External Spring Research Articles

Stochastic dynamics of small ensembles of non-processive molecular motors: The parallel cluster model

Non-processive molecular motors have to work together in ensembles in order to generate appreciable levels of force or movement. In skeletal muscle, for example, hundreds of myosin II molecules cooperate in thick filaments. In non-muscle cells, by contrast, small groups with few tens of non-muscle myosin II motors contribute to essential cellular processes such as transport, shape changes, or mechanosensing. Here we introduce a detailed and analytically tractable model for this important situation. Using a three-state crossbridge model for the myosin II motor cycle and exploiting the assumptions of fast power stroke kinetics and equal load sharing between motors in equivalent states, we reduce the stochastic reaction network to a one-step master equation for the binding and unbinding dynamics (parallel cluster model) and derive the rules for ensemble movement. We find that for constant external load, ensemble dynamics is strongly shaped by the catch bond character of myosin II, which leads to an increase of the fraction of bound motors under load and thus to firm attachment even for small ensembles. This adaptation to load results in a concave force-velocity relation described by a Hill relation. For external load provided by a linear spring, myosin II ensembles dynamically adjust themselves towards an isometric state with constant average position and load. The dynamics of the ensembles is now determined mainly by the distribution of motors over the different kinds of bound states. For increasing stiffness of the external spring, there is a sharp transition beyond which myosin II can no longer perform the power stroke. Slow unbinding from the pre-power-stroke state protects the ensembles against detachment.

The Repeatability and Reproducibility of the BioRID IIg in a Repeatable Laboratory Seat Based on a Production Car Seat

Objective: The United Nations Economic Commission for Europe Informal Group on GTR No. 7 Phase 2 are working to define a build level for the BioRID II rear impact (whiplash) crash test dummy that ensures repeatable and reproducible performance in a test procedure that has been proposed for future legislation. This includes the specification of dummy hardware, as well as the development of comprehensive certification procedures for the dummy. This study evaluated whether the dummy build level and certification procedures deliver the desired level of repeatability and reproducibility. Methods: A custom-designed laboratory seat was made using the seat base, back, and head restraint from a production car seat to ensure a representative interface with the dummy. The seat back was reinforced for use in multiple tests and the recliner mechanism was replaced by an external spring–damper mechanism. A total of 65 tests were performed with 6 BioRID IIg dummies using the draft GTR No.7 sled pulse and seating procedure. All dummies were subject to the build, maintenance, and certification procedures defined by the Informal Group. Results: The test condition was highly repeatable, with a very repeatable pulse, a well-controlled seat back response, and minimal observed degradation of seat foams. The results showed qualitatively reasonable repeatability and reproducibility for the upper torso and head accelerations, as well as for T1 Fx and upper neck Fx . However, reproducibility was not acceptable for T1 and upper neck Fz or for T1 and upper neck My . The Informal Group has not selected injury or seat assessment criteria for use with BioRID II, so it is not known whether these channels would be used in the regulation. However, the ramping-up behavior of the dummy showed poor reproducibility, which would be expected to affect the reproducibility of dummy measurements in general. Pelvis and spine characteristics were found to significantly influence the dummy measurements for which poor reproducibility was observed. It was also observed that the primary neck response in these tests was flexion, not extension. This correlates well with recent findings from Japan and the United States showing a correlation between neck flexion and injury in accident replication simulations and postmortem human subjects (PMHS) studies, respectively. Conclusions: The present certification tests may not adequately control front cervical spine bumper characteristics, which are important for neck flexion response. The certification sled test also does not include the pelvis and so cannot be used to control pelvis response and does not substantially load the lumbar bumpers and so does not control these parts of the dummy. The stiffness of all spine bumpers and of the pelvis flesh should be much more tightly controlled. It is recommended that a method for certifying the front cervical bumpers should be developed. Recommendations are also made for tighter tolerance on the input parameters for the existing certification tests.

