vibration had a consistent effect: the resonance frequency decreased from about 6 to 4 Hz when the magnitude of the vibration was increased from 0.25 to 2.0 ms-2 r.m.s. The apparent masses of all the subjects were remarkably similar when normalized with respect to sitting weight. However, there were statistically significant correlations between apparent mass and some body characteristics (such as weight and age).     

Identification of the head-neck complex in response to trunk horizontal vibration

A method is proposed for identifying the head-neck complex (HNC) in the seated human body when it is exposed to the trunk horizontal (fore-and-aft) vibration. It is assumed that the HNC only has the anteroposterior (flexion/extension) motion in the sagittal plane. An electrohydraulic vibrator is used as a source of vibration. To generate the trunk horizontal vibration, the trunk of the seated subject is fixed to the seatback. The subjects are exposed to the random vibration at a magnitude of 1.60 ms^-2 rms (root-mean-square) for 50 s. The coherence and frequency response function are then obtained in the frequency range 0.5–3 Hz. The results show that the HNC behavior is quasilinear with a resonance frequency between 1 and 1.4 Hz. Accordingly, a two-dimensional single-inverted pendulum is considered as a model for the HNC. The frequency domain identification method is then used to estimate the unknown parameters, including the HNC viscoelastic and inertia parameters. The model is examined in a time domain using the random vibration. Good agreement is obtained between experimental and simulation results, indicating the reliability of the proposed method.     

Quantitative measurement of cutaneous sensory response to vibration

This paper presents psychological and physical experiments carried out by using a vibrometer as an acoustical calibration apparatus. This study has shown the relationship between the vibratory sensibility and the electric signal generated in a living body. The threshold curve for square wave vibration is lower by 12.3 dB than that for sine wave vibration near 30 Hz. The stimulus level is taken as the horizontal axis, and potential variation and strengh evaluation are plotted on the vertical axis, the former has a nearly rectiliner relation with the latter.     

Predicting lower body power from vertical jump prediction equations for loaded jump squats at different intensities in men and women

The purpose of this study was to determine the efficacy of estimating peak lower body power from a maximal jump squat using 3 different vertical jump prediction equations. Sixty physically active college students (30 men, 30 women) performed jump squats with a weighted bar's applied load of 20, 40, and 60% of body mass across the shoulders. Each jump squat was simultaneously monitored using a force plate and a contact mat. Peak power (PP) was calculated using vertical ground reaction force from the force plate data. Commonly used equations requiring body mass and vertical jump height to estimate PP were applied such that the system mass (mass of body + applied load) was substituted for body mass. Jump height was determined from flight time as measured with a contact mat during a maximal jump squat. Estimations of PP (PP(est)) for each load and for each prediction equation were compared with criterion PP values from a force plate (PP(FP)). The PP(est) values had high test-retest reliability and were strongly correlated to PP(FP) in both men and women at all relative loads. However, only the Harman equation accurately predicted PP(FP) at all relative loads. It can therefore be concluded that the Harman equation may be used to estimate PP of a loaded jump squat knowing the system mass and peak jump height when more precise (and expensive) measurement equipment is unavailable. Further, high reliability and correlation with criterion values suggest that serial assessment of power production across training periods could be used for relative assessment of change by either of the prediction equations used in this study.     

Modelling, simulation and optimisation of a human vertical jump.

This paper describes an efficient biomechanical model of the human lower limb with the aim of simulating a real human jump movement consisting of an upword propulsion, a flying and a landing phase. A multiphase optimal control technique is used to solve the muscle force sharing problem. To understand how intermuscular control coordinates limb muscle excitations, the human body is reduced to a single lower limb consisting of three rigid bodies. The biomechanical system is activated by nine muscle-tendon actuators representing the basic properties of muscles during force generation. For the calculation of the minimal muscle excitations of the jump movement, the trajectory of the hip joint is given as a rheonomic constraint and the contact forces (ground reaction forces) are determined by force plates. Based on the designed musculoskeletal model and on the differential equations of the multibody system, muscle excitations and muscle forces necessary for a vertical jump movement are calculated. The validity of the system is assessed comparing the calculated muscle excitations with the registered surface electromyogramm (EMG) of the muscles. The achieved results indicate a close relationship between the predicted and the measured parameters.     

