Showing papers on "Inertia published in 1983"

The Calculation of Robot Dynamics Using Articulated-Body Inertias:

Abstract: This paper describes a new method for calculating the acceleration of a robot in response to given actuator forces. The method is applicable to open-loop kinematic chains containing revolute and prismatic joints. The algorithm is based on recursive formulas involving quantities called articulated-body inertias, which represent the inertia properties of collections of rigid bodies connected together by joints allowing constrained relative motion between the bodies. A new, matrix-based notation is introduced to represent articulated-body inertias and other spatial quantities. This notation is used to develop the algorithm, and results in a compact representation of the equations. The new algorithm has a computational requirement that varies linearly with the number of joints, and its efficiency is compared with other published algorithms.

A Geometrical Representation of Manipulator Dynamics and Its Application to Arm Design

Abstract: A new approach to the geometrical representation of manipulator dynamics is presented. The inertia ellipsoid, which is used to represent dynamic characteristics of a single rigid body, is extended to a general ellipsoid for a series of rigid bodies in order to represent the manipulator dynamics. The geometrical configuration of the generalized inertia ellipsoid (GIE) represents the characteristics of the manipulator as a whole. One can understand the complicated inertial effect and nonlinearity of multi-degree-of-freedom motion by simply investigating the GIE configuration. In the latter half of the paper, this method is applied to aid the design of a mechanical arm, in which dimensions of an arm structure and its mass distribution are optimized through the evaluation and graphical representation of the arm dynamics.

The effects of crossing trajectories on the dispersion of particles in a turbulent flow

Abstract: The effects of ‘crossing trajectories’ and inertia on the dispersion of particles suspended in a field of grid-generated turbulence were investigated experimentally. The effect of particle trajectories crossing the trajectories of fluid elements, under the influence of a potential field (usually gravity), is to force the particles from one region of highly correlated flow to another. In this manner, particles lose velocity correlation more rapidly than the corresponding fluid points and as a result disperse less.A homogeneous decaying turbulent field was created behind a square biplanar grid in a wind tunnel. Particles were charged by a corona discharge then passed into the test section through a small plastic tube. A uniform electric field within the test section was used to simulate the effect of gravity, forcing the charged particles out of regions of correlated fluid at a higher than normal rate, therefore inducing the effects of crossing trajectories. Two sizes of glass beads (5 μm and 57 μm diameter) were employed in order to observe inertial effects. Laser-Doppler anemometry was used to measure particle mean-square displacement, autocorrelation coefficient, and mean-square velocity, from which dispersion coefficients were calculated.For the two particle sizes used in the tests, it was found that the particle diffusion coefficient, after a suitably long time from their release, was influenced primarily by the effect of crossing trajectories. Only in the particle mean-square velocity was the particle inertia seen to have any effect. The ratio of the particle relaxation time to the Kolmogoroff timescale was found to be a good indicator for the effects of particle inertia.

Satellite attitude dynamics and control in the presence of environmental torques - A brief survey

Abstract: Introduction M of a spacecraft presents two dynamical aspects of interest. The most obvious one is the trajectory traced by its center of mass which is governed by the classical Keplerian relations. However, spacecraft are not point masses as Kepler assumed in the analysis of planetary bodies. They have finite size and hence inertia. Thus a satellite, while negotiating a trajectory, may execute rotational motion about its center of mass, commonly referred to as libration.

Viscoelastic squeeze-film flows – Maxwell fluids

Abstract: An exact solution for the squeeze-film motion in an upper convected Maxwell fluid is given for both the plane and axisymmetric cases. Inertia and viseoelastic effects are included, and it is shown that the solution depends only on the product of the Weissenberg and Reynolds numbers. Solutions are generated for values of this product up to 500 without numerical problems. The solutions show wave propagation and show a reduced load capacity relative to the Newtonian case.