Design of a Flexible Imaging Probe for Robotics Surgery

Minimally invasive surgery assisted by robots has shown higher efficiency and precision. In spite of the good performance of the state of the art surgery robotics systems, the size and number of external incisions required by instruments should be reduced to lower the scarring and incisional pain experienced by the patient. Other important improvement derived from the use of smaller incisions is the diminishment of time required for recovery. This research develops a flexible scope of small diameter driven by segmented multiple actuators to produce a deflection of the imaging probe at its distal end providing better visualization than the current rigid cameras. The research is conducted in cooperation with the Biorobotics Laboratory at the University of Washington USA, where our scope will be incorporated to Raven, a 7-DOF cable-actuated surgical robot. The flexible scope is composed of three segments as illustrated in Figure 1, where it is possible to see that the device contains a ring of cables enclosed externally and internally by two different springs and a semi rigid covering. The main mechanism of bending is the compression and extension of the external spring at the distal end. The change of length in this spring is controlled by an active system that combines pulling and releasing actions through the ring of cables. The device has advantages in its simplicity of actuation and the high elasticity and flexibility at the distal end. In the current state of the project, a testing system is under construction.

Mechanical Properties Analysis on Elongation Type of Pneumatic Artificial Muscles

This paper developed a novel elongation type of Pneumatic Artificial Muscle (PAM), which is mainly composed of the expandable internal rubber tube surrounded by the external cylindrical helical spring and the two ends are closed. The PAM is not only the actuator of the flexible joint but also the core components to make up of the flexible joint. Therefore, the mechanical properties of the PAM directly influence the performance of the flexible joint. A mathematical model on the axial deformation and bending stiffness of elongation type of PAM was built applying theoretical analysis and experimental research methods. The results show that the axial deformation of PAM and the air pressure supplying to the PAM are nonlinearly related due to the generic nonlinear of deformation of the rubber tube; the bending angle of the PAM is proportional to moment; Similarly, the bending angle of the PAM is also proportional to its length. Furthermore, it indicates that the air pressure indirectly affects the bending stiffness of PAM as the air pressure directly influences the elongation of PAM. Finally, this paper provides a powerful framework for the dynamic analysis and motion accuracy control of the flexible joint or the robot which is composed by the artificial muscles.

Mechanics of pressure-adaptive honeycomb and its application to wing morphing**This paper was originally presented at the 2010 ASME SMASIS conference, as paper‘SMASIS 2010-3634’. Despite the substantial changes that have been made to the paper,there are still various figures and text stemming from the original.

Current, highly active classes of adaptive materials have been considered for use in manydifferent aerospace applications. From adaptive flight control surfaces to wingsurfaces, shape-memory alloy (SMA), piezoelectric and electrorheological fluids aremaking their way into wings, stabilizers and rotor blades. Despite the benefitswhich can be seen in many classes of aircraft, some profound challenges are everpresent, including low power and energy density, high power consumption, highdevelopment and installation costs and outright programmatic blockages due toa lack of a materials certification database on FAR 23/25 and 27/29 certifiedaircraft. Three years ago, a class of adaptive structure was developed to skirtthese daunting challenges. This pressure-adaptive honeycomb (PAH) is capable ofextremely high performance and is FAA/EASA certifiable because it employs wellcharacterized materials arranged in ways that lend a high level of adaptivityto the structure. This study is centered on laying out the mechanics, analyticalmodels and experimental test data describing this new form of adaptive material. Adirectionally biased PAH system using an external (spring) force acting on the PAHbending structure was examined. The paper discusses the mechanics of pressureadaptive honeycomb and describes a simple reduced order model that can beused to simplify the geometric model in a finite element environment. The modelassumes that a variable stiffness honeycomb results in an overall deformation of thehoneycomb. Strains in excess of 50% can be generated through this mechanism withoutencountering local material (yield) limits. It was also shown that the energy density ofpressure-adaptive honeycomb is akin to that of shape-memory alloy, while exhibitingstrains that are an order of magnitude greater with an energy efficiency close to100%. Excellent correlation between theory and experiment is demonstrated in anumber of tests. A proof-of-concept wing section test was conducted on a 12%thick wing section representative of a modern commercial aircraft winglet orflight control surface with a 35% PAH trailing edge. It was shown that cambervariations in excess of 5% can be generated by a pressure differential of 40 kPa.Results of subsequent wind tunnel test show an increase in lift coefficient of 0.3 at23 m s − 1 through an angleof attack from − 6° to + 20°.

