Resultant Reaction Force Research Articles

Flow Reaction Forces upon Blowdown of Safety Valves

AbstractThe activation of safety valves causes the development of flow reaction forces that have to be transferred in an adequate way via the piping to the steel structure or via the connected vessel into the foundation. If the safety valve outlet piping is connected to a blowdown system or, in case of blowing off into the atmosphere, are equipped with a T‐piece at the outlet, the stationary reaction forces are compensated completely. The transient opening process, however, develops flow reaction forces which culminate in peaks of short duration. In this article, a simple method will be proposed for the estimation of the resulting reaction forces as a function of the length of the pipe at the safety valve outlet. CFD calculations and blowdown tests executed with a full‐lift safety valve have confirmed this method on principle. Special importance is attributed to the short duration of the effect of the reaction forces which seems to have only a negligible impact on the supporting steel structure.

Biomechanical Analysis of the Canine Hind Limb: Calculation of Forces During Three-legged Stance

This paper presents a three-dimensional biomechanical model of the canine hind limb, and describes the process of determining the muscle forces and joint reaction forces and moments occurring in the hind limb during three-legged stance. The model was based on anatomical and morphometric data presented in a previous paper. Equations of equilibrium were formulated for the different components of the hind limb. Since the number of unknowns exceeded the number of equations, the problem was statically indeterminate.Two optimization techniques were applied to solve this statically indeterminate problem. The resultant hip-joint reaction force (acting on the acetabulum) predicted by these optimization methods ranged between 0.73 and 1.04 times body weight, and was directed dorsally, medially and caudally. The resultant knee-joint reaction force (acting on the femur) ranged between 1.05 and 1.08 times body weight, and was directed dorsally, laterally and cranially. The largest muscle forces predicted by the minimization of maximal muscle stress (MMMS) criterion were in the biceps femoris (0.24 times body weight), rectus femoris (0.15 times body weight), medial gluteal (0.18 times body weight),semi-membranosus (0.09 times body weight), the lateral and intermediate vastus (0.18 times body weight) and the medial vastus (0.17 times body weight). The largest muscle forces predicted by the minimization of the sum of muscle forces (MSMF) criterion were in the biceps femoris (0.29 times body weight), lateral and intermediate vastus (0.45 times body weight)), and the deep gluteal (0.16 times body weight).The magnitudes and directions of the forces in the joints of the canine hind limb, as well as in the muscles that surround these joints, provide a database needed for future biomechanical analyses of the physiology and pathophysiology of the canine hind limb.

Le maintien dˈune posture dˈinclinaison vers lˈavant modifie davantage les amplitudes des déplacements du centre des pressions que celles du centre de gravité

OBJECTIVE: An ordinary and practical method to assess the postural control mechanisms is to measure, through a force platform, the point of application of the resultant reaction forces. The recorded signal, the centre of pressure CP, is used to compute the motions of the vertical projection of the centre of gravity (CG v) and those of the difference CP-CG v. The former is considered in this postural task as the controlled variable whereas the latter is thought to express the ankle resultant stiffness. Interestingly, the CG v motions can be extracted from the CP trajectory through a simple mathematical model. MATERIALS AND METHODS: The relationship between CP and the elementary motions CP-CG v and CG v has been tested in the present study by comparing the postural effects induced by a leaning forward position to a normal one consisting to stand still. RESULTS: A large increase is noticed for the amplitudes of the CP-CG v motions for both medio-lateral ML and antero-posterior AP directions. On the other hand, a similar effect appears for the CG v motions but only on the ML direction. Nevertheless, the frequency analysis indicates that the constancy of the CG v motions on the AP direction is accompanied by a change in the frequency distribution, as assessed by the MPF parameters. DISCUSSION - CONCLUSION: These features highlight the necessity, to interpret rigorously the postural performance, to take into account in separate ways each of the elementary CP-CG v and CG v motions which, combined, constitute the CP displacements.

