Showing papers on "Inertia published in 1990"

Direct calculation of minimum set of inertial parameters of serial robots

Abstract: The determination of the minimum set of inertial parameters of robots contributes to the reduction of the computational cost of the dynamic models and simplifies the identification of the inertial parameters. These parameters can be obtained from the classical inertial parameters by eliminating those that have no effect on the dynamic model and by regrouping some others. A direct method is presented for determining the minimum set of inertial parameters of serial robots. The method permits determination of most of the regrouped parameters by means of closed-form relations. >

Exact modeling of the flexible slewing link

Abstract: The exact eigenfunctions for the slewing link of a robot are found, taking into account a rotating inertia at the base and a payload at the tip. These derive from two equivalent formulations (pseudoclamped and pseudopinned) of the boundary value problem relative to the flexible slewing beam. The exactness of the solution makes it possible to prove the equivalence of these two approaches, which differ in the choice of the noninertial rotating frame. The two related dynamic linear models are then found, and a change of coordinates is given. Experimental measurements validate the theoretical results. >

Seismic bearing capacity factors of shallow strip footings

Abstract: In determining the bearing capacity of shallow strip footings under earthquake loading conditions, most seismic codes neglect the effect of the inertia of the soil mass underneath a footing. Seismic acceleration is considered to be acting on the structure only. In this Paper, the seismic bearing capacity factors (i.e. Nq, Nc and Nr), are determined by using the limit equilibrium technique of slope stability analysis with inclined slices. The analysis shows that the factor. Vq is dependent on the inertia of the surcharge load; the relationship between Nc and Vq given in the literature is found to be incorrect for inclined loads and the inertia of the soil mass certainly has an effect on Vy. Results of the analysis are shown in graphical forms as functions of the horizontal acceleration factor and of the angle of internal friction of the soil. The analysis does not include the effect of the excess pore water pressure generated by the earthquake. For small accelerations, smaller than 0·lg the effect of the i...

Dynamics of an Arbitrary Flexible Body in Large Rotation and Translation

Abstract: Conventional theories underlying my multibody codes used for simulating the behavior of elastic structures undergoing large rotation and translation with small vibrations fail to predict dynamic stiffening of the structures. This can lead to significantly incorrect simulations in many practical situations. A theory that does not suffer from this defect and is valid for an arbifnary structure is given here. The formulation is based on Kane's equations and consists of two steps: First, generalized inertia forces are written for an arbitrary structure for which one is forced to linearize prematurely in the modal coordinates; next, this defect in linearization is compensated for by the introduction of contributions to the generalized active forces from the "motion stiffness" of the stnrctwe. The stress associated with the motion stiffness is identified as due to 12 sets of inertia forces and 9 sets of inertia couples distributed throughout the body during ihe most general motion of its flying reference frame. An algorithm is set for a reader wishing to implement the theory, and illustrative examples are given to demonstrate tbe validity and generality of the formulation.

Non-linear non-planar oscillations of a cantilever beam under lateral base excitations

Abstract: The non-planar responses of a cantilevered beam subject to lateral harmonic baseexcitation are investigated using two non-linear coupled integrodifferential equations of motion. The equations contain cubic non-linearities due to curvature and inertia. Two uniform beams with rectangular cross sections are considered: one has an aspect ratio near unity, and the other has an aspect ratio near 6.27. A combination of the Galerkin procedure and the method of multiple scales is used to construct a first-order uniform expansion for the case of a one-to-one internal resonance and a primary resonance. The results show that the non-linear geometric terms are important for the responses of low-frequency modes because they produce hardening spring effects. On the other hand, the non-linear inertia terms dominate the responses of high-frequency modes. We also obtain quantitative results for non-planar motions and investigate their dynamic behavior. For different range of parameters, the non-planar motions can be steady whirling motions, whirling motions of the beating type, or chaotic motions. Furthermore, we investigate the effects of damping.

The simulation of aerial movement—III. The determination of the angular momentum of the human body

Abstract: A method is presented for determining the angular momentum of the human body about its mass centre for general three–dimensional movements. The body is modelled as an 11 segment link system with 17 rotational degrees of freedom and the angular momentum of the body is derived as a sum of 12 terms, each of which is a vector function of just one angular velocity. This partitioning of the angular momentum vector gives the contribution due to the relative segmental movement at each joint rather than the usual contribution of each segment. A method of normalizing the angular momentum is introduced to enable the comparison of rotational movements which have different flight times and are performed by athletes with differing inertia parameters. Angular momentum estimates were calculated during the flight phases of nine twisting somersaults performed on trampoline. Errors in film digitization made large contributions to the angular momentum error estimates. For individual angular momentum estimates the relative error is estimated to be about 10% whereas for mean angular momentum estimates the relative error is estimated to be about 1%.