Does the personal lift-assist device affect the local dynamic stability of the spine during lifting?

The personal lift-assist device (PLAD) is an on-body ergonomic aid that reduces low back physical demands through the restorative moment of an external spring element, which possesses a mechanical advantage over the erector spinae. Although the PLAD has proven effective at reducing low back muscular demand, spinal moments, and localized muscular fatigue during laboratory and industrial tasks, the effects of the device on the neuromuscular control of spinal stability during lifting have yet to be assessed. Thirty healthy subjects (15M, 15F) performed repetitive lifting for three minutes, at a rate of 10 lifts per minute, with and without the PLAD. Maximum finite-time Lyapunov exponents, representing short-term ( λ max-s) and long-term ( λ max-l) divergence were calculated from the measured trunk kinematics to estimate the local dynamic stability of the lumbar spine. Using a mixed-design repeated-measures ANOVA, it was determined that wearing the PLAD did not significantly change λ max-s ( μ NP=0.335, μ P=0.321, p=0.225), but did significantly reduce λ max-l ( μ NP=0.0024, μ P=−0.0011, p=0.014, η 2=0.197). There were no between-subject effects of sex, or significant interactions ( p>0.720). The present results indicated that λ max-s was not statistically different between the device conditions, but that the PLAD significantly reduced λ max-l to a negative (stable) value. This shows that subjects’ neuromuscular systems were able to respond to local perturbations more effectively when wearing the device, reflecting a more stable control of spinal movements. These findings are important when recommending the PLAD for long-term industrial or clinical use.

S1104-3-1 外部弾性・減衰要素の非線形性がヘリングボーン動圧気体軸受の安定性に及ぼす影響(トライボロジーの基礎と応用3)

It is well known that viscoelastic supports is an efficient way to improve the stability of journal bearings. However, inappropriate bearing supports decrease the stability threshold. A theory with considering the nonlinearity of external spring and damping elements can predict well whether the stability of bearing systems improve or not. The present paper describes the effect of the frequency dependence of the bearing support elements on the stability of herringbone grooved aerodynamic journal bearings. Several types of nonlinear properties were expressed by giving values to the unknown coefficients in an empirical fomula. Results show that too large spring coefficients in high frequency regions deactivate the advantage of the viscoelastic supports. Additionally, the stability threshold increases as the nonlinear ratio of the damping increases.

Dynamic Topology Optimization of Compliant Mechanisms and Piezoceramic Actuators

A topology optimization method is developed to design a piezoelectric ceramic actuator together with a compliant mechanism coupling structure for dynamic applications. The objective is to maximize the mechanical efficiency with a constraint on the capacitance of the piezoceramic actuator. Examples are presented to demonstrate the effect of considering dynamic behavior compared to static behavior and the effect of sizing the piezoceramic actuator on the optimal topology and the capacitance of the actuator element. Comparison studies are also presented to illustrate the effect of damping, external spring stiffness, and driving frequency. The optimal topology of the compliant mechanism is shown to be dependent on the driving frequency, the external spring stiffness, and whether the piezoelectric actuator element is considered design or nondesign. At high driving frequencies, it was found that the dynamically optimized structure is very near resonance.

Discussion of “Buckling of Columns with Intermediate Elastic Restraint” by C. M. Wang and I. M. Nazmul

