Rigid-body Behavior Research Articles

Geometrical analysis of the V–Y advancement flap applied to a keystone flap

The V-Y advancement flap and, more recently, the keystone flap are commonly used to cover skin defects. Both flaps allow for primary closure after advancement by substituting the initial defect for a narrower defect distributed over a greater length. The first objective of this study was to develop a geometrical analysis of the V-Y advancement flap. The second objective was to explain the benefit of using the keystone flap compared to a single V-Y advancement flap. A geometrical analysis is proposed using a two-dimensional analysis in which the flaps are assumed to have a rigid-body behaviour. First, in the case of the V-Y advancement flap, a trigonometric relationship is defined between the distance of closure before and after advancement, thus implying the value of the flap's apex angle. Second, by considering the keystone flap as the association of three V-Y advancement flaps, the trigonometric relationship is applied to the keystone flap. In the case of the V-Y advancement flap, the optimal apex angles are between 20° and 60°. At less than 20°, the length of the flap increases in an exaggerated manner. At greater than 60°, the distance of closure, particularly at the apex of the flap where a corner stitch is performed, is greater than the distance of closure of the initial defect. In the case of the keystone flap, the width of the final defect around the flap is clearly smaller and more regular compared to the final defect around a single V-Y advancement flap. The geometrical analysis of the V-Y advancement flap in our description illustrates the major benefit of the keystone flap over a single V-Y advancement flap.

Analysis of a kinetic multi-segment foot model. Part I: Model repeatability and kinematic validity

Kinematic multi-segment foot models are still evolving, but have seen increased use in clinical and research settings. The addition of kinetics may increase knowledge of foot and ankle function as well as influence multi-segment foot model evolution; however, previous kinetic models are too complex for clinical use. In this study we present a three-segment kinetic foot model and thorough evaluation of model performance during normal gait. In this first of two companion papers, model reference frames and joint centers are analyzed for repeatability, joint translations are measured, segment rigidity characterized, and sample joint angles presented. Within-tester and between-tester repeatability were first assessed using 10 healthy pediatric participants, while kinematic parameters were subsequently measured on 17 additional healthy pediatric participants. Repeatability errors were generally low for all sagittal plane measures as well as transverse plane Hindfoot and Forefoot segments (median<3°), while the least repeatable orientations were the Hindfoot coronal plane and Hallux transverse plane. Joint translations were generally less than 2mm in any one direction, while segment rigidity analysis suggested rigid body behavior for the Shank and Hindfoot, with the Forefoot violating the rigid body assumptions in terminal stance/pre-swing. Joint excursions were consistent with previously published studies.

Attitude simulation software to support Brazilian space missions

Cost reduction on system tests with hardware in the loop during qualification phase of the onboard attitude control software imply in increasingly simulation realism. Attitude simulation software not only has to mimic the dynamical behavior of the spacecraft, but also shall be easily configurable, to adapt to different orbit, attitude pointing requirements, environment disturbances, sensors, actuators, and to run in real-time among other minor requirements. As the requirements for accuracy and stability for attitude pointing has increased in many modern missions, so do the complexity of the simulation algorithms and necessity for dynamical realism. Rigid body dynamics can be considered excessively simple to model a satellite with several reaction wheels, non-rigid structures, unbalanced solar arrays, fuel and liquid sloshing, not to mention crew motion and vehicle docking. This work presents the efforts being carried out to fulfill the requirements of the Brazilian space missions, nominally Multi Mission Platform, with a simulation environment capable to accomplish from early definition and mission analysis phase up to acceptance tests of the attitude control software. Development is being conducted in order to achieve a high degree of realism and range of applicability of the simulation software, compatible with the expected cost reduction of the simulation hardware (ordinary PCs). The kinematics and dynamic models to support AOCS (Attitude and Orbit Control Subsystem) simulation and testing with or without hardware-in-the-loop for Brazilian space missions are presented. Normally the dynamic equations are expressed in angular momentum components, due to the high complexity of these equations when derived in terms of the angular velocity. This, of course, is particularly important in satellites composed by several articulated rigid bodies as solar panels, robotic arms, space booms, deployable antennas, etc. Nevertheless, the inverse of the inertia matrix shall be calculated on the run, since it varies in time. This can be somewhat slow, mainly considering the high degree of freedom in dynamics of satellites with articulated panels and reaction wheels. In this case a more complex but fast set of equations in terms of the angular velocity is the best choice. This work describes the attitude dynamic equations expressed in angular velocities for satellites with appendages (solar panels, telescopes, directional antennas, etc.) and reaction wheels. They can be easily extended, however, to include nutation dampers and robotic arms. As usual, this formulation requires the knowledge of the acting torque in the connection joint, which is not always understood, modeled or known. So the dynamic model presented in this work uses the angular acceleration instead of the torque at the joint, which simplifies and reduces the order of the differential equations. Simulation results are presented, emphasizing the difference between the behavior of rigid body and articulated rigid bodies.

