Martin Fritz

Description of the relation between the forces acting in the lumbar spine and whole-body vibrations by means of transfer functions

OBJECTIVE The purpose of this study was to display the relationships between the forces transmitted in the spine and the accelerations of the vibrating seat. BACKGROUND Investigations reveal that exposure to whole-body vibration can induce degenerative changes in the lumbar spine. Elevated spinal forces are probably the crucial component in the pathogenesis of this disease. DESIGN AND METHODS The spinal forces are simulated by means of a biomechanical model, where 16 rigid bodies represent the upper body and the arms of a sitting operator. The relationships between seat accelerations and spinal forces are displayed as frequency-dependent transfer functions. RESULTS Spinal forces are not only elevated in the direction parallel to the vibration excitation but also in the two other orthogonal vibration directions. According to the magnitudes of the transfer functions the highest oscillating parts of the forces are reached at frequencies below 10 Hz. CONCLUSIONS Using the transfer functions, the time course of the spine forces can be computed and a new kind of weighting function can be derived which enables a force related weighting of the seat acceleration. RelevanceVibration induced health risks are commonly assessed by the weighted acceleration (ISO 2631-1). These weighting factors resulted from subjective magnitude sensation. It is argued that a more valid assessment will be obtained if the accelerations are weighted in relation to spinal forces. These forces cannot be measured directly under vibration. However, they can be simulated by means of biomechanical models.

BaSiP : Batch process simulation with dynamically reconfigured process dynamics

Abstract Recipe-driven automatic production is widely used to reduce the load on the operators and to allow them to focus on the high level tasks of assignment of equipment, sequencing, and scheduling. Simulation can support these functions by answering if .. then questions, finding bottlenecks or underused equipment, testing of recipes, detecting illegal or dangerous operations. The major challenge of the simulation of batch plants is the hybrid nature of the system, combined with frequent changes of the structure of the system, which in our opinion necessitates a dynamic configuration of the simulation model during the simulation run. This is realized in the program BaSiP which is designed to simulate the operation of recipe-driven multipurpose batch plants.

Three-dimensional biomechanical model for simulating the response of the human body to vibration stress

Several investigations have revealed that long-term exposure to whole-body vibrations can induce low back pain. In analogy to materials handling, the health risk can be assessed if the forces transmitted in the spine during vibration are known. To estimate the forces a biomechanical model has been developed in which the human trunk, neck, head and arms are represented by 16 rigid bodies. An additional body simulates the vibrating seat. The bodies are connected by visco-elastic joint elements, and 56 force elements imitate the trunk and neck muscles. The motion equations are derived by means of the dynamics of systems of rigid bodies, and the motions are simulated in three directions. The frequency-response functions between the accelerations of the seat and the head satisfactorily correspond to data reported in the literature. The spine forces are composed of a static part, due to body posture, and a vibration-induced part. The relation between the oscillating parts of the forces transmitted from seat to pelvis and the spine forces are also described by frequency-response functions. To assess the health risk the simulated spine forces must be compared with the strength of the spine, bearing in mind that this is dependent on the number of load cycles.

Simulating the response of a standing operator to vibration stress by means of a biomechanical model

Under vibration stress the compressive forces transmitted in the joints of a standing operator are composed of nearly static and oscillating force parts. Because these forces can hardly be measured they were assessed by means of a biomechanical model. In the model, 27 rigid bodies with 103 degrees of freedom represent the segments of the human body. 106 force elements imitate the muscles of the trunk and the legs. At first, the model parameter were varied so that for the simulated sitting posture the model fits the seat-to-head transmissibility given in the literature and in ISO/CD 5982. For the standing posture, the transfer functions between the ground acceleration and the oscillating forces in the ankle, the knee, the hip, and the motion segment L3-L4 were computed. According to the moduli of these functions the forces in the ankles are higher than those in the knees or the hips and they nearly come up to the forces in the lumbar spine. Further the results of the simulation indicate that under equal vibration stress in the standing and the sitting posture the differences between the compressive forces in the lumbar spine are small.

Simulation of the influence of sports surfaces on vertical ground reaction forces during landing

In many biomechanical analyses, the vertical ground reaction force (GRF) is measured by force plates. However, if force plates are fixed on elastic surfaces, the force signals have low-frequency oscillations superimposed. The question arises, as to whether this oscillation results from the response of the athlete to the surface properties or from the fixation of the force plate on the elastic surface. For the simulation of the vertical GRF, a mechanical model was developed that combines three submodels representing the surface, the athlete and the force plate. The simulations were carried out for landings on concrete and wooden elastic surfaces, without and with the force plate, respectively. Comparison of the two surfaces showed that, on the elastic surface, the passive peak of the vertical GRF was lower and was reached later than on the concrete surface. Thus a lower force rate was possible during the landing on the elastic surface (concrete: 186 body weight per second; wooden: 164 body weight per second), which can reduce the risk of damaging the joint cartilage. The simulations also showed that the time course of the GRF was changed by a rippling effect when the force plate was fixed on the elastic surface. The rippling was not the result of a change in the athletes movements, because the parameters of the athlete submodel were not changed. The rippling induced by the force plate hinders the analysis of the GRF time course involving the real peak force and the force rate.

