Rigid Force Research Articles

Adhesion Energy Measurements in the Presence of Adsorbed Liquid Using a Rigid Surface Force Apparatus

We have measured force vs displacement profiles between hydrophobic silica surfaces at contact in the presence of a liquid meniscus. We show that the recent generalized theory of the adhesive contact by Maugis (J. Colloid Interface Sci.150,243 (1992)) aptly describes the full force curve, yielding accurate values of the adhesion energy. We outline the improvements that one can expect from this technique in the characterization of the contact between solids in the presence of adsorbed liquid.

The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1: Chip geometry analysis and cutting force prediction

The study of machining errors caused by tool deflection in the balkend milling process involves four issues, namely the chip geometry, the cutting force, the tool deflection and the deflection sensitivity of the surface geometry. In this paper, chip geometry and cutting force are investigated. The study on chip geometry includes the undeformed radial chip thickness, the chip engagement surface and the relationship between feed boundary and feed angle. For cutting force prediction, a rigid force model and a flexible force model are developed. Instantaneous cutting forces of a machining experiment for two 2D sculptured surfaces produced by the ball-end milling process are simulated using these force models and are verified by force measurements. This information is used in Part 2 of this paper, together with a tool deflection model and the deflection sensitivity of the surface geometry, to predict the machining errors of the machined sculptured surfaces.

Modeling considerations for in-phase actuation of actuators bonded to shell structures

A closed-form model to represent the in-phase actuation of induced strain actuators bonded to the surface of a circular shell is developed. Because of the inherent shell curvature, the equivalent discrete tangential forces generally used to represent the in-phase actuation of the actuators (such as in pin-force models) are not colinear and result in the application of rigid body forces on the shell. This nonequilibrium state violates the principle of self-equilibrium of fully integrated structures, such as piezoelectrically actuated shells. The solution to this nonequilibrium problem is to apply a uniform transverse pressure over the actuator region to maintain equilibrium. Using this adequate equivalent loading scheme for in-phase actuation, a response model for a circular ring is derived based on shell governing equations. To verify the in-phase actuation response model, finite element analysis is performed. A perfect match between the in-phase actuation response model and the finite elements results, when the actuator mass and stiffness are neglected, validates the derived analytical model. If the self-equilibrium is not maintained (point-force model), the predicted deformed shape is completely different from the actual shell response to in-phase actuation. Thus, by simply applying a uniform transverse pressure along with the discrete tangential forces to maintain the self-equilibrium of the shell, the shell response can be modeled accurately.

The effect of tendon on muscle force in dynamic isometric contractions: A simulation study

Recently, Baratta and Solomonow J. Biomechanics 24, 109–116 (1991) studied the effect of tendon on muscle-tendon complex behavior in cat tibialis anterior (TA) muscle. This was done by determining the relation between neural stimulation and muscle force in a dynamic isometric experiment, both before and after the removal of the distal tendon. From their results, Baratta and Solomonow concluded that in isometric and concentric contractions at mid-range force levels, tendon behaves as a rigid force conductor. This conclusion is in conflict with literature in which several functions are attributed to the elastic behavior of the series elastic element (SEE), of which tendon is the major part. The present study investigates the expected generalizability of their findings, by simulating the experiments using a straight-forward Hill-type muscle model. First, model predictions are shown to be in line with the experimental results on cat TA: in dynamic isometric experiments at mid-range force levels, the effect of SEE removal is indeed negligible. Second, the effect of SEE removal is predicted to vary largely among muscles. Third, the most important determinants of the effect of SEE removal in dynamic isometric contractions are shown to be maximum fiber shortening velocity and the ratio of SEE slack length to fibre optimum length.

Modeling of induced strain actuation of shell structures

Based on the thin-shell Donnell theory, a model to represent the action of discrete induced strain actuator patches symmetrically bonded to the surface of a circular cylindrical shell has been developed. The model provides estimates of the bending curvatures due to the out-of-phase actuation and the in-plane strains due to the in-phase actuation of the bonded actuator patches. The magnitudes of the induced curvature and the in-plane strain are found to be identical to those of plates; however, due to the strain-displacement relations in cylindrical coordinates, the in-plane and out-of-plane displacements are coupled. Expressions for the equivalent forces and moments that represent the action of the actuator patches have been developed. Due to the curvature of the shell, the representation of the in-phase actuation with an equivalent in-plane line force applied along the edge of the actuator results in the application of erroneous rigid-body transverse forces. To avoid these rigid body forces, a method to represent the in-phase actuation with a system of self-equilibrating forces is proposed. The action of the actuator is then represented by an equivalent in-plane force and a transverse distributed pressure applied in the region of the actuator patch. Finite element verification of the proposed model is presented. The displacements due to the actual actuator actuation are compared with the proposed model, and very good agreement is found.