Rocking Motion of Structures under Earthquakes (Overturning of 2-DOF System)

In recent years, huge earthquakes happen, for example, The South Hyogo prefecture Earthquake in 1995, The Mid Niigata Prefecture Earthquake in 2004, The Iwate-Miyagi Nairiku Earthquake in 2008. In The Niigataken Chuetsu-oki Earthquake in 2007, hundreds of drums fell down and water spilled out. A lot of studies about rocking behavior of rigid body had been performed from 1960's. However, these studies were only for a specific condition of the structure size or input vibration characteristics. Therefore, generalizes fall condition for earthquake is required. This paper deals with the analytical and the experimental study of the rocking vibration of 1-DOF rocking system, 2-DOF vibration-rocking system and 2-DOF rocking system under earthquakes. In this study, the equation of motion for each rocking systems are developed. The numerical model of 2-DOF rocking system is evaluated by free rocking experiment. In this paper, “Overturning Map” which can distinguish whether structures falls or not is proposed. The overturning map of each rocking systems excited by the artificial earthquake wave calculated from the design spectrum is shown. As the result, overturning condition of structures is clarified.

ChemInform Abstract: Structure of Hexaaquanickel(II) Bromate

[Ni(H2O)6](BrO3)2, Mr = 422.60, cubic, Pa3, a = 10.2987 (6) A, V = 1092.3 (2) A3, Z = 4, F(000) = 824, Dx = 2.57 g cm-3, lambda(Mo K alpha) = 0.71073 A, mu = 90.79 cm-1, T = 296 K, R = 0.024 for 360 unique reflections having I greater than sigma I. The single type of nickel ion is coordinated by six water-molecule O atoms, each at an observed distance of 2.061 (2) A, in an almost regular octahedral array. The single type of bromate ion has an observed Br--O bond length of 1.655 (2) A and O--Br--O bond angle 104.25 (9) degrees. Both the nickel-oxygen complex and the bromate ion were found to manifest rigid-body behavior. The Ni--O distance corrected for rigid-body motion is 2.065 A, while the corrected Br--O bond length is 1.663 A. Location and refinement of the two inequivalent H atoms permitted a detailed analysis of the hydrogen bonding, which occurs principally between the oxygen octahedron and the bromate groups. This structure is isomorphic to the structures of hexaaquanickel(II) chlorate and hexaaquacobalt(II) bromate which have been reported recently from this laboratory.

ChemInform Abstract: Structure of Hexaaquacopper(II) Bromate.

[Cu(H2O)6](BrO3)2, Mr = 427.44, cubic, Pa3, a = 10.3240 (6) A, V = 1100.38 (4) A3, Z = 4, Dx = 2.580 g cm-3, lambda (Mo K alpha) = 0.71073 A, mu = 92.32 cm-1, F(000) = 828, T = 296 K, R = 0.038 for 336 unique reflections having I greater than sigma I. The single type of copper ion (site symmetry 3) is coordinated by six water-molecule O atoms, each at an observed distance of 2.079 (4) A, in an array which is virtually regular octahedral, the nominal 90 degree angles measuring 89.95 (15) and 90.05 (15) degrees. Thus, this is not a typical CuII complex in which (consistent with a static Jahn-Teller effect) a distorted octahedral array displays '(2 + 2 + 2)' coordination; rather, it is the sixth strict example of a CuII static structure inconsistent with the Jahn-Teller theorem. The presence of a dynamic Jahn-Teller effect is supported by the data. The single type of bromate ion has an observed Br-O bond length 1.649 (3) A and O-Br-O bond angle 104.17 (15) degrees. The bromate ion was found to manifest rigid-body behavior but, consistent with a dynamic Jahn-Teller effect, the copper-oxygen complex did not. The Br-O bond length corrected for rigid-body motion is 1.663 A. Refinement of the positional parameters of the two inequivalent H atoms permitted a detailed analysis of hydrogen bonding, which occurs principally between the oxygen octahedra and the bromate groups.(ABSTRACT TRUNCATED AT 250 WORDS)