Sliding sheets: lubrication with comparable viscous and inertia forces

Abstract: A rigid plane thin sheet is sliding steadily at speed U close to a plane wall, in a fluid of kinematic viscosity v. The sheet is infinitely wide and is of length L in the direction of motion, and its leading edge is a distance h0 [Lt ] L from the wall. A solution is sought for arbitrary finite values of R = Uh20/νL. In the limit as e = h0/L→0, the problem reduces to that of solving the boundary-layer equation in the gap region between sheet and wall, and this is done here both by an empirical linearization, and by direct numerical methods. The solutions have the property that they reduce to those predicted by lubrication theory when R is small, and to those predicted by an inviscid small-gap theory when R is large. Special attention is paid to the correct entrance and exit conditions, and to the location of the centre of pressure.

Neutron interference: general theory of the influence of gravity, inertia and space-time torsion

Abstract: The general theory of the influence of gravity, inertia (i.e. interferometer motion) and space-time torsion on the outcome of neutron interference experiments is presented. The exact results are obtained in a general relativistic treatment based on the description of a stationary working interferometer in Riemann-Cartan space-time and on the WKB approximation for the neutron waves. Particular attention is paid to the influence on the spinor amplitude. There are two types of resulting amplitude effects; one originates in the non-integrability of the spinor connection and represents the influence of a modified Riemann-Cartan curvature; the other is caused by the influence of the interferometer rotation and acceleration and of space-time torsion during the time interval between the emission of the two coherent neutron waves. For practical purposes small effects are treated in an approximation. Two examples of a global evaluation of the expressions are given. Applications including a gravitational Aharonov-Bohm effect are discussed.

On the dynamic behavior of the wobblestone

Abstract: The wobblestone is a generalized form of a top with distinct inertias and a nonspherical surface at the point of contact to the horizontal plane on which it moves. Some wobble-stones exhibit a curious property of allowing steady rotation about the vertical principal inertia axis only when rotated in one direction, while other wobblestones exhibit repeated reversals of the direction of rotation after being spun. Here, nonlinear equations governing the motion of a wobblestone are derived assuming no slippage at the point of contact to the supporting rigid plane, which corresponds to a conservative model. The equations are formulated in a manner suitable for numerical integration. The major observed properties of the motion of these asymmetrical tops are demonstrated in numerical simulations. The results lead to a better understanding of their complex and fundamentally nonlinear motion.

Dynamic analysis of tension leg platforms

Abstract: The dynamic response of tension-leg platforms subjected to wave loading was investigated using a deterministic dynamic analysis. The model employed in this study is based on coupled nonlinear stiffness coefficients and closed form inertia and drag forcing functions derived using Morison's equation. The forcing functions include relative motion behavior between the fluid particles and the structure. These forcing functions are integrated manually thereby avoiding the need for expensive numerical integration. A set of coupled nonlinear differential equations was integrated sequentially in the time domain using the Newmark beta-method. A computer program was developed to simulate the time history response of the platform motion.

The haptic radial-tangential effect: Two tests of Wong’s “moments-of-inertia” hypothesis

Abstract: When a given length is haptically traced, the direction of hand movements (relative to the body) influences the length perceived. A recent theory by Wong (1977) states that the source of the illusion is undetected differences in the moments of inertia associated with different directions of hand movement: Radial directions produce greater resistance to inertia (and, therefore, slower movements) than do tangential directions. Because subjects rely on time estimates to determine a fixed distance and because they are unable to perceive that they are moving more slowly in the radial than in the tangential direction, they overestimate “radial” lengths relative to“tangential” lengths. Experiment 1 examines the effect of altering inertia by changing the distance of the hand from the axis of rotation; Experiment 2 does so by changing the mass of the moving hand. Both manipulations fail to support the predictions derived from the moments-of-inertia hypothesis.