This paper presents the classical flexural buckling solution to an ideal prismatic column with an intermediate lateral elastic restraint and subjected to a concentrated axial load at the top end only. The end conditions are ideal ~clamped, hinged, and free!. The discussor finds this paper useful, particularly for testing a matrix solution proposed by the writer that appears much more general and simpler to program. Consider the stepped column that connects points A and B ~Fig. 1!. This consists of two column segments, AC and CB, with semirigid connections at ends A and B and at the intermediate joint C. It is assumed that ~1! both column segments, AC and CB, are made of homogeneous linear elastic materials with mechanical and geometric properties Et I t At ht and Eb I b Ab hb ~where E5elastic modulus; I5moment of inertia; A5cross-sectional area; and h5span). The subindices t and b indicate the top and bottom column segments, respectively; ~2! the centroidal axis of each segment is a straight line with their centroidal axes lineup; ~3! the column is subject simultaneously to axial loading Pa and transverse load Va at point A, to concentrated loads Pc and Vc , and bending moment Mc at the intermediate joint C; and ~4! the lateral sways of the column are partially inhibited by linear springs Sa and Sc located at A and C, respectively, and by an external rotational spring of magnitude SQ at joint C. The rotational fixity factors at ends A and B and the intermediate joint C ~of column segment AC! are assumed to be r a , r b , and r c , respectively. Further details of this model are given by Aristizabal-Ochoa ~1997b!. A general solution to the second-order analysis and buckling load of the column in Fig. 1 is as follows:

Discussion of “Effect of Base Fixity on Buckling of Heavy Column with End Load” by C. Y. Wang

This paper presents the classical flexural buckling solution to an ideal prismatic column with an intermediate lateral elastic restraint and subjected to a concentrated axial load at the top end only. The end conditions are ideal ~clamped, hinged, and free!. The discussor finds this paper useful, particularly for testing a matrix solution proposed by the writer that appears much more general and simpler to program. Consider the stepped column that connects points A and B ~Fig. 1!. This consists of two column segments, AC and CB, with semirigid connections at ends A and B and at the intermediate joint C. It is assumed that ~1! both column segments, AC and CB, are made of homogeneous linear elastic materials with mechanical and geometric properties Et It At ht and Eb Ib Ab hb ~where E5elastic modulus; I5moment of inertia; A5cross-sectional area; and h5span). The subindices t and b indicate the top and bottom column segments, respectively; ~2! the centroidal axis of each segment is a straight line with their centroidal axes lineup; ~3! the column is subject simultaneously to axial loading Pa and transverse load Va at point A, to concentrated loads Pc and Vc , and bending moment M c at the intermediate joint C; and ~4! the lateral sways of the column are partially inhibited by linear springs Sa and Sc located at A and C, respectively, and by an external rotational spring of magnitude SQ at joint C. The rotational fixity factors at ends A and B and the intermediate joint C ~of column segment AC! are assumed to be ra , rb , and rc , respectively. Further details of this model are given by Aristizabal-Ochoa ~1997b!. A general solution to the second-order analysis and buckling load of the column in Fig. 1 is as follows:

Dynamic external fixation for complex intraarticular phalangeal fractures

Intraarticular phalangeal fractures are difficult to treat. The advantages of using dynamic external fixation devices include distraction of impacted fracture fragments and reduction in joint stiffness by allowing early joint mobilization. Previous reports have concentrated on pilon fractures and dorsal fracture dislocations affecting the proximal interphalangeal joint. We report our experience using a dynamic external spring fixator in the management of 15 patients with a variety of fracture patterns affecting the metacarpophalangeal, proximal interphalangeal and distal interphalangeal joints. In three cases the device spanned two adjacent joints. Long-term follow-up has shown excellent range of joint movement and no major complications. We consider that this device is an effective tool in the management of a range on complex intraarticular phalangeal fractures.

Current Treatments for Primary Injuries of the Flexor and Extensor Tendons

Background: Treatment procedures for injuries of the flexor and extensor tendons have not been principally altered by the introduction of refined surgical techniques, new suture material, or the results of functional post-treatment. However, the treatment procedures have been more accurately defined and are now performed with greater precision. Methods: The concept of decompressing the suture, as described by Kleinert, is based on the principle of reciprocal innervation of agonists and antagonists. Pressure on the suture site is reduced by external dynamic spring splints. Results: Thus, the favourable results of functional post-treatment for injuries of the flexor tendon could be applied to extensor tendon injuries in zones IV–VIII as well. Three hundred and fifty patients have been treated by this suture technique and a dynamic splint, and were then followed. With the exception of three re-ruptures in the first ray, very good or good results were achieved. However, injuries in zones I–III are still mainly treated by static procedures. Three hundred and four flexor tendon injuries were treated with a primary flexor tendon suture. Seven per cent of our patients achieved a very good or good result, 3 % a satisfactory result. The re-rupture rate was less than 0.7 %, being below the rates reported in the published literature. Conclusions: A dynamic cast following surgery for recent extensor and flexor tendon injuries, in conjunction with an exact surgical technique, are essential for a smooth, early and good functional outcome of the treatment. The cast must provide complete decompression of the sutured tendon.

