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NASA NTRS1987

Nonlinear beam kinematics for small strains and finite rotations

A simple matrix expression is obtained for the strain components of a beam in which the magnitudes of neither beam displacements nor rotations are explicitly restricted. The only kinematical restrictions are that: (1) strains are small compared to unity and (2) components of local rotation, a newly identified kinematical quantity, are of the order of the strains to a fractional power equal to at least one half. Local rotations are defined as the change of orientation of material elements off the beam reference axis relative to those on the beam reference axis. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of both open- and closed-section beams in applications of the theory. The resulting strain components are expressed in a local Cartesian coordinate system and can be calculated directly in that way. Thus, one can use a curvilinear coordinate system that is natural to the beam problem without the complications that usually surround such an approach. Examples show the simplicity and the generality of the present approach as well as why previously published results differ among themselves concerning tension-torsion coupling.

Hodges, Dewey H.↗

NASA NTRS1988

Modeling human perception and estimation of kinematic responses during aircraft landing

The thrust of this research is to determine estimation accuracy of aircraft responses based on observed cues. By developing the geometric relationships between the outside visual scene and the kinematics during landing, visual and kinesthetic cues available to the pilot were modeled. Both fovial and peripheral vision was examined. The objective was to first determine estimation accuracy in a variety of flight conditions, and second to ascertain which parameters are most important and lead to the best achievable accuracy in estimating the actual vehicle response. It was found that altitude estimation was very sensitive to the FOV. For this model the motion cue of perceived vertical acceleration was shown to be less important than the visual cues. The inclusion of runway geometry in the visual scene increased estimation accuracy in most cases. Finally, it was shown that for this model if the pilot has an incorrect internal model of the system kinematics the choice of observations thought to be 'optimal' may in fact be suboptimal.

Schmidt, David K.↗

NASA NTRS1989

Completing the forward kinematic calibration of open loop manipulators when single point position sensors are used

Single-point sensors can measure the position of one point fixed to a manipulator's end effector. When single-point sensors have been used for calibration, it has not been possible to calibrate the orientation of the tool. Furthermore, it can be difficult to calibrate the sensor system. Results in the literature seldom provide a complete kinematic calibration of the manipulator. Presented here is a technique that enables single-point sensors to gather sufficient information to complete kinematic calibration. In addition, the method can reduce the burden of calibrating the sensor system.

Everett, Louis J.↗

NASA NTRS1988

Local flow structures defined by kinematic events in isotropic turbulence

The spatial structure of turbulent motion in incompressible isotropic turbulence is investigated using a conditional average in which the conditional event specifies the local deformation tensor in addition to the local velocity vector. This average gives the best estimate of the flow field around a fixed point x given the kinematic state at x. Estimates are calculated for various kinematic states in isotropic turbulence, including pure translation, pure shear, plane strain, axisymmetric strain, and pure rotation. It is demonstrated that the large-scale motion is dominated by a vortex ring structure associated with the translational component, except at critical points of the velocity vector field.

Adrian, R. J.↗

NASA NTRS1989

New results concerning the use of kinematically redundant manipulators in microgravity environments

This paper is concerned with the development of control strategies for kinematically redundant manipulators to be used in Space Station laboratories. These robots must be able to conduct experiments and manufacturing processes without disturbing the microgravity environment, and thus their dynamic base reactions/motions must be nearly eliminated. Redundant degrees of freedom permit the inverse kinematics problem to be solved in conjuction with the minimization of a cost function defined as a weighted sum of the base reactions. It is shown that the weights in the cost function should be used as an additional set of parameters in the minimization problem. The actual performance of the local optimal trajectory approach is demonstrated to be not as good as was previously reported.

Quinn, R. D.↗

NASA NTRS1989

The development of the Canadian Mobile Servicing System Kinematic Simulation Facility

Canada will develop a Mobile Servicing System (MSS) as its contribution to the U.S./International Space Station Freedom. Components of the MSS will include a remote manipulator (SSRMS), a Special Purpose Dexterous Manipulator (SPDM), and a mobile base (MRS). In order to support requirements analysis and the evaluation of operational concepts related to the use of the MSS, a graphics based kinematic simulation/human-computer interface facility has been created. The facility consists of the following elements: (1) A two-dimensional graphics editor allowing the rapid development of virtual control stations; (2) Kinematic simulations of the space station remote manipulators (SSRMS and SPDM), and mobile base; and (3) A three-dimensional graphics model of the space station, MSS, orbiter, and payloads. These software elements combined with state of the art computer graphics hardware provide the capability to prototype MSS workstations, evaluate MSS operational capabilities, and investigate the human-computer interface in an interactive simulation environment. The graphics technology involved in the development and use of this facility is described.

