Showing papers on "Inertia published in 1992"

On the robust control of robot manipulators

Abstract: A simple robust nonlinear control law for n-link robot manipulators is derived using the Lyapunov-based theory of guaranteed stability of uncertain systems. The novelty of this result lies in the fact that the uncertainty bounds needed to derive the control law and to prove uniform ultimate boundedness of the tracking error depend only on the inertial parameters of the robot. In previous results of this type, the uncertainty bounds have depended not only on the inertia parameters but also on the reference trajectory and on the manipulator state vector. The presented result also removes previous assumptions regarding closeness in norm of the computed inertia matrix to the actual inertial matrix. The design used thus provides the simplest such robust design available to date. >

Dynamic analysis of geared rotors by finite elements

Abstract: A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of on shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.

Stability and Instability in the Computation of Flows with Moving Immersed Boundaries: A Comparison of Three Methods.

Abstract: This paper describes thee different numerical methods for the computation of flows with moving immersed elastic boundaries. A two-dimensional incompressible fluid and a boundary in the form of a simple closed curve are considered. The inertia is assumed to be negligible and the Stokes equations are solved. The three methods are explicit, approximate-implicit, and implicit. The first two have been used before, but the implicit method is new in the context of flows with moving immersed boundaries. They differ only with respect to the computation of the boundary force. The results of the above methods at various values of the time-step size are compared in order to explore the numerical stability of the computation.

Stability and instability in the computation of flows with moving immersed boundaries: a comparison of three methods

Abstract: This paper describes thee different numerical methods for the computation of flows with moving immersed elastic boundaries. A two-dimensional incompressible fluid and a boundary in the form of a simple closed curve are considered. The inertia is assumed to be negligible and the Stokes equations are solved. The three methods are explicit, approximate-implicit, and implicit. The first two have been used before, but the implicit method is new in the context of flows with moving immersed boundaries. They differ only with respect to the computation of the boundary force. The results of the above methods at various values of the time-step size are compared in order to explore the numerical stability of the computation.

New motion control with inertia identification function using disturbance observer

Abstract: In the proposed system, the disturbance observer is used for the inertia identification as well as for disturbance compensation. The inertia value is obtained by using the orthogonality relation among the torque components of the estimated disturbance torque. An inertia term of both the torque feedforward control and the disturbance observer is automatically readjusted by using the identification. The proposed motion control system consists of four parts: velocity feedback control, inertia torque feedforward control, disturbance observer. and inertia identification part. Experimental results show that precise control is achieved by the proposed motion control system. >

The effects of inertia on the viscoelastic Dean and Taylor–Couette flow instabilities with application to coating flows

Abstract: The effects of inertia on the elastic instabilities in Dean and Taylor–Couette flows are investigated through a linear stability analysis The critical conditions and the structure of the vortex flow at the onset of these instabilities are presented The results reveal that the purely elastic Dean flow is destabilized by inertial effects It is also found that inertia destabilizes elastic Taylor–Couette flow if the rotation of the inner cylinder is the flow driving force, while it stabilizes the flow driven by rotation of the outer cylinder The mechanism of destabilization or stabilization of these viscoelastic instabilities is investigated through an examination of the disturbance‐energy equation It is shown that Dean flow is destabilized by two separate mechanisms: a purely elastic mechanism discussed previously (ie, energy production due to the coupling of a perturbation velocity to the polymeric stress gradient in the base state) [see Phys Fluids A 3, 1691 (1991)] and a purely inertial mechanism discussed by Dean [Proc R Soc London Ser A 121, 402 (1928)] (ie, energy production from Reynolds stresses) It is also shown that, when rotation of the inner cylinder drives Taylor–Couette flow, the Reynolds stresses produce energy, and thus are destablizing, while for the flow driven by the rotation of the outer cylinder alone, the Reynolds stresses dissipate energy, thus stabilizing the flow The elastic forces remain destabilizing in both modes of operation In a second study, a pressure‐driven viscoelastic coating flow over a curved surface is examined The results demonstrate the existence of a purely elastic stationary instability in the coating flow on a concave wall which is very similar to that which occurs in viscoelastic Dean flow It is demonstrated that the mechanisms of instability in Dean flow and the coating flow are the same, again through an examination of the disturbance‐energy equation