Multi Agent/Object Simulation in Human Swimming

In human swimming, there are many situations in which the target of the analysis is not only the swimmer but also other swimmers or other equipment, such as synchronized swimming by multiple swimmers, swimming with fins, and so on. The objective of this study was to extend the swimming human simulation model SWUM so that it could handle the dynamic behavior of multiple rigid bodies and could freely describe the mechanical interactions among the rigid bodies. In this paper, the outline of SWUM is described first. The extension to the multi agent/object simulation and its implementation are explained next. Finally, its validity and usefulness are examined by discussing three examples of analysis. The first example was synchronized swimming by three swimmers. From the simulation results, it was found that the three swimmers gradually gathered, and finally the swimmers' upper limbs stably formed a hexagon. The second example was monofin swimming. The monofin was divided into five rigid plates in this simulation in order to represent its elastic deformation. From the simulation results, it was found that the swimmer accelerated at the moments of downward and upward kicks. The third example was the shooting motion in water polo. From the simulation results, it was found that the ball was smoothly released and flew in an appropriate direction. Since reasonable results were obtained in these examples of analysis, the validity and usefulness of the extension were confirmed.

Transient thermal regimes in the Sierra Nevada and Baja California extinct outer arcs following the cessation of Farallon subduction

We examine the thermal relaxation of the Sierra Nevada and Baja California extinct outer arc blocks following the progressive cessation of Farallon subduction under western North America beginning at ∼30 Ma. Being parts of the same outer arc until the inland jump of the San Andreas transform fault at ∼5 Ma, these two regions show many similarities in their geology, geomorphology, rigid body behavior, and their relatively low seismicity. In the thermal model, we combine results of different geophysical and geophysical studies to constrain the thermal state and geometry of the outer arcs before the cessation of subduction and then model the postsubduction temperature responses in these regions using the results of the tectonic reconstructions. A well‐constrained regional thermal model of these blocks using the results of many earlier studies in these regions confirms that the present low heat flow values in these regions are the remnants of the very cold outer arc thermal regime of the subduction zone even as long as 30 Ma after cessation of subduction. Thus the entire Pacific boundary of the North American plate is still in a transient thermal state. The calculated low lithospheric temperatures in the Sierra Nevada and Peninsular blocks correlate very well with their rigid body behavior obtained from geodetic studies, and seismogenic layer thicknesses obtained from seismological studies. This is in contrast with the fact that both regions are surrounded by intense deformation associated with the western North America intraplate and extraplate motions. These low‐temperature islands play important roles in the present interaction of the North American and Pacific plates and contribute to the broad deformation of the transform boundary. The thermal relaxation of the extinct outer arcs includes both vertical heating from the underlying asthenosphere and the lateral heating from the extinct back arc (Basin and Range), which has remained as a high heat flow region after the cessation of the subduction. We suggest that the significant lateral heat transfer from the Basin and Range in the Sierra Nevada (and from the Gulf of California spreading center in the Peninsular block since ∼5 Ma) may be the main driving mechanism of the postsubduction volcanism/magmatism along the extinct volcanic arc and the recent tilted uplift of the Sierra Nevada block. The low lithospheric temperatures in Sierra Nevada region may also explain the observation of the high seismic velocities in the mantle beneath the southern Sierra Nevada where the downwelling of the mantle lithosphere proposed.

Modeling vibration isolator performance with hybrid finite element/statistical energy (FE‐SEA) analysis

Vibration isolators are often modeled as simple single degree of freedom systems. Such an approach is often adequate for characterizing the low frequency performance of a vibration isolator (assuming that the effective spring stiffness and damping loss factor of the isolator can be obtained). However, at mid to high frequencies, two problems are often encountered. The first is that the impedance of the structures connected to the isolator become important (assumptions of rigid body behavior of the components of interest are generally not valid). The second is that the internal dynamic behavior of the isolator becomes important (internal resonances of the isolator degrade the isolation performance). This paper describes the development of a hybrid FE‐SEA model of an in situ vibration isolator that addresses these problems. The key factors affecting the mid and high frequency performance of an isolator are investigated.