A phenomenology of boundary lubrication: the lumped junction model

We propose a phenomenological model of boundary lubricated junctions consisting of a few layers of small molecules which describes the rheological properties of these sytems both in the static, frozen, and sliding, molten, states as well as the dynamical transition between them. Two dynamical regimes can be distinguished, according to the level of internal damping of the junction, which depends on its thickness and on the normal load. In the overdamped regime, under driving at constant velocity v through an external spring, the motion evolves continuously from “atomic stick-slip” to modulated sliding. Underdamped systems exhibit, under given external stress, a range of dynamic bistability where the sheared static state coexists with a steadily sliding one. The frictional dynamics under shear driving is analyzed in detail, it provides a complete account of the qualitative dynamical scenarios observed by Israelashvili et al., and yields semiquantitative agreement with experimental data. A few complementary experimental tests of the model are suggested.

Continuum Model for Ion Gating in Cochlear Hair Cells

The details of ion flow in cells are important for the macro mechanical response of sensory organs, as in the inner ear of vertebrates. A continuum model for the flow of an ionized fluid through a pore in an elastic wall is considered. With this, the electro-mechanical behavior is readily computed. An interesting result is that two equilibria exist for the flow through a pore with a soft elastic entrance region. At one equilibrium point, the entrance opening is more restricted and the corresponding ion flow rate is much lower. Thus it appears that the tendency of ion channels to pop from an open to a closed state may be a consequence of basic fluid-elastic interaction. With the simple continuum model, various effects can be explored. One is the presence of an external spring force, corresponding to the force of the tip fiber between stereocilia. Another is the effect of an adjacent membrane and pore. The input physical parameters are reasonable and the results for flow rate are consistent with experimental measurements.

Power and Energy Characteristics of Solid-State Induced-Strain Actuators for Static and Dynamic Applications

The power and energy characteristics of solid-state induced-strain actuators are studied. Piezoelectric (PZT), electrostrictive (PMN) and magnetostrictive (TERFENOL) actuators are considered. The principles and internal construction of solid-state induced-strain actuators are briefly reviewed. Typical performance curves are presented and discussed. The basic equations of piezoelectricity and piezomagnetism are presented. A linearization procedure is adopted whereby apparent values for the piezoelectric and piezomagnetic constants are derived from full-stroke ven-dor data using the secant approximation principle. Values for the apparent electromagnetic conversion coefficient for full-stroke operation are obtained. The static analysis considers the one-directional operation of the induced strain actuators against an external spring load. It is found that the maximum energy output from the induced-strain actuator is obtained when the internal and external stiffnesses are matched. Expressions for the maximum energy output, and the energy densities per unit volume, mass, and cost are derived. Numerical examples and comparative charts are given for a number of piezoelectric, electrostrictive and magnetostrictive actuators. The influence of casing and pre-stress mechanism on the overall energy density values is also highlighted. The electromechanical conversion efficiency is studied, and two separate expressions are derived, one for the best efficiency, and another for the conversion efficiency at the stiffness match point. The dynamic analysis considers the cyclic motion of the induced-strain actuators about a midpoint bias position. The dynamic full-stroke is found approximately one-half the static full-stroke. The correspondingly maximum output energy and energy densities under dynamic conditions are calculated. The dynamic energy conversion efficiency is studied and the influence of bias voltage or current is included. Numerical examples and comparative charts are given for a number of piezoelectric, electrostrictive and magnetostrictive actuators operating under dynamic conditions.