Beyer, G.↗

NASA NTRS1989

An inverse kinematics algorithm for a highly redundant variable-geometry-truss manipulator

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry-truss manipulator (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. A solution is presented to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm was developed primarily for variable-geometry-truss manipulators, it is general enough for application to a number of manipulator designs.

Naccarato, Frank↗

NASA NTRS1989

A global approach for using kinematic redundancy to minimize base reactions of manipulators

An important consideration in the use of manipulators in microgravity environments is the minimization of the base reactions, i.e. the magnitude of the force and the moment exerted by the manipulator on its base as it performs its tasks. One approach which was proposed and implemented is to use the redundant degree of freedom in a kinematically redundant manipulator to plan manipulator trajectories to minimize base reactions. A global approach was developed for minimizing the magnitude of the base reactions for kinematically redundant manipulators which integrates the Partitioned Jacobian method of redundancy resolution, a 4-3-4 joint-trajectory representation and the minimization of a cost function which is the time-integral of the magnitude of the base reactions. The global approach was also compared with a local approach developed earlier for the case of point-to-point motion of a three degree-of-freedom planar manipulator with one redundant degree-of-freedom. The results show that the global approach is more effective in reducing and smoothing the base force while the local approach is superior in reducing the base moment.

Chung, C. L.↗

NASA NTRS1990

Kinematically redundant arm formulations for coordinated multiple arm implementations

Although control laws for kinematically redundant robotic arms were presented as early as 1969, redundant arms have only recently become recognized as viable solutions to limitations inherent to kinematically sufficient arms. The advantages of run-time control optimization and arm reconfiguration are becoming increasingly attractive as the complexity and criticality of robotic systems continues to progress. A generalized control law for a spatial arm with 7 or more degrees of freedom (DOF) based on Whitney's resolved rate formulation is given. Results from a simulation implementation utilizing this control law are presented. Furthermore, results from a two arm simulation are presented to demonstrate the coordinated control of multiple arms using this formulation.

Robert W Bailey↗

NASA NTRS1989

Kinematic sensitivity of robot manipulators

Kinematic sensitivity vectors and matrices for open-loop, n degrees-of-freedom manipulators are derived. First-order sensitivity vectors are defined as partial derivatives of the manipulator's position and orientation with respect to its geometrical parameters. The four-parameter kinematic model is considered, as well as the five-parameter model in case of nominally parallel joint axes. Sensitivity vectors are expressed in terms of coordinate axes of manipulator frames. Second-order sensitivity vectors, the partial derivatives of first-order sensitivity vectors, are also considered. It is shown that second-order sensitivity vectors can be expressed as vector products of the first-order sensitivity vectors.

Vuskovic, Marko I.↗

NASA NTRS1989

Kinematics and control algorithm development and simulation for a redundant two-arm robotic manipulator system

An efficient approach to cartesian motion and force control of a 7 degree of freedom (DOF) manipulator is presented. It is based on extending the active stiffness controller to the 7 DOF case in general and use of an efficient version of the gradient projection technique for solving the inverse kinematics problem. Cooperative control is achieved through appropriate configuration of individual manipulator controllers. In addition, other aspects of trajectory generation using standard techniques are integrated into the controller. The method is then applied to a specific manipulator of interest (Robotics Research T-710). Simulation of the kinematics, dynamics, and control are provided in the context of several scenarios: one pertaining to a noncontact pick and place operation; one relating to contour following where contact is made between the manipulator and environment; and one pertaining to cooperative control.

Hennessey, Michael P.↗

NASA NTRS1990

The kinematics and dynamics of space manipulators - The virtual manipulator approach

Future robotic manipulator systems will be required to perform complex tasks in space such as satellite repair. These robotic manipulators will encounter a number of kinematic, dynamic, and control problems caused by the dynamic coupling between the manipulators and its spacecraft. This dynamic coupling also makes it difficult to analyze these systems. This paper introduces a new analytical modeling method for space manipulators called the Virtual Manipulator (VM), which has a fixed based in inertial space at a point called a Virtual Ground. The kinematics and dynamics of the manipulator, spacecraft, and payload can be described relatively easily in terms of the VM. With its fixed base, the Virtual Manipulator is shown to have the potential to be an effective aid for the analysis, design, and development of future space manipulator systems.

Vafa, Z.↗

NASA NTRS1991

The Kinematics of Turbulent Boundary Layer Structure

The long history of research into the internal structure of turbulent boundary layers has not provided a unified picture of the physics responsible for turbulence production and dissipation. The goals of the present research are to: (1) define the current state of boundary layer structure knowledge; and (2) utilize direct numerical simulation results to help close the unresolved issues identified in part A and to unify the fragmented knowledge of various coherent motions into a consistent kinematic model of boundary layer structure. The results of the current study show that all classes of coherent motion in the low Reynolds number turbulent boundary layer may be related to vortical structures, but that no single form of vortex is representative of the wide variety of vortical structures observed. In particular, ejection and sweep motions, as well as entrainment from the free-streem are shown to have strong spatial and temporal relationships with vortical structures. Disturbances of vortex size, location, and intensity show that quasi-streamwise vortices dominate the buffer region, while transverse vortices and vortical arches dominate the wake region. Both types of vortical structure are common in the log region. The interrelationships between the various structures and the population distributions of vortices are combined into a conceptual kinematic model for the boundary layer. Aspects of vortical structure dynamics are also postulated, based on time-sequence animations of the numerically simulated flow.