Kinetics of leaping primates: Influence of substrate orientation and compliance

Our current knowledge about the forces leapers generate and absorb is very limited and based exclusively on rigid force platform measurements. In their natural environments, however, leapers take off and land on branches and tree trunks, and these may be compliant. We evaluated the influence of substrate properties on leaping kinetics in prosimian leapers by using a combined field and laboratory approach. Tree sway and the timing of takeoffs relative to the movements of trees were documented for animals under natural conditions in Madagascar. Field data collected on three species (Indri indri, Propithecus diadema, Propithecus verreauxi) indicate that in the majority of takeoffs, the substrate sways and the animals takeoff before the elastic rebound of the substrate. This implies that force is "wasted" to deform supports. Takeoff and landing forces were measured in an experimental setting with a compliant force pole at the Duke University Primate Center. Forces were recorded for 2 Propithecus verreauxi and 3 Hapalemur griseus. Peak takeoff forces were 9.6 (P. verreauxi) and 10.3 (H. griseus) times body weight, whereas peak landing forces were 6.7 (P. verreauxi) and 8.4 (H. griseus) times body weight. As part of the impulse generated does not translate into leaping distance but is used to deform the pole, greater effort is required to reach a given target substrate, and, consequently, takeoff forces are high. The landing forces, on the other hand, are damped by the pole/substrate yield that increases the time available for deceleration. Our results contrast with previous studies of leaping forces recorded with rigid platform measuring systems that usually report higher landing than takeoff forces. We conclude that 1) Leapers generate and are exposed to exceptionally high locomotory forces. The takeoff forces are higher than the landing forces when using compliant supports, indicating that the takeoff rather than the landing may be critical in interpreting leaping behavior and related aspects of musculoskeletal design. 2) Large-bodied vertical clingers and leapers do not usually take advantage of the elastic energy stored in substrates. Rather, force (and energy) is wasted to deform compliant supports. 3) A compliant force pole approximates the conditions faced by large-bodied vertical clingers and leapers in the wild more closely than do rigid force platforms.

Structure and dynamics of water and aqueous solutions: The role of flexibility

The role molecular flexibility plays in the chemistry of bulk water and ionic solutions is evaluated using molecular dynamics simulations. For simplicity the flexible water model used here is the revised central force (CF) model of Stillinger and Rahman [J. Chem. Phys. 68, 666 (1977)]. A companion, rigid central force (RCF) model is invented to provide the most accurate average description of CF water. Discussion of the role of flexibility is divided into effects due to Coulombic and non-Coulombic parts of the potential energy. The Coulombic part provides the connection between flexibility and nuclear polarizability. A variety of thermodynamic and dynamical properties of the two models are compared. These include the static dielectric constant, orientational correlation functions, self-diffusion coefficient, pressure, intermolecular energy, and pair correlation functions. The effect of flexibility is greatest for dielectric properties, but in general it is found to be small. The dielectric constant of CF water is measured to be approximately 77, in good—perhaps fortuitous—agreement with the experimental value. A variety of ionic solution properties, including the free energy and dynamics of ionic association, are reported for model sodium chloride solutions at two concentrations. For these quantities also the effect of water flexibility is found to be small.

Analysis of the robotic disc grinding process

Two major aspects of the robotic rigid disc grinding process, namely, disc wear and grinding forces have been examined in the present study. The disc wear is observed to be nonuniform, being greatest at the outer edge of the disc. A simple wear model has been developed by assuming that the amount of wear can be approximated as having a triangular cross section. The dynamic grinding force model developed includes the effects of disc wear and nonlinear stiffness of the robot system. Experiments have been conducted on an actual robotic grinding system to verify the validity of these system models. Several practical issues which should be considered during robotic grinding are discussed.

An Overview of Modeling and Simulation of the Milling Process

In this paper, various models of the milling process in frequent use are reviewed. They are classified in order of increasing sophistication and accuracy as (1) the Average Rigid Force Static Deflection Model, (2) the Instantaneous Rigid Force Model, (3) the Instantaneous Rigid Force, Static Deflection Model, (4) the Instantaneous Force With Static Deflection Feedback Model, and (5) the Regenerative Force, Dynamic Deflection Model. In each case, the validity, possible applications, and limitations of the model are discussed. In the final section, several applications of the Regenerative Force, Dynamic Deflection Model are used to illustrate the wide range of applicability of this model.