A spring force formulation for elastically deformable models

Continuous deformable models are generally represented using a grid of control points. The elastic properties are then modeled using the interactions between these points. The formulations based on elasticity theory express these interactions using stiffness matrices. These matrices store the elastic properties of the models and they should be evolved in time according to changing elastic properties of the models. However, forming the stiffness matrices at any step of an animation is very difficult and sometimes the differential equations that should be solved to produce animation become ill-conditioned. Instead of modeling the elasticities using stiffness matrices, the interactions between model points could be expressed in terms of external spring forces. In this paper, a spring force fomulation for animating elastically deformable models is presented. In this formulation, elastic properties of the materials are represented as external spring forces as opposed to forming complicated stiffness matrices.

Resonance Tuning in Rhythmic Arm Movements

The hypothesis was tested that the preferred frequency of rhythmic movement corresponds to the resonant frequency of the muscle-limb system, as proposed by the hybrid spring-pendulum model (Kugler Turvey, 1987). In contrast to previous studies, the resonant frequency and stiffness of the system were estimated independently, which permitted quantitative predictions of the preferred frequency to be made. Human subjects (N = 5) were asked to oscillate their forearms in the vertical plane at their preferred frequency under conditions of added mass and external spring loading. Subjects also oscillated their arms at frequencies below and above the preferred frequency, which enabled the investigators to estimate the resonant frequency and stiffness of the elbow joint by using the phase transfer method (Viviani, Soechting, Terzuolo, 1976). The preferred frequency corresponded to the resonant frequency of the muscle-limb system under each condition, as predicted. The oscillation amplitude varied inversely with the preferred frequency, which was also predicted. Finally, the internal joint stiffness was modulated so that it matched the impedance of the external springs but was unaffected by added mass. The results are consistent with an autonomous oscillator model that incorporates proprioception about the dynamics of the periphery.

Modeling, Simulation, and Modal Analysis of a Hydraulic Valve Lifter With Oil Compressibility Effects

A two-degree-of-freedom (2-DOF), analytical model of a hydraulic valve lifter is derived. Special features of the model include the effects of bulk oil compressibility, multimode behavior due to plunger check valve modeling, and provision for the inclusion of third and fourth body displacements to aid in the use of the model in extended, multi-DOF systems. It is shown that motion of the lifter plunger and body must satisfy a coupled system of third-order, nonlinear differential equations of motion. It is also shown that the special cases of zero oil compressibility and/or 1-DOF motion of lifter plunger can be obtained from the general third-order equations. For the case of zero oil compressibility, using Newtonian fluid assumptions, the equations of motion are shown to reduce to a system of second-order, linear differential equations. The differential equations are numerically integrated in five scenarios designed to test various aspects of the model. A modal analysis of the 2-DOF, compressible model with an external contact spring is performed and is shown to be in excellent agreement with simulation results.

緩衝能の測定に関する研究 : 着地動作時の床反力波形の分析

Multicomponent forces were exerted and recorded electrically upon the measuring platform, on which subjects landed from standing position. These experiments were designed in four measuring conditions of landing motion and were aimed to obtain data of shock-absorbability in these activities. Experimental conditions were (1) landing posture-soft or hard motion, (2) attaching load to the body- 0, 5 or 10kg, (3) height of standing at jumping-70 or 110cm and (4) coefficient of attaching spring on the platform - 0 or 1.05kg/mm. Analyzing these recording data of multicomponent forces by the control theory, landing motions were divided into the absorbable and the non-absorbable motions for external disturbances and function of absorbability was measured and estimated quantitatively. That absorbability was assumed by the following value α=Hf/At (Hf : amplitude of max. force, At : absorbed time). When absorbable motions were shown in these landing experiments, the vertical force was composed of one phase of force peak, but on the other hand when non-absorbable motions were revealed that peak of force was made of two phase and also fore-backward and left-rightward forces were deviated from the center line of stability. Characteristics of the most absorbable landing motion were shown on the constant value of multicomponent forces in spite of many disturbances exerted from external load, height and spring. Then the length of absorbed time in absorbable force waves was marked in the oscillation of multicomponent forces and large angle of declining curves were characterized remarkedly.