Compliant walking in primates

AbstractIt is now well recognized that terrestrial mammals can maintain equivalent bone stresses despite dramatic differences in body size through the adoption of extended limb positions during locomotion. However, this dynamic solution is not available to all mammals. Medium‐ and large‐bodied arboreal mammals, such as anthropoid primates, must maintain relatively gracile and mobile limbs in order to manoeuvre in a discontinuous arboreal environment. But they must also use flexed (i.e. crouched) limb positions in order to maintain balance on arboreal substrates, thus subjecting their gracile limbs to relatively high loads. To determine how primates resolve this conflict between their kinematics and their morphology, five species of Old World monkeys were videotaped with lateral, frontal, and overhead cameras while they walked at a range of natural speeds along a runway and raised horizontal poles instrumented with a force platform. Kinematic and kinetic data on the forelimb show that during arboreal quadrupedalism, Old World monkeys do crouch when travelling on arboreal supports compared to the ground. Simultaneously, they lower vertical peak reaction forces and thereby reduce and reorient the peak resultant substrate reaction force, so that moment arms and moments are roughly equivalent on poles and the ground. This is accomplished through the adoption of a compliant walking gait characterized by high degrees of forelimb protraction, substantial elbow yield, low vertical oscillations of the body, and long contact times. The use of a compliant walking gait appears to be extremely rare among mammals and is most likely related to an initial primate adaptation to quadrupedal locomotion on terminal branches. This gait represents a previously unrecognized dynamic postural mechanism for maintenance of similar bone stresses and safety factors in both arboreal and terrestrial environments.

A perturbation/correlation method for force guided robot assembly

Force guided robot control is a control scheme based on the interpretation of measured force acting on the robot end effector. A functional map relating the correction of motion to force measurements is generated based on the geometry of the workpiece and its kinematic behavior in interacting with the environment. In the traditional force guided control schemes, the contact force measured by a force sensor is directly fed back to a feedback controller to generate a motion correction signal. In the paper, instead of simply measuring contact forces, we take positive actions by giving perturbation to the end effector and observing the reaction forces to the perturbation in order to obtain much richer and more reliable information. By the correlation between the input perturbation and the resultant reaction forces, we can determine the gradient of the force profile and guide the part correctly. By applying a type of direct adaptive control, the contact force is maintained at the lowest level. This algorithm is applied to a pipe insertion task, in which the insertion force is minimized during the insertion. Based on the process model and stability analysis using the Popov stability criterion, conditions for stable, successful insertion despite nonlinearities and uncertainties in the environment are obtained. The theoretical results are verified using the experimental data. To generate high frequency perturbation, a vibratory end effector using piezoelectric actuators is designed and built. Through both simulations and experiments, the feasibility and usefulness of these methods are demonstrated.

Estimation of Actuating Force of Running by Viscoelastic Model with a Characteristics of Muscle.

Although a ball's rebound height decreases for every fall, a man's rebound height in running is kept constant by supplying the actuating force in a certain amount through the ground reaction force of landing. Purpose of this study is to propose an estimation method of the actuating force from the ground reaction force. In this paper, the mechanical model of running is represented by the mass-nonlinear Voigt model which is composed of the nonlinear spring element whose stiffness decreases with time because of the biomechanical properties of passive tension of muscle and the nonlinear damping element which is expressed by polynomial of viscous element and some elastic-viscous interactive elements. In this model, when the resultant reaction force of the viscous and interactive elements agrees with the velocity of mass center in direction, the force is estimated as the actuating force.

A Finite Element Analysis of the Human Temporomandibular Joint

A 2-D finite element model of the human temporomandibular joint (TMJ) has been developed to investigate the stresses and reaction forces within the joint during normal sagittal jaw closure. The mechanical parameters analyzed were maximum principal and von Mises stresses in the disk, the contact stresses on the condylar and temporal surfaces, and the condylar reactions. The model bypassed the complexity of estimating muscle forces by using measured joint motion as input. The model was evaluated by several tests. The results demonstrated that the resultant condylar reaction force was directed toward the posterior side of the eminence. The contact stresses along the condylar and temporal surfaces were not evenly distributed. Separations were found at both upper and lower boundaries. High tensile stresses were found at the upper boundaries. High tensile stresses were found at the upper boundary of the middle portion of the disk.

A Dynamic Biomechanical Model of the Wrist Joint

This paper describes a biomechanical model of the wrist joint that incorporates the dynamic component of angular acceleration. Repetition, which has been found to be a risk factor for cumulative trauma disorders (CTDs), is essentially cyclic angular acceleration and velocity. The objective of the dynamic model presented here, which is based on Armstrong's and Chaffin's (1979) static model, is to explain how the component of angular acceleration could increase a worker's risk of developing CTDs. When the wrist is accelerated in the flexion/extension plane, the resultant reaction force on the tendons and median nerve from the carpal bones and flexor retinaculum increases. This increase in reaction force is due solely to the acceleration of the wrist without any external grasp or pinch force. External grasp or pinch forces would increase the resultant reaction force even more.