Robinson, Stephen Kern↗

NASA NTRS1990

Development of a sensor coordinated kinematic model for neural network controller training

A robotic benchmark problem useful for evaluating alternative neural network controllers is presented. Specifically, it derives two camera models and the kinematic equations of a multiple degree of freedom manipulator whose end effector is under observation. The mapping developed include forward and inverse translations from binocular images to 3-D target position and the inverse kinematics of mapping point positions into manipulator commands in joint space. Implementation is detailed for a three degree of freedom manipulator with one revolute joint at the base and two prismatic joints on the arms. The example is restricted to operate within a unit cube with arm links of 0.6 and 0.4 units respectively. The development is presented in the context of more complex simulations and a logical path for extension of the benchmark to higher degree of freedom manipulators is presented.

Jorgensen, Charles C.↗

NASA NTRS1990

High spectral resolution observations and kinematic modeling of the 1667 MHz hyperfine transition of OH in Comets Halley (1982i), Giacobini-Zinner (1984e), Hartley-Good (1985l), Thiele (1985m), and Wilson (1986l)

High-sensitivity, high spectral resolution 18 cm observations of Comets Giacobini-Zinner, Halley, Hartley-Good, Thiele, and Wilson are used here to probe the kinematics of the coma gas of these comets. The day/night outgassing ratio for all these comets is 1.39 (0.13 or - 0.12), independent of gas productivity and heliocentric distance. It is found that the gas productivity of a comet plays a critical role in determining the coma kinematics for bright comets near the sun.

Tacconi-Garman, L. E.↗

NASA NTRS1990

A kinematic model for the late Cenozoic development of southern California crust and upper mantle

A model is developed for the young and ongoing kinematic deformation of the southern California crust and upper mantle. The kinematic model qualitatively explains both the overall seismic structure of the upper mantle and much of the known geological history of the late Cenozoic as consequences of ongoing convection beneath southern California. In this model, the high-velocity upper-mantle anomaly of the Transverse ranges is created through the convergence and sinking of the entire thickness of subcrustal lihtosphere, and the low-velocity upper-mantle anomaly beneath the Salton Trough region is attributed to high temperatures and 1-4 percent partial melt related to adiabatic decompression during mantle upwelling.

Humphreys, Eugene D.↗

NASA NTRS1991

Three-dimensional kinematic reconnection of plasmoids

The kinematic reconnection model of Lau and Finn (1990) is applied in a theoretical investigation of three-dimensional plasmoid morphology, as seen in the solar corona and earth magnetotail. The derivation of the governing equations is outlined; long, short, and periodic plasmoid models are developed; and the evolution of the stable and unstable manifolds in these models is presented graphically. It is inferred that sheet currents and tangential discontinuities can form on surfaces topologically identical to those where Delta(phi) about equal to Delta(z) singularities occur in the kinematic reconnection model, and can be broadened in a similar way by nonideal effects. Two such surfaces exist in long plasmoids, and also in short plasmoids in the presence of finite resistivity; the intertwined surfaces characteristic of the periodic plasmoid form a fractal set but merge in the presence of finite resistivity, producing structures similar to those proposed by the sheet-current theory of Parker (1983).

Lau, Yun-Tung↗

NASA NTRS1992

Kinematics of an in-parallel actuated manipulator based on the Stewart platform mechanism

This paper presents kinematic equations and solutions for an in-parallel actuated robotic mechanism based on Stewart's platform. These equations are required for inverse position and resolved rate (inverse velocity) platform control. NASA LaRC has a Vehicle Emulator System (VES) platform designed by MIT which is based on Stewart's platform. The inverse position solution is straight-forward and computationally inexpensive. Given the desired position and orientation of the moving platform with respect to the base, the lengths of the prismatic leg actuators are calculated. The forward position solution is more complicated and theoretically has 16 solutions. The position and orientation of the moving platform with respect to the base is calculated given the leg actuator lengths. Two methods are pursued in this paper to solve this problem. The resolved rate (inverse velocity) solution is derived. Given the desired Cartesian velocity of the end-effector, the required leg actuator rates are calculated. The Newton-Raphson Jacobian matrix resulting from the second forward position kinematics solution is a modified inverse Jacobian matrix. Examples and simulations are given for the VES.

Williams, Robert L., II↗