Behavior Of Rigid Bodies In Buildings

The behavior of rigid bodies with different shape ratios, located in some levels of buildings of the valley of Mexico and Acapulco, subjected to events of near and distant sources is modeled step by step. A fast estimation of the movement in the base of the content in a floor level of the building comes through a simplified model whose accuracy was proven in a parallel work to this (Arredondo et al [1]). Maps for toppling of contents appear as well as expressions to determine the amplification of the movement in a story of the building.

The resonance frequencies and mode shapes of dental implants: Rigid body behaviour versus bending behaviour. A numerical approach

The purpose of this study was to evaluate the modal behaviour of the bone–implant–transducer (Osstell) system by means of finite element analyses. The influence of different parameters was determined: (1) the type of implant anchorage being trabecular, cortical, uni-cortical, or bi-cortical, (2) the implant diameter, (3) the length of the implant embedded in the bone, and (4) the bone stiffness. The type of anchorage determines the resulting modal behaviour of the implant–transducer system. A rigid body behaviour was found for a uni-cortical anchoring and for a homogeneous anchoring with low bone stiffness (⩽1000 MPa), whereas a bending behaviour was found for a homogeneous anchoring with a high bone stiffness (⩾5000 MPa) and for a bi-cortical anchorage. The implant dimensions influence the values for the resonance frequencies. Generally, an increase in implant diameter or implant length (in bone) results in higher resonance frequencies. This study also showed that resonance frequencies in case of rigid body behaviour of the implant–transducer system are more sensitive to changes in bone stiffness than resonance frequencies in case of bending behaviour. In conclusion, it seems that the Osstell transducer is suited for the follow-up in time of the stability of an implant, but not for the quantitative comparison of the stability of implants.

Experimental and Analytical Study of Free Lift-Off Motion Induced Slip Behavior of Rectangular Rigid Bodies

The mechanism of the slip of a rectangular rigid body during free lift-off motion is investigated analytically and experimentally. Equations of motion of slipping rectangular rigid body during free lift-off motion are derived by the variational approach. The time histories of both slip and lift-off motions are numerically computed and compared with corresponding experimental results to discuss the analytical accuracy; given an initial enforced lift-off angle to the rectangular rigid body and then gently released. The mechanical energy balance of simultaneous slip and lift-off motions is clarified to explain the considerable reduction of lift-off angle due to the slip.

On the rigid body behavior of foreign exchange markets

Abstract We propose a method to characterize the behavior of a foreign exchange market, introducing a mapping from the N assets to a liquid of N particles, which is studied by means of its empirical kinetic properties. We present the resulting rigid body behavior investigating daily foreign exchange market data for USD, DEM and YEN in the period of time from 9 April 1973 to 15 November 1997.

Behavior of a pulsating rigid body in a viscous fluid in the presence of gravity

The paper considers the motion of a rigid sphere due to specified pulsations of the sphere and gravity in a viscous fluid which is at rest away from the sphere.

EFFECTS OF FILTERING THE ANGULAR MOTION OF THE CRANKSHAFT ON THE ESTIMATION OF THE INSTANTANEOUS ENGINE FRICTION TORQUE

The focus of this study is to investigate the effects of filtering the actual angular displacement, velocity and acceleration of the crankshaft on the computation of the instantaneous engine friction torque. These effects are isolated from those of measurement errors and/or noise by relying on a detailed model of the crank-slider mechanism to generate the rigid and flexible motions of the piston/connecting-rod/crankshaft mechanism along with the engine friction torque. The (P−ω) method is used herein to estimate the instantaneous engine friction torque based on the actual and the filtered angular displacement, velocity and acceleration of the crankshaft. The digital simulation results have demonstrated that the (P−ω) method cannot produce an acceptable estimation of the instantaneous engine friction torque in spite of filtering the actual angular motion of the crankshaft. It should be mentioned that the low-pass filter is commonly implemented to attenuate the measurement noise and the effects of structural deformations on the measured angular velocity of the crankshaft. However, the ineffectiveness of the low-pass filter stems from the non-linearities of the crank-slider mechanism that induced superharmonic and combination resonance frequencies in the angular displacement, velocity and acceleration of the crankshaft. The filter has severely attenuated some of the superharmonic resonance frequencies, which constitute an important part of the rigid-body behavior of the crankshaft that is needed by the (P−ω) method to accurately predict the engine friction torque. Moreover, the filtered signals would still be contaminated by the combination resonance frequencies that may appear in the low-frequency range commonly assumed to be dominated by the frequency components of the rigid-body motion of the crankshaft.