Vibrot,a Simple Device for the Conversion of Vibration into Rotation Mediated by Friction: Preliminary Evaluation

While “vibrational noise” induced by rotating components of machinery is a common problem constantly faced by engineers, the controlled conversion of translational into rotational motion or vice-versa is a desirable goal in many scenarios ranging from internal combustion engines to ultrasonic motors. In this work, we describe the underlying physics after isolating a single degree of freedom, focusing on devices that convert a vibration along the vertical axis into a rotation around this axis. A typical Vibrot (as we label these devices) consists of a rigid body with three or more cantilevered elastic legs attached to its bottom at an angle. We show that these legs are capable of transforming vibration into rotation by a “ratchet effect”, which is caused by the anisotropic stick-slip-flight motion of the leg tips against the ground. Drawing an analogy with the Froude number used to classify the locomotion dynamics of legged animals, we discuss the walking regime of these robots. We are able to control the rotation frequency of the Vibrot by manipulating the shaking amplitude, frequency or waveform. Furthermore, we have been able to excite Vibrots with acoustic waves, which allows speculating about the possibility of reducing the size of the devices so they can perform tasks into the human body, excited by ultrasound waves from the outside.     

Force platforms as ergometers.

Walking and running on the level involves external mechanical work, even when speed averaged over a complete stride remains constant. This work must be performed by the muscles to accelerate and/or raise the center of mass of the body during parts of the stride, replacing energy which is lost as the body slows and/or falls during other parts of the stride. External work can be measured with fair approximation by means of a force plate, which records the horizontal and vertical components of the resultant force applied by the body to the ground over a complete stride. The horizontal force and the vertical force minus the body weight are integrated electronically to determine the instantaneous velocity in each plane. These velocities are squared and multiplied by one-half the mass to yield the instantaneous kinetic energy. The change in potential energy is calculated by integrating vertical velocity as a function of time to yield vertical displacement and multiplying this by body weight. The total mechanical energy as a function of time is obtained by adding the instantaneous kinetic and potential energies. The positive external mechanical work is obtained by adding the increments in total mechanical energy over an integral number of strides.     

Vibration training: an overview of the area, training consequences, and future considerations

The effects of vibration on the human body have been documented for many years. Recently, the use of vibration for improving the training regimes of athletes has been investigated. Vibration has been used during strength-training movements such as elbow flexion, and vibration has also been applied to the entire body by having subjects stand on vibration platforms. Exposure to whole-body vibration has also resulted in a significant improvement in power output in the postvibratory period and has been demonstrated to induce significant changes in the resting hormonal profiles of men. In addition to the potential training effects of vibration, the improvement in power output that is observed in the postvibratory period may also lead to better warm-up protocols for athletes competing in sporting events that require high amounts of power output. These observations provide the possibility of new and improved methods of augmenting the training and performance of athletes through the use vibration training. Despite the potential benefits of vibration training, there is substantial evidence regarding the negative effects of vibration on the human body. In conclusion, the potential of vibration treatment to enhance the training regimes of athletes appears quite promising. It is essential though that a thorough understanding of the implications of this type of treatment be acquired prior to its use in athletic situations. Future research should be done with the aim of understanding the biological effects of vibration on muscle performance and also the effects of different vibration protocols on muscle performance.     

Effects of vibration intensity on lower limb joint moments during standing

Muscle activity and joint moment of the lower limbs can provide different information about the stimulation of controlled whole-body vibration (CWBV) on human body. Previous studies investigated the immediate effects of the intensity of CWBV on enhancing lower-limb muscle activity. However, no study has examined the possible influence of CWBV intensity on joint loading. It remains unexplored how CWBV intensity impacts joint loading. This study was carried out (1) to quantify the effects of CWBV intensity in terms of vibration frequency and amplitude on the lower limb joint moments and (2) to examine the relationship between leg joint moments and vibration intensity characterized by the platform’s acceleration, that is determined by frequency and amplitude, during standing among young adults. Thirty healthy young adults participated in this study. Each participant experienced nine vibration intensity levels dependent upon the frequency (10, 20, and 30 Hz) and amplitude (1, 2, and 3 mm) while standing on a side-alternating vibration platform. Their body kinematics and vertical reaction forces between the feet and platform were collected. Inverse dynamics was employed to calculate the resultant moment for the ankle, knee, and hip joints in the sagittal plane. Our results revealed that the root-mean-square moment significantly increases with increasing vibration frequency or amplitude for all three joints. Further, all joint moments are strongly and positively correlated with the platform acceleration.     