Exact Kinematic Analysis of pumping units

Abstract: A new pumping unit Kinematic Analysis method was developed for the calculation of position, velocity, acceleration of the polished rod, and torque factors as functions of crank angle. This method can also be used to calculate the angular position, velocity and acceleration of any part of the pumping unit mechanism. It is more accurate than previous methods because it produces exact results. It can be used to compare pumping units, and can analyze units with varying crank speeds. It can improve gearbox torque analysis by including inertia effects, and can allow the use of conventional dynagraphs for the prediction of downhole dynagraphs.

The Effect of Fluid Inertia in Squeeze Film Damper Bearings: A Heuristic and Physical Description

Abstract: Fluid inertia forces are comparable to viscous forces in squeeze film dampers in the range of many practical applications. This statement appears to contradict the commonly held view in hydrodynamic lubrication that inertia effects are small. Upon closer inspection, the latter is true for predominantly sliding (rather than squeezing) flow bearings.The basic equations of hydrodynamic lubrication flow are developed, including the inertia terms. The appropriate orders of magnitude of the viscous and inertia terms are evaluated and compared, for journal bearings and for squeeze film dampers. Exact equations for various limiting cases are presented: low eccentricity, high and low Reynolds number. The asymptotic behavior is surprisingly similar in all cases. Due to inertia, the damper force may shift 90° forward from its purely viscous location. Inertia forces are evaluated for typical damper conditions.The effect of turbulence in squeeze film dampers is also discussed. On physical grounds it is argued that the transition occurs at much higher Reynolds numbers than the usual lubrication turbulence models predict.Copyright © 1983 by ASME

Dynamic analysis of mooring cables

Abstract: A finite element model for numerical analysis of the dynamic response of mooring cables is presented. The model takes into account the elasticity of the cable, inertia forces, drag forces and frictional forces between the sea bottom and the cable, and is capable of handling both two- and three-dimensional problems.

Mounting construction for engine-transmission assembly

Abstract: An engine-transmission assembly is supported in an engine room of a vehicle by two elastic support devices supporting it substantially at opposite ends of its rolling axis of inertia and two other elastic support devices supporting it substantially at opposite ends of its pitching axis of inertia. The major part of the weight of the engine-transmission assembly may be borne by the two elastic support devices on the rolling axis of inertia, which may be simple rubber block type support devices; and the two elastic support devices on the pitching axis of inertia may be of a type able to present variable spring constant and/or damping coefficient, optionally according to the driving conditions of the vehicle.

Inertial and viscous effects in the nonlinear growth of the tearing mode

Abstract: The nonlinear self‐similar tearing‐mode solution of Rutherford is revisited. The steam function for the plasma flow including inertia, convection, and viscosity is explicitly computed. In all cases, Rutherford’s solution is asymptotically valid.

Remarks about the interpretation of impulse experiments in shear flows of viscoelastic liquids

Abstract: The effect of inertia in three popular impulse experiments in shear flows of viscoelastic liquids is considered. Dynamics of the flow is used to evaluate the stress observables such as the shear stress and the first normal stress difference at the walls. In particular we find that for many linear viscoelastic models with slowly fading memory, the difference between experimental observables and a theory based on the assumption of ignorable inertia could be quite substantial.

Optimal controlcn of a voltage-driven stepping motor

Abstract: The single-step optimal control of a voltage-driven variable-reluctance stepping motor, with an inertia load, is considered. A solution for the optimal control policy is achieved by a conjugate gradient method in function space, optimising the response of a well established nonlinear motor model. The open-loop bang-bang policy which results is refined using a switching-times algorithm which is more economical in computer requirements. The technique is implemented as a microprocessor controller and is shown, by experimental results on a typical motor, to be effective over a wide range of load inertia.

