Showing papers on "Coordinate system published in 1981"
TL;DR: A new conceptually simple approach to controlling compliant motions of a robot manipulator that combines force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system is presented.
Abstract: A new conceptually simple approach to controlling compliant motions of a robot manipulator is presented. The 'hybrid' technique described combines force and torque information with positional data to satisfy simultaneous position and force trajectory constraints specified in a convenient task related coordinate system. Analysis, simulation, and experiments are used to evaluate the controller's ability to execute trajectories using feedback from a force sensing wrist and from position sensors found in the manipulator joints. The results show that the method achieves stable, accurate control of force and position trajectories for a variety of test conditions.
2,991 citations
TL;DR: In this article, a nonlinear finite element formulation is presented for the three-dimensional quasistatic analysis of shells which accounts for large strain and rotation effects, and accommodates a fairly general class of nonlinear, finite-deformation constitutive equations.
575 citations
TL;DR: In this article, a numerical analysis is carried out to investigate the local and overall heat transfer between concentric and eccentric horizontal cylinders, based on Stone's strongly implicit method, is extended to the 3 × 3 coupled system of the governing partial differential equations describing the conservation of mass, momentum, and energy.
Abstract: A numerical analysis is carried out to investigate the local and overall heat transfer between concentric and eccentric horizontal cylinders. The numerical procedure, based on Stone's strongly Implicit method, is extended to the 3 × 3 coupled system of the governing partial differential equations describing the conservation of mass, momentum, and energy. This method allows finite-difference solutions of the governing equations without artificial viscosity, and conserves its great stability even for arbitrarily large time steps. The algorithm is written for a numerically generated, body-fitted coordinate system. This procedure allows the solution of the governing equations in arbitrarily shaped physical domains Numerical solutions were obtained for a Raylelgh number In the range 102-103, a Prandtl number of 0.7, and three different eccentric positions of the inner cylinder. The results are discussed in detail and are compared with previous experimental and theoretical results.
120 citations
Patent•
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TL;DR: In this article, a predetermined operation is executed by a robot (10) taught an end position (TCP) of an operation member (13) mounted on its wrist, and an instruction for correcting the rotation of position of a tool coordinate system (Xt-Yt-Zt) is obtained through a simple operation.
Abstract: A predetermined operation is executed by a robot (10) taught an end position (TCP) of an operation member (13) mounted on its wrist (11). Even when the data on the position of a work (12) sent from a sensor (14) indicates that a grip-direction vector (W) of the work (12) is not in parallel with the plane on which it is placed, the angle of rotation is determined by an operation control unit (15) relying upon a projection (W') of the grip-direction vector and an instruction for correcting the rotation of position of a tool coordinate system (Xt-Yt-Zt) is obtained through a simple operation, so that the rotation of the tool position can be corrected and controlled.
112 citations
TL;DR: In this article, the problem of maintaining quality control of manufactured parts is considered and an explicit least squares solution is obtained using the singular value decomposition of a related matrix, and an appropriate angular representation of the resulting orthogonal transformation matrix is presented.
Abstract: The problem of maintaining quality control of manufactured parts is considered This involves matching points on the parts with corresponding points on a drawing The difficulty in this process is that the measurements are often in different coordinate systems Using the assumption that the relation between the two sets of coordinates is a certain rigid transformation, an explicit least squares solution is obtained This solution requires the singular value decomposition of a related matrixOther topics in the paper include an appropriate angular representation of the resulting orthogonal transformation matrix, and a computational algorithm for the various required quantities
109 citations
Patent•
18 Nov 1981
TL;DR: In this article, a controlled motion apparatus capable of at least three degrees of freedom, such as apparatus for vibration testing of equipment, comprises a support suspended from a reaction mass by three anti-rotation, linear motion displacement actuator devices each extending and movable along one axis of an XYZ coordinate system.
Abstract: A controlled motion apparatus capable of at least three degrees of freedom, such as apparatus for vibration testing of equipment, comprises a support suspended from a reaction mass by three anti-rotation, linear motion displacement actuator devices each extending and movable along one axis of an XYZ coordinate system. Each actuator may be independently activated to cause the support to undergo simultaneously controlled motion along the three axes.
96 citations
TL;DR: A mathematical method is presented which is easily applied and applicable to a wide variety of complex three-dimensional treatment planning problems and is found to reduce to two general types.