Dynamic Properties of the Biomechanical Model of the Human Body-Influence of Posture and Direction of Vibration Stress

Previous studies have shown that exposure to whole-body vibration can interfere with comfort, activities, and health. In analogy to materials handling it is assumed that the elevated spinal forces are a crucial component in the pathogenesis of the health impairment. To estimate the forces a biomechanical model was developed. In the model the human trunk, neck and head, the legs, and the arms are represented by 27 rigid bodies. An additional body simulates the vibrating vehicle or machinery. The bodies are connected by visco-elastic joint elements. In total 106 force elements imitate the trunk, neck, and leg muscles. The motion equations were derived by means of the dynamics of systems of rigid bodies. Motions were simulated in different standing and sitting postures and in three vibration directions. The transfer functions between the accelerations of the surface or the seat and the spinal forces were computed. By means of these functions it can be shown that under the conditions investigated the compressive forces seem to be the dominant stressor between the forces transmitted in the lumbar spine. However, it cannot be stated that under horizontal vibration the health risk is only dependent from the compressive forces. Here the relationship with the shear strength of the spine being much lower than the compressive strength must be regarded.

HYBRID SIMULATION OF FLEXIBLE BATCH PLANTS

Abstract In this contribution the structure of a simulation system for flexible batch plant operation, which tracks the complete state of the plant and includes both continuous and discrete dynamics, is described. The system consists of two parts, the batch plant and its operational functionality and the recipe, which describes the production process. The object-oriented model of the production process is based on the concept of recipe controlled operation.

Simulating the Impact During Human Jumping by Means of a 4-Degrees-of-Freedom Model With Time-Dependent Properties

Abstract The authors simulated the vertical movements of a jumper and the force time courses by means of a 4-degrees-of-freedom model consisting of 4 masses, springs, and dampers. Of the motions simulated, only that of the mass imitating the trunk corresponded to the measured data. The best fit to the measured force curves were obtained in the simulation in which time-dependent model parameters were used. From the results, the authors concluded that at the beginning of the landing, a jumper behaves like a 2-mass model in which the leg segments (thighs, shanks, and feet) effectively combine into 1 mass. After approximately 60 ms, the connections between the leg segments become more compliant and the jumper behaves like a 4-mass model with a soft coupling between the leg segments. The process is equivalent to an increase of the degrees of freedom of the movements. At the end of the ground contact phase during hopping, the jumper has to contract the muscles in order to reach the envisaged jump height. In the model, that contraction could not be satisfactorily simulated.

Influence of the Posture of the Trunk on the Spine Forces During Whole-Body Vibration

Typically drivers of container-bridge cranes are forced to sit with a forward bent upper trunk to control the position and motion of the container. Fork-lift truck drivers incline the upper trunk to the side to look forward or they twist to one side during reversing. Assuming that these inclined postures result in a higher health risk than vibration exposure in the upright sitting posture the forces transmitted in the lumbar spine were assessed by means of a biomechanical model. Under realistic vibration stress the bent postures result in an increase of the compressive and the shear forces. By the enhanced shear forces a displacement of the upper motion segments is prevented. The quantitative relationship between the mean values of the forces and the chest inclination can be sufficiently approximated by regression functions. The increase of the spine forces is the result of the increased muscle forces stabilizing the inclined trunk. On container bridge cranes or fork-lift trucks the typical postures of the drivers result in enhanced spinal forces compared with the upright sitting posture. This effect must be considered in the risk analysis of workplaces with whole-body vibration.

Effect of Repeated External Perturbations on the Reflex Control of Human Posture — Influence of Reflex Delay, Duration and Gain

The aim of the study was to assess the effects of muscle responses on the trunk motions during repeated perturbations by external forces. Patients with low back pain have delayed muscle reflex latencies to perturbations compared with healthy controls. The perturbation provoked trunk accelerations were simulated by a model consisting of four rigid bodies and six force elements representing trunk and hip muscles. The influence of the muscle responses were assessed by varying the reflex delays, the reflex durations, and the reflex gains. Trunk accelerations can be reduced by the simulated muscle responses. The optimal solution is not the result of extreme values of the reflex delay and duration range but of intermediate values. The relationship between the trunk accelerations and the reflex delay and duration respectively can be described by asymmetrical u-shape functions. As patients with low back pain showed delayed reflexes, their trunk motions are probably increased compared with healthy subjects.