Vibration settling time of the gastrocnemius remains constant during an exhaustive run in rear foot strike runners

In this study, vibrations of human gastrocnemius during an exhaustive run protocol are considered for analysis. Previous studies have shown increased vibration intensity and damping coefficient within the soft tissue with fatigue. The question of this study was to investigate if the vibration settling time remains constant during a prolonged running. Eleven semi-professional middle/long distance runners ran to exhaustion on a treadmill with their preferred constant speed (4.29 ± 0.33 m/s) for 3873 ± 1147 m. Vibration of the gastrocnemius lateralis, electrical activity of the tibialis anterior and the gastrocnemius medialis along with ground reaction force (GRF) were recorded. The results demonstrated significant increase in impact peak and loading rate, and the frequency content of the impact, with no significant change in active peak of the vertical GRF. Fatigue resulted in increased vibration intensity, damping coefficient, and energy dissipation of vibration with no change in vibration settling time. Furthermore, peak acceleration significantly linearly (R = 0.59) increased as a function of running time. The mean frequency of muscle activity of the gastrocnemius medialis and the intensity of muscle activity in TA significantly decreased. The results suggest that constant vibration settling time might either be an objective for muscle tuning which is more pronounced in fatigued state or a passive by-product of muscle function in running. Further studies are needed to address this point.     

The effects of whole-body vibration on human biodynamic response

The objective of vibration research at the Armstrong Laboratory includes the expansion and improvement of the measurement, quantification, analysis, and modeling of human vibration response. The driving-point impedance and transmissibility techniques have been expanded and are rigorously applied in the research efforts. Driving-point impedance is defined as the ratio between the transmitted force and input velocity at the point of load application. Transmissibility is typically defined as the ratio between the acceleration level measured at some location on the body and the input acceleration at the seat. These two ratios are used to assess the magnitude and frequency location of resonance behaviors where maximum motions occur in the body. From these data, analytical models are developed which can simulate the motions and coupling behaviors, and predict the stiffness and damping characteristics of the affected anatomical structures. The ultimate goal of the research is to provide new and improved data and modeling capability for revising exposure standards and for developing equipment design guidelines and criteria for improving tolerance and reducing physiological consequences. This paper describes the results of recent studies conducted to identify the biodynamic behavior of major anatomical structures affected by seated whole-body vibration, to develop an analytical model for simulating human vibration response, and to apply the model to evaluate the effects of seat cushion materials on the transmission/attenuation pathways.     

An improved cost function for modeling of muscle activity during running

This paper tries to improve a recently developed mass-spring-damper model of the human body during running. The previous model took the muscle activity into account using a nonlinear controller that tuned the mechanical properties of the soft-tissue package based on two physiological hypotheses, namely "constant-force" and "constant-vibration". Three cost functions were used, out of which one was based on the constant-force hypothesis and two others were based on the constant-vibration hypothesis. The results of the study showed that the proposed cost functions are only partially successful in capturing the experimentally observed trends of the ground reaction force and vibration. The current paper proposes an improved cost function that combines both above-mentioned hypotheses. It is shown that the improved cost function can capture all the trends that were observed in the measurements of the ground reaction force and vibration level. It is therefore advised to use the new cost function in place of the previous ones.     

Body Size Regression Formulae,Proximate Composition and Energy Density of Eastern Bering Sea Mesopelagic Fish and Squid

The ecological significance of fish and squid of the mesopelagic zone (200 m–1000 m) is evident by their pervasiveness in the diets of a broad spectrum of upper pelagic predators including other fishes and squids, seabirds and marine mammals. As diel vertical migrators, mesopelagic micronekton are recognized as an important trophic link between the deep scattering layer and upper surface waters, yet fundamental aspects of the life history and energetic contribution to the food web for most are undescribed. Here, we present newly derived regression equations for 32 species of mesopelagic fish and squid based on the relationship between body size and the size of hard parts typically used to identify prey species in predator diet studies. We describe the proximate composition and energy density of 31 species collected in the eastern Bering Sea during May 1999 and 2000. Energy values are categorized by body size as a proxy for relative age and can be cross-referenced with the derived regression equations. Data are tabularized to facilitate direct application to predator diet studies and food web models.