Dynamic Modeling and Simulation of Flexible Robots With Prismatic Joints

A dynamic model for flexible manipulators with prismatic joints is presented in Part I of this study. Floating frames following a nominal rigid body motion are introduced to describe the kinematics of the flexible links. A Lagrangian approach is used in deriving the equations of motion. The work done by the rigid body axial force through the axial shortening of the link due to transverse deformations is included in the Lagrangian function. Kinematic constraint equations are used to describe the compatibility conditions associated with revolute joints and prismatic joints, and incorporated into the equations of motion by Lagrange multipliers. The small displacements due to the flexibility of the links are then discretized by a displacement based finite element method. Equations of motion are derived for the cases of prescribed rigid body motion as well as prescribed joint torques/forces through application of Lagrange’s equations. The equations of motion and the constraint equations result in a set of differential algebraic equations. A numerical procedure combining a constraint stabilization method and a Newmark direct integration scheme is then applied to obtain the system response. An example, previously treated in the literature, is presented to validate the modeling and solution methods used in this study.

Plane Poiseuille flow: Rigid sphere gas

Plane Poiseuille flow of a rarefied gas is a problem of fundamental interest in vacuum science and technology. In this paper, this problem is solved as based on the linearized Boltzmann equation, rigid sphere intermolecular force, and diffuse reflection at the planar surfaces. Explicit results for the flow rate and velocity profile are obtained. The flow rates, as obtained by two independent methods, are in good mutual agreement, and provide a reasonably good description of the available experimental data.

Rotating ideal magnetohydrodynamic flow in General relativity

The field equations and the equation of motion for stationary, axisymmetric, rotating ideal magnetohydrodynamic flow are presented. Exact solutions are obtained for rigid rotation, for vanishing and nonvanishing Lorentz force.

Steady state response of mechanisms with elastic links by finite element methods

A new analysis procedure for directly obtaining the steady state displacements and stresses within the elastic links of a mechanism is described in the present work. The method of analysis combines the rigid body harmonic analysis of a mechanism with a novel application of the finite element methods. The analysis includes the higher order elastic acceleration terms and the effects of the axial rigid body forces on the transverse vibrations of the links. Finally the harmonic series expressions for the element displacements are obtained in terms of the crank angle by solving a set of linear algebraic equations. The method also possesses a high computational efficiency.

Kineto-elastodynamic analysis of mechanisms by finite element method

In the present paper a systematic finite element method for kineto-elastodynamic analysis of high speed mechanisms has been presented. Effects of number of divisions have been investigated and it is found that a certain minimum number of divisions of links is necessary to yield accurate results. A new approach for eliminating the singularity in the stiffness matrices of mechanisms has been developed and it has been shown in this paper that this new approach yields improved results with negligible additional effort. Finite element expressions for the coriolis, tangential and normal components of elastic accelerations have been derived for a moving link and a new geometric stiffness matrix has been developed to include the effects of the rigid body pinforces and the distributed axial rigid body inertia forces on the transverse vibrations of the links. The method has been further extended to take into account the nonlinear elastic axial forces. Several examples have been solved.

Rotational flow for the spectra of deformed even–even nuclei using an anisotropic harmonic oscillator force

It is shown that, starting from an anisotropic harmonic oscillator force obtained by including non-rigidity in the rigid body force, it is possible to obtain the rotational flow in two dimensions used in the study of ground-state rotational band spectra of deformed even–even nuclei in the rare-earth region. Using the known quadratic dependence of the vorticity parameter (k) on the nuclear deformation (β), the average potential energy is shown to depend quadratically on β to a first order in β. Finally, the rotational Hamiltonian is expressed purely as a function of β, and a comparison of the same with other model Hamiltonians is done. Also, it is concluded that the adiabatic rotational flow is not physically possible on the basis of the RFM. Throughout this paper, only ground-state rotational bands of even–even spheroidal nuclei are considered.

The molecular and crystal structure of an allylpalladium- (II) triazenido complex: [(1-3-η-C 3H 5)Pd(II)( p-CH 3C 6H 4NNNC 6H 4CH 3- p)] 2

For the class of compounds mentioned in the title it is difficult to the stucture unambiguously on the molecular and crystal structure of CH 3- p)] 2 by single crystal X-ray analysis. The crystal data are: M == 743 a.m.u. Space group P2 1/ c. a = 8.510(2), b = 40.652(9), c = 9.762(2) Å, β = 103.61(2)° D c = 1.50 g/cm 3. R = 0.041, R = 0.060, based on 3978 independent reflections. The two π-allylpalladium residues are bridged azenido groups, gaining an approximate square planar coordination around each heavy atom. The two allyl units are stereochemically equivalent, with the central carbon atoms pointing outwars. The rigid triazenido groups force the two palladium atoms into close contact (2.86 Å). The aromatic rings are somewhat rotated with respect to the bonded NNN planes, but some π-conjugation over the whole ligand is still retained.