Biomechanical analysis of drop and countermovement jumps.

For 13 subjects the performance of drop jumps from a height of 40 cm (DJ) and of countermovement jumps (CMJ) was analysed and compared. From force plate and cine data biomechanical variables including forces, moments, power output and amount of work done were calculated for hip, knee and ankle joints. In addition, electromyograms were recorded from five muscles in the lower extremity. The results obtained for DJ appeared to depend on jumping style. In a subgroup of subjects making a movement of large amplitude (i.e. bending their hips and knees considerably before pushing off) the push-off phase of DJ closely resembled that of CMJ. In a subgroup of subjects making a movement of small amplitude, however, the duration of the push-off phase was shorter, values for moments and mean power output at the knees and ankles were larger, and the mean EMG activity of m. gastrocnemius was higher in DJ than in CMJ. The findings are attributed to the influences of the rapid pre-stretch of knee extensors and plantar flexors after touch-down in DJ. In both subgroups, larger peak resultant reaction forces were found at the knee and ankle joints, and larger peak forces were calculated for the Achilles tendon in DJ than in CMJ.

Electromyography and mechanics of mastication in the albino rat.

The masticatory apparatus in the albino rat was studied by means of electromyography and subsequent estimation of muscular forces. The activity patterns of the trigeminal and suprahyoid musculature and the mandibular movements were recorded simultaneously during feeding. The relative forces of the individual muscles in the different stages of chewing cycles and biting were estimated on the basis of their physiological cross sections and their activity levels, as measured from integrated electromyograms. Workinglines and moment arms of these muscles were determined for different jaw positions. In the anteriorly directed masticatory grinding stroke the resultants of the muscle forces at each side are identical; they direct anteriorly, dorsally and slightly lingually and pass along the lateral side of the second molar. Almost the entire muscular resultant force is transmitted to the molars while the temporo-mandibular joint remains unloaded. A small transverse force, produced by the tense symphyseal cruciate ligaments balances the couple of muscle resultant and molar reaction force in the transverse plane. After each grinding stroke the mandible is repositioned for the next stroke by the overlapping actions of three muscle groups: the pterygoids and suprahyoids produce depression and forward shift, the suprahyoids and temporal backward shift and elevation of the mandible while the subsequent co-operation of the temporal and masseter causes final closure of the mouth and starting of the forward grinding movement. All muscles act in a bilaterally symmetrical fashion. The pterygoids contract more strongly, the masseter more weakly during biting than during chewing. The wide gape shifts the resultant of the muscle forces more vertically and moreposteriorly. The joint then becomes strongly loaded because the reaction forces are applied far anteriorly on the incisors. The charateristic angle between the almost horizontal biting force and the surface of the food pellet indicates that the lower incisors produce a chisel-like action. Tooth structure reflects chewing and biting forces. The transverse molar lamellae lie about parallel to the chewing forces whereas perpendicular loading of the occlusal surfaces is achieved by their inclination in the transverse plane. The incisors are loaded approximately parallel to their longitudinal axis, placement that avoids bending forces during biting. It is suggested that a predominantly protrusive musculature favors the effective force transmission to the lower incisors, required for gnawing. By grinding food across transversely oriented molar ridges the protrusive components of the muscles would be utilized best. From the relative weights of the masticatory muscles in their topographical relations with joints, molars and incisors it may be concluded that the masticatory apparatus is a construction adapted to optimal transmission of force from muscles to teeth.

Geometrical Basis of Lagrange Multipliers and System Constraints in Mechanics

The effects of constraints imposed on mechanical systems may be analyzed when the constraints are recognized as geometrical surfaces. Each component constraint restricts the motion due to the applied active forces; taken together the constraint surfaces intersect, forming a new dimensionally reduced surface and thus a single constraint. The gradient vectors on each of the component constraint surfaces must sum to the gradient on the reduced surface. Lagrange multipliers are then just scalars which adjust the magnitudes and senses of the gradient vectors on each component geometrical surface so that the gradient on their intersection has the proper magnitude and is directed along the resultant reaction force. Since the resultant gradient lies in a subspace with a basis formed by the component gradients, these component gradients must be linearly independent. The existence of a nonsingular Jacobian transformation from the subspace to the constraint surfaces guarantees its existence with the required dimension, and thus, the validity of the constraints is guaranteed.