Frictionless Hinges Research Articles

Discrete Model of Fabric Yarn ‐ Deflection and Stability Analysis

The paper addresses the issue of the modelling of the mechanical behaviour of yarns using a massspring system of discrete elements. For this purpose, the yarn is discretized into straight, elastic bars modelled by stretching springs which are connected at frictionless hinges by rotational springs. Shear springs are used, in order to model the shearing stiffness of the yarn. An energy study is conducted, taking into account the various strain energy contributions of the yarn and the work of the external forces. From the energy expression, a stability analysis is performed, relying on the Dirichlet‐Lagrange stability criterion. The effects of boundary conditions as well as the heterogeneity of the nodes’ rigidity are analysed. The equilibrium shapes of the structure, submitted to its own weight, are obtained as shapes associated to the minimum of the total potential energy versus the whole set of kinematic translational and rotational variables. The obtained results show that the effects of boundary conditions and heterogeneity of the yarn’s rigidity on the stability of the structure are important.

Optimisation of frequencies of a two-span shaft system joined with a hinge

A driveshaft with discontinuities (i.e. joints) is a major component in various industries. A multi-piece driveshaft in automotive applications is joined using constant velocity or universal joints or a combination of both. This article presents an exact solution for the vibration of a two-piece driveshaft with an intermediate single joint. The joint is modelled as a frictionless internal hinge. The Euler-Bernoulli beam theory is used. Lumped masses are placed on each side of the joint to represent the joint mass. Equations of motion are developed using the appropriate boundary conditions and then solved using exact solutions. Natural frequencies and modes shapes are obtained. Numerical results obtained here are compared with those obtained using experimental and analytical tools (e.g. finite elements). Parametric studies are performed and optimisation studies are conducted to maximise bending frequencies. Effects of many parameters are examined.

Consideration of the yarn–yarn interactions in meso/macro discrete model of fabric. Part I: Single yarn behaviour

A mesoscopic discrete model of dry fabric has been developed, based on the yarn–yarn interactions occurring at the yarns crossing points. The fabric yarns, described initially by a Fourier series development, are discretized into elastic straight bars represented by stretching springs and connected at frictionless hinges by rotational springs. The motion of each node is described by a lateral displacement and a rotation. The expression of the reaction force exerted by the transverse yarns at the contact points is assessed, from which the work of the reaction forces is established. The equilibrium shape of the yarn is obtained as the minimum of its total potential energy, accounting for the work of the reaction forces due to the transverse yarns. Simulations of a traction curve of a single yarn are performed, that evidence the effect of the yarn interactions. The two principal deformation mechanisms, the variation of undulation and the yarn stretching, are separately analysed.

Consideration of the yarn–yarn interactions in meso/macro discrete model of fabric: Part II: Woven fabric under uniaxial and biaxial extension

A mesoscopic discrete model of fabric has been developed, accounting for the yarn–yarn interactions occurring at the yarn crossing points. The fabric yarns, described in their initial state by a Fourier series development, are discretized into elastic straight bars represented by stretching springs, and connected at frictionless hinges by rotational springs. In the first part of the paper, the behavior under uniaxial tension of a single yarn has been investigated, and the impact of the interactions of the transverse yarns has been quantitatively assessed. The consideration of the yarn interactions is extended in this second part at the scale of the whole network of interwoven yarns, under uniaxial and biaxial loading conditions. The effect of the transverse yarns properties under uniaxial tension is evidenced, as well as the impact of the biaxial loading ratio.

Dynamics of a cable with an attached sliding mass

I describe the development of a three dimensional numerical model of a cable system with an interacting sliding mass. The cable is modelled using a lumped parameter approximation, where the cable is discretised into a collection of viscoelastic point mass elements articulated by frictionless hinges. The sliding mass is modelled as a point mass which is free to move in all three dimensions. The dynamics of the sliding mass are formulated to take into account the constraint provided by the cable, and incorporates a variety of active forces including friction and air drag.