Abstract: The majority of radiation treatment planning problems are relatively straightforward, involving only specified gantry angles in a treatment plane which is perpendicular to the patient longitudinal axis. In addition, there are a number of more complex three‐dimensional problems which require combined rotation of the gantry, collimator, and turntable for their solutions. These include, for example, the use of non‐coplanar fields and oblique treatment planes, the matching of field edges in three dimensions, the treatment of the breast with opposing tangential fields, and the treatment of inclined elongated lesions. Unfortunately, there is no general systematic approach to the solution of these more complex problems. One may attempt an analytic solution, but this approach is often too cumbersome and tedious. On the other hand, one may resort to a ‘‘trial and error’’ session with the simulator. This paper, therefore, presents a mathematical method which is easily applied and applicable to a wide variety of complex three‐dimensional treatment planning problems. The method considers the gantry, collimator, and turntable as coordinate systems. These coordinate systems are derivable from each other by specified coordinate transformations, which contain the rotation angles of the gantry, collimator, and turntable. Within this mathematical framework, the treatment planning problems are found to reduce to two general types, of which various clinical examples are then given. Key words: treatment planning, coordinate systems, coordinate transformations, three‐dimensional treatment planning, rotation operators
92 citations
TL;DR: In this paper, the conservation-law form of the Navier-Stokes equations for non-steady coordinate systems is presented. But the results of this paper are restricted to the case of viscous subsonic and supersonic flow prediction.
Abstract: Introduction R interest in the generation of general bodyoriented curvilinear coordinate systems," for the purpose of solving the complete Navier-Stokes system of equations for subsonic and supersonic flows, has given rise to many forms of presentations of the equations both in conservative and nonconservative formulations. Based on the available solutions of the gasdynamic equations (e.g., Ref. 5) the conservation-law form of the equations seems definitely preferable, particularly when shocks are present. Although the above statement cannot be repeated in a definitive sense for the case of viscous subsonic and supersonic flow prediction through the Navier-Stokes equations, nevertheless, it is expected that the conservation-law form may eventually be more acceptable for numerical purposes. The purpose of this paper is to derive the conservation-law form of the Navier-Stokes equations in general nonsteady coordinate systems in a simple and direct fashion. Previous work on this subject has been done by McVittie, Viviand, and Vinokur. It will be shown in this Note that the equations in the conservation-law form can be obtained simply by a little manipulation of some standard vector and tensor formulas.
86 citations
TL;DR: In this paper, a new technique of moving mesh points in physical space is introduced so as to reduce the error in a computed asymptotic solution relative to that obtained using a fixed mesh.
72 citations
TL;DR: In this paper, a methodology is presented for numerical solution of transient two-dimensional diffusion-type problems (e.g., heat conduction) in which one of the boundaries of the solution domain moves with time.
67 citations
TL;DR: In this article, a tensor transformation procedure is used to ensure physical invariance of the primitive equations between the Cartesian and terrain-following systems, and the results of tensor transformations are used to derive a terrain following coordinate system that is frequently used in a number of regional and mesoscale hydrostatic models.
Abstract: This article uses tensor transformation procedures in order to derive a terrain-following coordinate system that is frequently used in a number of regional and mesoscale hydrostatic models. Tensor transformation procedures are used so as to ensure physical invariance of the primitive equations between the Cartesian and terrain-following systems. Among the major conclusions are as follows: Applying the chain rule to the hydrostatic equation, before transforming from a Cartesian to a terrain-following coordinate system, yields a different set of equations than if the hydrostatic assumption is applied after the tensor transformation is made. The hydrostatic equations in the two terrain-following representations are the same only when the slope of the terrain in the model is much less than 45°. Variations of the metric tensor across a grid volume appear in the set of conservation equations as a result of averaging the equations over a grid volume. Such deviations have always been ignored in existing ...
01 Jan 1981
TL;DR: FISHPAK is a package of FORTRAN subroutines that has been developed at the National Center for Atmospheric Research that provides a basic capability to automatically produce finite difference approximations to Helmholtz's equation defined on a rectangle in a particular co-ordinate system.
Abstract: Publisher Summary
This chapter discusses the efficient FORTRAN subprograms for the solution of elliptic partial differential equations. FISHPAK is a package of FORTRAN subroutines that has been developed at the National Center for Atmospheric Research. The package provides a basic capability to automatically produce finite difference approximations to Helmholtz's equation defined on a rectangle in a particular co-ordinate system. Also, there are routines for the more general separable elliptic equation and three-dimensional Helmholtz equation in Cartesian coordinates. The package is comprised of a set of drivers, a set of solvers, and an extensive subpackage for computing Fourier transforms. Drivers are available on two different types of finite difference grids, namely, centered, and staggered. In a centered grid, the physical boundaries coincide with the grid lines, whereas in a staggered grid, the physical boundaries are located at one-half grid spacing away from the grid lines. All drivers use a uniform or equally spaced grids in the given coordinate system.