Wave mechanical inertia and the containment of fundamental particles of matter

Abstract: It is shown that the form of a non-dispersive wave mechanical packet representing a rotating particle of matter has a sharp and finite boundary in the equatorial plane and is entirely consistent with earlier models of phase-locked cavities. The latter have been shown to possess the properties of inertia without the need of Mach's principle. Hence, it appears that the origin of inertia for all finitely bounded particles of matter lies in the feedback process that is intrinsic to phase-locked particles. The sharp bounding of the wave mechanical packet befits models of some elementary particles and may shed light on the remarkable process whereby the actions of quantum phenomena are concentrated into particular space-time events and are not diluted over large regions of the Universe.

Optimum Design of Variable-Material Flywheels

Abstract: This paper deals with design configurations that would maximize energy stored per unit mass of flywheel and would also lead to more uniform stress distribution within yield limits. A “shape factor” is herein used to relate inertia per unit mass to specific strength (viz., yield strength per unit density), the flywheel being equally stressed in both radial and tangential directions. A proposed “optimum design function” is shown to facilitate the search for an optimum design of an isotropic variable-material flywheel. Multimaterial flywheels, made up of suitable groups of materials may well provide higher inertia per unit mass than the corresponding constant-strength disk made of any material in the group. Examples of two-element alloy flywheels (lead-tin and aluminum-magnesium) with higher inertia per unit mass than the constant-strength disk are displayed.

Non-isothermal developing flow of a power-law fluid in a converging slit

Abstract: A numerical solution of the developing non-isothermal flow of a generalised power-law fluid in a slightly converging slit is presented, a problem which is relevance to some polymer processing operations. The results are presented in graphical form. They indicate that inertia forces and kinetic energy increases along the slit and these factors affect the development of the velocity and stress distributions. The effect of other parameters on the process is also brought out.

Film Blowing, Blow Moulding and Thermoforming

Abstract: In this chapter we discuss processes involving the stretching of thin sheets of molten or soft solid polymers. The mechanics are modelled on the basis of membrane theory (sheet thickness very small, in particular, small compared with principal radii of curvature of the sheet) and here, as in every published calculation, axial symmetry is assumed. The most significant forces acting on the polymer are boundary tractions and the force arising from any pressure difference across the sheet. Once the problem has grown to the complexity where computer solution of the equations is sought, the incorporation of the less significant forces into the model is straightforward. The influence of gravity may be moderately important and may easily be taken into consideration, as may inertia which is generally insignificant. Surface tension is not likely to be important unless very thin films are being produced, but only requires physical data in order to be incorporated in the model. Air drag likewise requires physical data, probably in the form of a correlation and some empirically determined coefficients.

Elements of hydrodynamic propulsion

Abstract: This is a treatment of a number of aspects of the theory of hydrody namic propulsion. It has been written with in mind technical propulsion systems generally based on lift producing profiles. We assume the fluid, which is admitted in conventional hydrody namics, to be incompressible. Further we assume the occurring Reynolds numbers to be sufficiently high such that the inertia forces dominate by far the viscous forces, therefore we take the fluid to be inviscid. Of course it must be realized that viscosity plays an important part in a number of phenomena displayed in real flows, such as flow separation at the nose of a profile and the entrainment of fluid by a ship's hull. Another ap proximation which will be used in general is that the problems are linearized. In other words it is assumed that the induced disturbance velocities are sufficiently small, such that their squares can be neglected with respect to these velocities themselves. Hence it is necessary to evaluate the domain of validity of the results with respect to these two a priori assumptions. Anyhow it seems advisable to have first a good understanding of the linearized non-viscous theory before embarking on complicated theories which describe more or less realistic situations. For elaborations of the theory to realistic situations we will refer to current literature. In low Reynolds number flow, singular external forces and moments are very useful."

Phenomenological surface inertia in the MIT bag model

Abstract: A phenomenological kinetic-energy term for the surface of the MIT bag is added to the Hamiltonian, and its consequences are studied for light-quark systems and heavy-quark systems. The value of the surface inertia must be less than approx.0.2 GeV in order to avoid a fifth S state in the portion of the UPSILON spectrum in which only four have been observed.