Stabilization of rigid body dynamicsby the Energy-Casimir method

Abstract: We show how the Energy-Casimir method can be used to prove stabilizability of the angular momentum equations of the rigid body about its intermediate axis of inertia, by a single torque applied about the major or minor axis. We also show how this system has associated with it, a Lie-Poisson bracket which is invariant under SO(3) for small feedback, but is invariant under SO(2, 1) for feedback large enough to achieve stability.

Three-dimensional nonlinear vibrations of composite beams — I. Equations of motion

Abstract: Newton's second law is used to develop the nonlinear equations describing the extensional-flexural-flexural-torsional vibrations of slewing or rotating metallic and composite beams. Three consecutive Euler angles are used to relate the deformed and undeformed states. Because the twisting-related Euler angle ϕ is not an independent Lagrangian coordinate, twisting curvature is used to define the twist angle, and the resulting equations of motion are symmetric and independent of the rotation sequence of the Euler angles. The equations of motion are valid for extensional, inextensional, uniform and nonuniform, metallic and composite beams. The equations contain structural coupling terms and quadratic and cubic nonlinearities due to curvature and inertia. Some comparisons with other derivations are made, and the characteristics of the modeling are addressed. The second part of the paper will present a nonlinear analysis of a symmetric angle-ply graphite-epoxy beam exhibiting bending-twisting coupling and a two-to-one internal resonance.

Generalized diffusion wave equation with inertial effects

Abstract: A generalized diffusion wave equation, which includes inertial effects, is derived on the basis of the linear analogs of the complete equations of continuity and motion of free-surface flow. Specializations of this equation lead to four types of diffusion wave models, depending on whether the inertia terms (local and convective) are excluded from or included in the formulation: (1) full inertial, (2) local inertial, (3) convective inertial, and (4) noninertial. Analysis of these diffusion wave models reveals substantial differences in their behavior, particularly with regard to the Froude number dependence of their hydraulic diffusivities. The full inertial and local inertial models have neutral Froude numbers, while the convective and noninertial models do not. In addition, the neutral Froude number of the full inertial model (wide channel with Chezy friction) simulates that of the complete equations (Fr = 2). For low Froude number flows the noninertial model is shown to be a good approximation to the full inertial model. The noninertial model is a better approximation to the full inertial model than either local or convective models.

Method and system for improving smoothness of upshifts in an automatic transmission

Abstract: To reduce shift bump and increase smoothness during shifts, pressure into an on-coming clutch of an automatic transmission is electronically controlled using a turbine speed adaptive strategy. Because of the change in engine speed that accompanies this torque flow path transition, such shifts include a torque phase and an inertia phase. To make the shift smooth, the torque phase is completed quickly by boosting pressure at the beginning of the shift. Just before the torque phase is commpleted, the pressure is lowered so the inertia phase bump is reduced. The end of the torque phase is predicted by monitoring the turbine speed rise since the start of the shift and comparing it with a value which is derived from an adaptive table. During the inertia phase, the pressure is ramped up to complete the shift quickly and smoothly. Ignition spark timing is reduced in the inertia phase to further improve shift feel.

Vehicle inertia and center of gravity estimator

Abstract: A vehicle inertia and center of gravity estimator uses averaged displacement measurements to estimate changes in vehicle body mass, vehicle center of gravity location, and vehicle pitch moment of inertia, due to variations in fuel load, passenger load, and cargo load. The system is responsive to the acceleration of the vehicle for providing displacement readings, the mass of the vehicle, and the rotation of the vehicle to optimally adjust vehicle parameters. Variables used in estimating vehicle conditions include vehicle vertical displacement, vehicle ride height, vehicle mass, vehicle pitch moment of inertia, vehicle center of gravity location, and vehicle wheel base.

Bingham Award Lecture—1989: The role of instrument inertia in controlled‐stress rheometers

Abstract: Instrument inertia can produce spurious effects in controlled‐stress rheometry whenever the imposed torque changes with time, as in step‐jump or ramp‐function programming of the torque. These errors are especially serious with samples of low to moderate viscosity, where spurious time‐dependent viscosities are found even with Newtonian samples. The usual way of dealing with this problem, that of slowing the speed change program sufficiently to eliminate errors caused by inertia, both lengthens the time of measurement and obscures any rapid thixotropic transformations. This paper analyzes errors due to instrument inertia for both step‐jump and ramp‐function programming in terms of an inertial response time β=KI/η, where K is the usual instrument constant for the particular rotational geometry, I the moment of inertia of the rotating part of the instrument, and η the viscosity of the sample. It then shows that ramp times of the order of 400β are needed to reduce inertial errors to acceptable levels. Finally,...