Adaptive control of space robot system with an attitude controlled base

Abstract: The authors discuss adaptive control of a space robot system with an attitude-controlled base on which the robot is attached. An adaptive control scheme in joint space is proposed. Since most tasks are specified in inertia space, instead of joint space, the authors discuss the issues associated to adaptive control in inertia space and identify two potential problems, unavailability of the joint trajectory (since mapping from inertia space trajectory is dynamics-dependent and subject to uncertainty), and nonlinear parameterization in inertia space. For a planar system, the linear parameterization problem is investigated, the design procedure of the controller is illustrated, and the validity and effectiveness of the proposed control scheme are demonstrated. >

Stretching behaviour of large polymeric and Newtonian liquid bridges in plateau simulation

Abstract: Large liquid bridges of constant volume (initial length L0 = 50 mm and radius R0 = 25 mm) placed between two equal plane circular disks have been stretched in Plateau simulations (neutral buoyancy tank) by moving one disk with a constant velocity. While interfacial tension forces minimize the surface area, leading to contraction and break-up of the liquid bridge, inertia and friction forces act against it. Increasing inertia, friction and flow resistance, due to elongational viscosity, tend to stabilize the liquid bridge and thus form more cylindrical bridges. It has been found that none of the forces, especially inertia and interfacial tension forces, can be neglected even at elongation rates as low as 0.1 s−1.

Effect of the convective inertia term on benard convection in a porous medium

Abstract: The thermal impact of the convective inertia term, which resembles the term used in the Navier-Stokes equation for pure fluids, is investigated numerically considering Benard convection in a fluid-saturated porous medium. There has been some theoretical discussion in the archival literature about the correctness of including an inertia term in the form of a velocity divergent. The present study shows numerically that this convective term (inertia) is negligible for most cases and has a negligible effect on the overall heat transfer. The relative importance of the inertia and Forchheimer terms bated on scale analysis is found to agree with the numerical results. This evidence adds strength to the theoretical assessment found in the literature.

Hybrid machine modelling and control.

Abstract: Non-uniform motion in machines can be conceived in terms of linkage mechanisms or cams which transform the notionally uniform motion of a motor. Alternatively the non-uniform motion can be generated directly by a servo~motor under computer control. The advantage of linkage mechanisms and cams is that they are capable of higher speeds. They usually admit the means of introduction of dynamic balancing without extra parts and a high degree of energy conservation exists within the arrangement in motion. The advantage of servo~motors is that it is easier to re-program their motion to provide the versatility required of many manufacturing processes. To generate non-uniform mechanism motion, two alternative techniques are envisaged in the work presented. (i) where a servo-motor drives a linkage to produce an output. The motion transformation is determined with the geometry of the linkage. The mechanism acts as a non-uniform inertia buffer between the output and the motor. (ii) where a constant speed motor acts in combination with a servo-motor and a differential mechanism to produce the output motion of a linkage. Machines of these two kinds combine both linkage and a programmable driver. The first configuration is referred to a programmable machine, the second one is referred to as a hybrid machine. The focus of interest here is on the hybrid machine. One anticipated benefit, the second would have over the first, is that the size of the servo-motor power requirement should come down. In order to explore the idea an experimental rig involving a slider-crank mechanism is designed and built. Initially a computer model is developed for this so-called hybrid machine. The motion is implemented on an experimental rig using a sampled data control system. The torque and power relations for the system are considered. The power flow in the rig is analysed and compared with the computer model. The merits of the hybrid machine are then compared with the programmable machine. The hybrid machine is further represented with bond graphs. Lastly, the observations on the present work are presented as a guide for the development and use of hybrid machines.

Pneumatic impulse tool

Abstract: A pneumatic inertia tool for applying a cyclic percussive force to an orthopedic article via a reciprocating shuttle comprising a passageway extending between a first port and a second port. The shuttle travels within the passageway and strikes an anvil, imparting its momentum to the orthopedic article. The mass of the shuttle and its velocity at impact are selected to fix a bone relative to the orthopedic article via the existing inertia of the bone. The shuttle reciprocates within the passageway by alternating pressure and vacuum forces applied at the first port and at the second port.