Investigation of stresses in a hollow cylinder near rigid force elements

Investigation of stresses in a hollow cylinder near rigid force elements

Precision measurements of the colligative properties of solutions of strong electrolytes and of sea and brackish water: Theoretical calculation of the osmotic coefficient

The osmotic coefficients of sea and brackish water are determined by means of cryoscopic measurements. From these data the “best values” of the individual ionic radii and the dependence of the dielectric constant on concentration are calculated using a two-parametric minimum-square-method of best fitting by applying the Debye-Hückel theory according to Bonino, with the effect of the “higher terms” of Gronwall and La Mer. The method is valid for recalculating experimental cryoscopies with an error of a few thousandths of a degree over the whole concentration interval of sea and brackish water, which represents its dilutions. These techniques may also be applied to the prediction of other thermodynamic properties of sea water, and above all, of brackish water, which today are assuming great importance in less expensive desalting methods such as reverse osmosis and electrodialysis. In order o make theoretical calculations on the thermodynamic properties of sea and brackish water, it is necessary to refer to the theory of concentrated solutions of strong electrolytes. In this field there have been a great number of studies, some quite recent, but it cannot be said that the problem has been definitely resolved, even though the most modern theoretical formulations, based on Mayer's theory of “ionic clusters” 1 and on the “hyperreticulated chains” equation 2, may hopefully lead to an interpretation more closely bound to the microscopic properties of the ions and of the solvent. In any case, every theory regarding solutions of strong electrolytes amplifies the original formulation of Debye and Hückel ( 3) and in fact is compared to it as a first test of validity for dilute solutions of salts of the NaCl or KCl type. In this theory, an “ionic radius” averaged from all ions present, is introduced for concentrations which are not greatly diluted, and at higher concentrations it becomes necessary to consider even the short range forces and introduce a relative parameter. The first treatment in this sense was carried out by Hückel ( 4) on the basis of dielectric saturation, conglobating such interactions toward the lower powers of l/r. There have also been attempts ( 5) to conglobate toward infinite powers, that is, toward rigid exclusion forces, but only the cluster theory has met the problem satisfactorily. At any rate, even the original theory of Hückel succeeds well in rendering experimental results up to fairly high concentrations for solutions of simple electrolytes, so long as a more ample meaning than the initial one is given to the variation of the dielectric constant. Bonino ( 6) has interpreted this variation as the “efficacious dielectric constant”, finding an exponential law D = D oe -μ (1) with D o as the dielectric constant of the solvent and μ proportional to an appropriate power of the concentration (5/4 in the applications made): in this way absurd negative values of D are avoided and trends closer to the experimental ones are obtained for macroscopic dielectric constants ( 7). An attempt was also made to extend the theory to individual ionic radii or averaged on the dimensions of the second ion only, which approaches the first. In fact, a definitive theory should contemplate the two-by-two minimum distances between all the ion couples for these “maximum approach radii”. In any case, the introduction of Bonino's individual ionic radii also allows better separation of the characteristic behaviours of single ions in different solutions, than the mere average radius, and above all aids in the search for correlations with other physical quantities. In this way linear relations with the crystallographic-radius/polarizability ratio were found both for cations ( 8) and for anions ( 9). This formulation has made possible the determination of these ion radii from experimental data by means of bi-parametric optimization with electronic computers. This therefore requires the most precise and consistent experiments possible for the whole concentration field and on complete series of electrolytes. For this purpose, high precision cryoscopies represent the best experiments, but another series of apparatus for ebullioscopy ( 10), vapour tension and osmotic pressure in order to obtain precise thermodynamic data comparable at different temperatures are also being set up. From the cryoscopies of alkali chlorides, ionic radii and variation constants of D were found ( 11) for wide concentration intervals (the smallest from 0.02 to 1 mol/l) with average disparities between those calculated and those found of one thousandth of a degree, starting from the hypothesis of the equality of the ionic radii of the chlorine anion and the potassium cation, which was discussed in the paper mentioned. This work is being continued and extended to other halides, bivalent ions and different solvents. The theoretical extension to the cluster theory is also being planned.