Mesoscopic fabric models using a discrete mass-spring approach: Yarn-yarn interactions analysis

A meso/macro discrete model of fabric has been developed, accounting for yarn-yarn interactions occurring at the crossing points. The fabric yarns, described initially by a Fourier series development, are discretized into elastic straight bars represented by stretching springs and connected at frictionless hinges by rotational springs. The motion of each node is described by a lateral displacement and a rotation. The compressibility of both yarns is expressed as a kinematic relationship, considering frictionless motions of the yarns. The expression of the reaction force exerted by the transverse yarns at the contact points is then assessed, from which the work of the reaction forces is established. The equilibrium shape of the yarn is obtained as the minimum of its total potential energy, accounting for the work of the reaction forces due to the transverse yarns. Simulations of a traction curve of a single yarn are performed, that evidence the effect of the yarn interactions and the main deformation mechanisms.

Can co-activation reduce kinematic variability? A simulation study

Impedance modulation has been suggested as a means to suppress the effects of internal 'noise' on movement kinematics. We investigated this hypothesis in a neuro-musculo-skeletal model. A prerequisite is that the muscle model produces realistic force variability. We found that standard Hill-type models do not predict realistic force variability in response to variability in stimulation. In contrast, a combined motor-unit pool model and a pool of parallel Hill-type motor units did produce realistic force variability as a function of target force, largely independent of how the force was transduced to the tendon. To test the main hypothesis, two versions of the latter model were simulated as an antagonistic muscle pair, controlling the position of a frictionless hinge joint, with a distal segment having realistic inertia relative to the muscle strength. Increasing the impedance through co-activation resulted in less kinematic variability, except for the lowest levels of co-activation. Model behavior in this region was affected by the noise amplitude and the inertial properties of the model. Our simulations support the idea that muscular co-activation is in principle an effective strategy to meet accuracy demands.

OPTIMAL STANDING LONG JUMP SIMULATION FROM DIFFERENT STARTING POSTURES

A planar 4-segment human body model is used to simulate and study the effects of starting posture on standing long jumping performance. The model consists of frictionless hinge joints and is driven by joint torque actuators. The four segments represent feet, shanks, thighs, and trunk with head and arms. Movement simulations start from three different postures: high squat, squat, and low squat. The control variables are the joint torque activation levels and takeoff time. The objective function is the maximum horizontal distance from the toe point at takeoff to the center of mass (c.m.) position at landing. Optimal simulation results agree reasonably well with measurements. Different from previous high jump simulation study, slight dependence of initial posture on jump distance is found. Longer jump distance from a higher initial posture is probably due to greater range of countermovement that results in larger extension joint torque generation.

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk–head–arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum–height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models’ prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.

Statics of a gillnet placed in a uniform current

The configuration and tension distribution of a gillnet are very important for catching fish. A nonlinear mixed method is employed to determine the equilibrium configuration and tension distribution of a gillnet set in a uniform current, based on a finite element formulation a gillnet composed of mesh bars and ropes can be modeled as an infinitely flexible, straight rope element, connected at each end to other elements by a frictionless hinge. The basic nonlinear equations describing the equilibrium state of the gillnet system are solved by the Newton–Raphson method. The numerical solutions are obtained by a loading iteration in addition to a common shape iterative procedure. The method has excellent global convergence and good accuracy by comparing the numerical values with measured results from circulating water tank model testing.

A Simulation Study of the Effect of Arm Swing on Maximum Vertical Jump Performance

2359 Maximum vertical jumps have proven to be a valuable tool for examining human movement. When studying vertical jumping in the laboratory, it is common to ask subjects to perform jumps without arm swing. Outside of the laboratory jumps are more often performed with arm swing, and arm swing does increase jump height. Previous studies have suggested two mechanisms that would allow arm swing to increase takeoff velocity: production of additional momentum or slowing leg extension, which may permit muscles to work on a more favorable region of the forcevelocity curve. PURPOSE: To examine the contributions of these mechanisms in maximum vertical jumping with arm swing. METHODS: The jumps were simulated using an optimal control direct dynamics muscle moment driven model. The model had five rigid links (foot, shank, thigh, trunk, and arm), connected by frictionless hinge joints. The foot was connected to the ground by a hinge joint at the metatarsalphalangeal joint. It had a rotational spring-damper at this joint to represent the heel. The model was actuated by eight, Hill-type muscle models consisting of a series elastic element and a contractile element. Jumps were simulated with and without arm swing. RESULTS: Kinematics of the simulated jumps were similar to that measured for a group of experimental subjects. The simulated jump with arm swing was 8cm higher jumps than the simulated jump without arm swing. The magnitude of this improvement was similar to what was seen in previous experimental studies. The total work produced by the muscles of the lower body was nearly the same (3J difference) in both jumps. The muscles crossing the shoulder joint produced 164J of work in the jump simulated with arm swing. CONCLUSIONS: Although arm swing did slow the extension of the legs, no addition work was produced by the lower extremity musculature compared with jumps without arm swing. The work produced by the arms was more than sufficient to produce the increase in energy needed to improve jump height by 8cm.