Effects of Misalignment on Static and Dynamic Characteristics of Hybrid Bearings

Abstract: The analysis of actual lubrication problems needs to take into account particularities in flow caused by kinematic conditions and contact geometry. For hybrid journal bearings lubricated by low dynamic viscosity fluid, turbulence and pressure drops due to inertia forces in the recess outlets are phenomena which must be taken into account to compute their working characteristics. These bearings serve as both vertical and horizontal shaft guides particularly under low speed conditions. They are used in mechanisms which are highly loaded at start-up and which cannot generate hydrodynamic load-carrying capacities at low speeds. They avoid damage because of their stabilizing effects, but cannot conceptually cope with shaft misalignment. In this paper, the influence of misalignment of geometrical parameters on static and dynamic characteristics of hybrid bearings in laminar and turbulent flow regimes is presented. Experimental results and numerical results obtained with two numerical procedures, i.e., the finit...

Adaptive fluid mount

Abstract: A double pumper mount useful as a front mount for an aircraft engine. A pair of fluid chambers are selectively interconnectable by one of a plurality of inertia tracks by use of an adjustable cylindrical member which has the tracks formed as generally helical grooves extending about the periphery of the cylindrical member. These inertia tracks have different flow characteristics so as to produce differing notch frequencies so as to attenuate different vibrational frequencies. A second embodiment has a single inertia track whose length can be altered by rotating the cylindrical member to change the point at which the ingress/egress port of the fluid chamber engages the circumferential portion of the inertia track.

Use of neural networks to identify and compensate for friction in precision, position controlled mechanisms

Abstract: A special neural network topology has been developed that compensates for friction in precision, position controlled mechanisms. A major contribution is that knowledge of the friction's form is used to determine the neural network's structure. This unique approach solves network sizing and weight initializing problems. The friction model is used for feedforward decoupling of friction-induced torque. The neural network also explicitly incorporates inertia compensation and linear feedback control. Another contribution is a demonstration of the trajectory dependence of static friction compensation with a discrete time controller. The authors include both the theoretical formulation and practical implementation results for the control of a commercial DC motor having a significant amount of static friction. >

An identification method for estimating the inertia parameters of a manipulator

Abstract: This article presents an off-line identification method to estimate the minimal knowledge of the inertia parameters for determining the dynamic model of a manipulator. A new approach is proposed to find a set of the minimal knowledge of the inertia parameters. This set is recursively estimated by moving one joint at a time. The off-line identification procedure also provides a sufficient condition for a persistently exciting trajectory. A simulation example of Stanford arm illustrates the validity and simplicity of the identification procedure.

Linearizing coordinate transformations and Riemann curvature

Abstract: Using the Lagrangian framework and point transformations, an alternative derivation of an existing result on the special decomposition of the inertia matrix is presented. The Riemann curvature tensor is introduced as a computational tool to test for this special decomposition. An example with configuration-dependent inertia which admits such a factorization is presented. For the cart-pole problem, it is shown that such a decomposition is possible and the linearizing transformation is computed. It is shown that a planar two-link manipulator cannot be linearized by point transformations only. >

Non-Darcy Couette Flow in a Porous Medium Filled With an Inelastic Non-Newtonian Fluid

Abstract: Newtonian and non-Newtonian Couette flows through inelastic fluid saturated porous media due to a moving plate boundary have been investigated analytically. The momemtum equation which includes both the viscous and inertia terms is solved to examine the effects of the pseudoplasticity, boundary friction, and porous inertia on the velocity profile and wall shear stress at the moving wall. Closed-form exact solutions are presented for three distinct cases of practical interest

Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods

Abstract: In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.