Dynamic damping control: implementation issues and simulation results

Abstract: Dynamic damping laws have been investigated. The approach is based on modulating the velocity feedback gain based on a model of the manipulator inertia and the desired stiffness. By using different stiffness gains, different dynamic damping laws can be obtained. In particular, joint space, gripper space, and constant bandwidth versions have been developed. Simulations have been used to illustrate the advantages and disadvantages of using dynamic damping control laws over conventional computed torque and proportional-derivative (PD) control laws. The disadvantages are greater computational requirements and greater coupling of joints. The advantages are guaranteed stability, greater bandwidth for small inertias, and more effective utilization of torque. It is shown that as the manipulator inertia decreases, the amount of torque commanded by the dynamic damping control law exceeds the torque commanded by computed torque and PD controllers, resulting in greater bandwidth. >

Geodetic precession or dragging of inertial frames

Abstract: In General Relativity, the Principle of General Covariance allows one to describe phenomena by means of any convenient choice of coordinate system. Here, it is shown that the geodetic precession of a gyroscope orbiting a spherically symmetric, nonrotating mass can be recast as a Lense-Thirring frame-dragging effect, in an appropriately chosen coordinate frame whose origin falls freely along with the gyroscope and whose spatial coordinate axes point in fixed directions.

Mount with adjustable length inertia track

Abstract: The fluid inertia mount (10) or the like has an inertia track (52) with an adjustable fluid path length located between variable volume fluid chambers (34,50) of the mount By adjusting the fluid path length of the inertia track (52) the mount (10) may be dynamically tuned continuously between a range of frequencies in a manner to provide a low stiffness notch for isolating input excitations that produce undesirable vehicle vibrations A tuning plate assembly (60,64) adjustably locates an opening (62) of the inertia track in a desired location along the length thereof between extreme positions in which the fluid path length is relatively long and relatively short

Hydraulic control system for automatic transmission

Abstract: During minimal load or so called power off upshifts, the level of the line pressure which is applied during the inertia phase of a friction element which becomes engaged as a result of the upshift, is controlled in accordance with the rotational speed difference between parts of the friction element which are rotatable relative to one another.

Efficient Methods For The Calculation Of Dynamic Mooring Line Tension

Abstract: The paper presents two simple and efficient frequency domain methods for the calculation of the dynamic tension of single and multiple segment mooring lines. The first method, MODEL 1, is an analytical approach based on the catenary equations and an estimate of the line drag resistance. To include inertia loads, drag loads and a dynamic description of the mooring line motion, a dynamic system based on a single degree of freedom (SDOF) is developed (MODEL 2). Both methods are extensively tested versus the nonlinear finite element computer program RIFLEX, and the correspondence with respect to dynamic tension amplitudes is very good for a wide range of line configurations, water depths and excitation levels. MODEL 2 is implemented in the MARINTEK positioning computation program MIMOSA 2.

Non-Darcian effects on forced convection heat transfer over a flat plate in a highly porous medium

Abstract: The effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer flow over a semi-infinite flat plate embedded in a saturated porous medium of high porosity are studied. It is shown that the inertia forces have a significant influence on the flow characteristics in this problem.

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

Abstract: Minimum weight designs of helicopter rotor blades with constraints on multiple coupled flap-lag natural frequencies are studied. Constraints are imposed on the minimum value of the blade autorotational inertia to ensure sufficient rotary inertia to autorotate in case of engine failure and on stresses to guard against structural failure due to blade centrifugal forces. Design variables include blade taper ratio, dimensions of the box beam located inside the airfoil and magnitudes of nonstructural weights. The program CAMRAD is used for the blade modal analysis; the program CONMIN is used for the optimization. A linear approximation involving Taylor series expansion is used to reduce the analysis effort. The procedure contains a sensitivity analysis consisting of analytical derivatives for objective function and constraints on autorotational inertia and stresses. Central finite difference derivatives are used for frequency constraints. Optimal designs are obtained for both rectangular and tapered blades. Using this method, it is possible to design a rotor blade with reduced weight, when compared to a baseline blade, while satisfying all the imposed design requirements.

Efficient O(N) computation of the operational space inertia matrix

Abstract: The development of a recursive algorithm for the operational space inertia matrix, the inertia propagation method, which reduces the computational complexity to O(N) for any manipulator is presented. The algorithm is based on a single recursion which begins at the base of the manipulator and progresses out to the last link. Spatial articulated transformations are utilized in the recursion procedure. The algorithm is the most efficient method known for N>or=6. The numerical accuracy of the algorithm is tested for a PUMA 560 robot with a fixed base. The results demonstrate the accuracy of the inertia propagation method for such a configuration. >