A static analysis of the tension and configuration of submerged plane nets

A non-linear finite element method is employed to determine the equilibrium configuration and tension distribution of a net set in a uniform current. The method models each mesh bar in the net as an infinitely flexible rope element connected at each end to other elements by a frictionless hinge. The Newton-Raphson method is used to solve the basic non-linear simultaneous equations with respect to tension in mesh bar and knot displacements. Global convergence to the correct solution from an initially estimated state is ensured using a loading iteration in addition to the common configuration iterative procedure in order to accurately model the shape-dependent characteristic of hydrodynamic forces. The method is shown to predict the shape and tension distribution of fishing nets with reasonable accuracy in the case examined in the present study.

A Two-dimensional Sail In Turbulent Flow

The two-dimensional, incompressible flow at Reynolds number based on chord length of 1.3. 106 around an inextensible, massless sail (flexible membrane airfoil) with varying excess length is examined solving the Reynolds-Averaged NavierStokes (RANS) equations on computational grids deforming according to the sail movement. The grid deformation is computed using the same numerical procedure solving the basic equations of displacements for an isotropic, linearly elastic continuum. Results are presented for fully turbulent conditions employing closure models of different degree of complexity in comparison with experimental and analytical results obtained from literature. The sail is modelled as a chain with frictionless hinges. Good agreement can be found for low angle of attack and small excess length. However, for higher angle of attack, approaching onset of separation and beyond, the predictive accuracy varies significantly with the representation of turbulence in conjunction with strong unsteady phenomena.

Minimum weight design of continuous beams

If frictionless hinges are placed at all the points in the beam where the bending moment is zero, it is shown that the number and positions of these hinges are such as to render the elastic or plastic minimum weight beam statically determinate. This fact can be used to obtain particular designs. In the plastic design a collapse mechanism exists such that there is no change in slope at these hinges. In the elastic design the deformed beam will in general have a change in slope at these points, although under special circumstances the change is zero. Both the elastic and plastic designs are shown to be fully stressed.

The Egyptian Shadouf and the Rate of Human Work

THE interesting paper by Drs. Haldane and Henderson in NATURE for August 28, p. 308, merits emphasis on two or three points. Above all, the mechanical beauty of the shadouf, in spite of its crude construction, deserves notice. It will be observed that trunnion bearings, which would wear and need lubrication, are replaced by almost frictionless hinges in the form of ropes. These ropes, in addition to their antifriction qualities as hinges, confer an important property on the system, namely, elasticity.

Functional Inertia, a Property of Protoplasm

‘Dead’ matter has two forms of inertia—that of rest (mass), and that of motion (momentum) —and it seems to me that living matter possesses a property, not hitherto recognised as such, which might be called functional inertia, or metabolic inertia of protoplasm whether animal or vegetable. It is owing to the inertia of matter at rest that the heavy gate, swung even on almost frictionless hinges, cannot be instantaneously set in motion; and when it has been set swinging, it is owing to its inertia of motion (momentum) that it continues to swing for some time after we have ceased to push it. By functional inertia of protoplasm I mean the power or property of protoplasm to remain in the metabolic status quo ante; if resting—anabolising—to remain doing so, even after the reception of a stimulus tending to bring about the opposite metabolic state, this might be called anabolic inertia; if active—katabolising—to remain so even after the reception of a stimulus tending to induce anabolism, or after the cessation of the stimulus that elicited the activity—katabolic inertia or functional momentum. Functional inertia is the power or property which bioplasm has of maintaining its functional status quo for a longer or shorter time according to the function considered; it is that power of continuing to exhibit the particular phenomena it has been exhibiting even after the death of the organism of which it is a constituent.