A Controller for an Impacted Single Flexible Link

A single-mode model of a continuous beam with a payload that has been subjected to an impulsive external impact disturbance is used to illustrate the application of a finite time controller to control the rigid body and elastic vibration behavior of an elastic slewing link. The controller is initially designed in the time and Laplace domains and is then converted to the discrete case in anticipation of implementation. Once in the discrete form, the controller is shown to be stable and its performance is established via simulation results. The controller is found to allow fast accurate repositioning of the end effector after impact and is also found to be robust to variations in impact magnitude and the prescribed set point.

Rigid-Body Dynamics with Friction and Impact

Rigid-body dynamics with unilateral contact is a good approximation for a wide range of everyday phenomena, from the operation of car brakes to walking to rock slides. It is also of vital importance for simulating robots, virtual reality, and realistic animation. However, correctly modeling rigid-body dynamics with friction is difficult due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law. This is particularly crucial for handling situations with large coefficients of friction, which can result in paradoxical results known at least since Painleve [C. R. Acad. Sci. Paris, 121 (1895), pp. 112--115]. This single example has been a counterexample and cause of controversy ever since, and only recently have there been rigorous mathematical results that show the existence of solutions to his example. The new mathematical developments in rigid-body dynamics have come from several sources: sweeping processes and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.-L. Lions in the 1970s, and the use of complementarity problems to formulate frictional contact problems by Lotstedt in the early 1980s. However, it wasn't until much more recently that these tools were finally able to produce rigorous results about rigid-body dynamics with Coulomb friction and impulses.

Tangential Forces between Nontouching Colloidal Particles

By measuring the orientation of colloidal doublets suspended in water under the opposing alignment forces of gravity and electrophoresis, we observed tangential forces between nontouching particles. We found a new phenomenon of time-dependent switching between ``slipping'' (no tangential force) and ``sticking'' (tangential forces producing rigid-body behavior of the doublet) for heterodoublets of silica/polystyrene. Tangential forces between particle surfaces across a fluid gap and their transient nature are important to the dynamics of colloidal suspensions and the evolution of floc morphology.

Measurement of Restitution Behavior of Strings and Rigid Body.

The relationship between restitution behavior of strings and its mechanical properties was measured and discussed. An impact test device that could control the initial tension and impact velocity on speed area of less than 10 m/s was developed for measuring the restitution behavior of hammer and tensioned strings. About this device, influence to the measurement results of mass and materials of the hamnler and slipping on the clamps was examined. Using this device, restitution behavior of tennis strings was measured. A dynamic restitution model considering tensile viscoelasticity of materials was suggested with approximating it by Voigt model. The restitution behavior was simulated by numerical computation. In experimental range for all samples, coefficient of restitution increases with initial tension and decreases with initial velocity, and when the mass of a hammer is small, the coefficient becomes big. The calculation results of the model could show the tendency of experimental results well.

Experimental investigation of the effects of fluid heterogeneity upon the motion of rigid ellipsoidal inclusions during bulk inhomogeneous shortening

An experimental study of the motions of rigid ellipsoidal inclusions within deforming homogeneous and heterogeneous fluid systems indicated that the time behaviour of such objects, measured relative to the experimental apparatus, can vary significantly between the two system types during inhomogeneous time-dependent flow. Initially aligned ellipsoidal inclusions within a deforming homogeneous fluid were rotated in the same sense as an adjacent passive strain marker. Introduction of heterogeneity, by partially enclosing the ellipsoidal inclusions with a less viscous fluid, resulted in three different rigid-body behaviours during deformation. The behaviours observed for initially aligned ellipsoids in the system containing fluid heterogeneities were: (1) opposite-sense rotation to that of the strain marker; (2) negligible rotation of the objects; and (3) same sense of rotation as that of the strain marker. A computerized, time-based, analysis of the deformation, possible through the incorporation of marker particles into each of the two different deforming systems, revealed similar deformation kinematics for the two experimental types at both the system and sub-system scale. Results of the experiments indicate that significant differences can occur in rigid-body behaviour between apparently similarly deforming homogeneous and heterogeneous systems. The results suggest that fluid flow theory, as derived for rigid-body behaviour in homogeneous fluids, may be unsuitable for the purpose of qualitatively predicting rigid-object behaviour within deforming rock systems that are highly anisotropic at the porphyroblast/porphyroclast scale. This notion is supported by an examination of the assumptions and simplifications upon which the theory relating to rigid-body behaviour in homogeneous fluids was originally based.