Forces and moments on a small body moving in a 3-D unsteady flow

Abstract: Complete expressions are derived for the inertia forces and moments acting on a small body in a six degree of freedom motion in a three dimensional unsteady flow in an unbounded ideal fluid. The far-field approximation of the body motion is represented by a series of multipoles located at the origin of the body. Unsteady terms are expanded in a series of dual to the multipole series. Lagally integrals are expressed in terms of multipoles as well, by using Legendre polynominal expansions. New inertia term expressions are derived by truncating the multipole series after the quadrupoles. Corresponding terms for moments are also developed. The derived formulas are still compact enough for engineering applications. Many practical problems involving fixed and oscillating cylinders, piles, and risers are studied numerically. Comparisons to the Morison equation approach prove that nonlinear convective terms are not negligible in multidimensional relative flows.

General structure of time-optimal control of robotic manipulators moving along prescribed paths

Abstract: The structure is addressed of time-optimal control of robotic manipulators along a specified geometric path subject to constraints on control torques. Both regular and singular (where one or more effective inertia components is/are zero on any finite time interval) cases are studied by using the extended Pontryagin's minimum principle and a parametrization method. It is shown that the structure of the time-optimal control law requires either (a) one and only one control torque to be always in saturation in every finite time interval along its optimal trajectory, while the rest of them adjust their values so that the motion of the robot is guaranteed along the constrained path, or (b) at least one of the actuators to take on its extremal values. The first form of the control law dominates the robot motion along the optimal trajectory although the second form may exist. The theoretical results are verified by various existing numerical examples.

Dynamic Characteristic Analysis of Short Elliptical Journal Bearings in Turbulent Inertial Flow Regime

Abstract: In this paper, dynamic behavior of elliptical journal bearings in the turbulent inertial flow regime was examined theoretically based on the nonlinear analysis for three different ellipticity ratios of m = 0, 0.5 and 1.0. The nonlinear equations of motion for a rigid shaft supported on two identical aligned bearings were solved by the improved Euler's method, and the relations between the transient journal center motion and the corresponding pressure distribution were presented in the graphic form. From the numerical results, the effects of ellipticity ratio, turbulence, and fluid film inertia on the dynamic behavior of elliptical journal bearings were clarified. Presented at the 45th Annual Meeting in Denver, Colorado May 7–10, 1990

Measurement of the relaxation time in Darcy flow

Abstract: The inertia of a liquid flowing through a porous medium is normally ignored, but if the acceleration is great, it may be important. The relaxation time, defined so that it alone accounts for the inertia, has been determined experimentally with a simple oscillator. A U-Tube is provided with a porous plug and filled with a liquid. During pendulation of the liquid, the frequency and the damping define the relaxation time. The measured value of the relaxation time is about 10 times the theoretical estimate derived from Navier-Stokes equation.

Forces and moments on a small body moving in a 3-D unsteady flow

Abstract: Complete expressions are derived for the inertia forces and moments acting on a small body in a six degree of freedom motion in a three dimensional unsteady flow in an unbounded ideal fluid. The far-field approximation of the body motion is represented by a series of multipoles located at the origin of the body. Unsteady terms are expanded in a series of dual to the multipole series. Lagally integrals are expressed in terms of multipoles as well, by using Legendre polynominal expansions. New inertia term expressions are derived by truncating the multipole series after the quadrupoles. Corresponding terms for moments are also developed. The derived formulas are still compact enough for engineering applications. Many practical problems involving fixed and oscillating cylinders, piles, and risers are studied numerically. Comparisons to the Morison equation approach prove that nonlinear convective terms are not negligible in multidimensional relative flows.

Accuracy of finite dimensional dynamic models of flexible manipulators for controller design

Abstract: The dynamics of mechanical systems with distributed flexibility are described by infinite dimensional mathematical models, yet a real controller must be finite dimensional due to the limited bandwidth capabilities of the sensor-actuator system and real-time control computer hardware. Therefore, simplified finite dimensional dynamic models must be obtained for the purpose of controller design. This article addresses the issue of selecting the shape and number of mode functions in developing finite order models using a flexible robot arm as an example. The results of this work have consistently shown that the clamped-free mode shape predicts the closed-loop system dynamics under a feedback controller much more accurately than pinned-free mode shapes. However, as the hub inertia increases relative to the flexible beam inertia the difference between the clamped-free and pinned-free mode shape model predictions becomes smaller.