TL;DR: In this article, a technique for moving the mesh points in physical space in order to reduce the error in the computed asymptotic solution relative to that obtained using a fixed mesh is presented.
Abstract: Coordinate system selection is an important consideration in the asymptotic numerical solution of any fluid-flow or heat transfer problem. This paper uses a new technique that provides a simple way of moving the mesh points in physical space in order to reduce the error in the computed asymptotic solution relative to that obtained using a fixed mesh. Applications to fluid-flow problems are presented, including boundary layer flow and inviscid supersonic flow over cylinders, and wedges with associated detached shocks. The treatment of curved boundaries, stationary and nonstationary boundaries, and systems of PDE's is discussed. Significant error reductions are demonstrated.
TL;DR: In this article, an algorithm is presented for obtaining a minimal-order state-space realization of a strictly proper rational function matrix, which can also be used to compute the observability indices of any given state space system.
Abstract: In this paper, an algorithm is presented for obtaining a minimal-order state-space realization of a strictly proper rational function matrix. The algorithm can also be used to compute the observability indices of any given state-space system. A controllable but unobservable state-space realization of the given rational function matrix is first obtained, by inspection. The algorithm then performs a sequence of simple coordinate transformations on the state vector of the system. The coordinate transformation matrices are orthogonal and are easily constructed from the system matrices. Each coordinate transformation operates on submatrices (of the state-space system matrices) of lower dimension than the preceding one. The sequence of coordinate transformations terminates after at most v 1 + 1 transformations, where v 1, is the maximal observability index of the state-space model. The observability indices of the system are also determined at this time. The transformed system matrices are obtained in a form wh...
01 Dec 1981
TL;DR: In this article, a computer code was developed to solve the full two dimensional Navier-Stokes equations in a supersonic combustion ramjet (scramjet) inlet.
Abstract: A computer code was developed to solve the full two dimensional Navier-Stokes equations in a supersonic combustion ramjet (scramjet) inlet. In order to be able to consider a general inlet geometry with embedded bodies, a numerical coordinate transformation is used which generates a set of boundary-fitted curvilinear coordinates. The explicit finite difference algorithm of MacCormack is used to solve the governing equations. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow. The code can analyze both inviscid and viscous flows with no strut, one strut, or multiple struts in the flow field. The application of the two dimensional analysis in the preliminary parametric design studies of a scramjet inlet is discussed. Detailed results are presented for one model problem and for several actual scramjet-inlet configurations.
TL;DR: In this article, a moving, deforming coordinate system (MDCS) is applied to the standard transport equation test case, and great efficiency and accuracy are obtained in early time, using no more nodes and time steps overall than during early time runs.
Abstract: Transport problems with sharp transitions or high convection often stress even the most advanced computational methods beyond feasibility limits. One promising line of attack involves transforming problems to a moving, deforming coordinate system (MDCS). Using MDCS as recently developed, one may concentrate computational attention when and where it is most appropriate, also possibly greatly reducing the effective magnitude of terms which cause trouble. In principle, MDCS may be used with finite difference, finite element, or other numerical methods, according to preference. In the particular finite element system advanced here, mesh movement may be variable in time and space, so that physically fixed boundaries may remain fixed in the transformed coordinate system. A simple finite difference system is used in time. When the method is applied to the standard transport equation test case, great efficiency and accuracy are obtained in early time. Even very steep fronts may be represented well, with no oscillations, using space and time step sizes well beyond conventional (Peclet, Courant number) constraints. More important problems are solved, involving transport over much longer times and larger spaces, when diffusion has some chance to operate and hence a parabolic model is more warranted. The same accuracy and stability are achieved as during early time, using no more nodes and time steps overall than during early time runs. This constitutes orders of magnitude savings in effort over what the application of conventional constraints would require. Relative efficiency from application of MDCS to other problems would depend on the particulars of each case.
TL;DR: In this article, the coordinate systems of each of the Galilean satellites are defined and coordinates of features seen in the Voyager pictures of these satellites are presented, and the control nets of the satellites were computed by means of single block analytical triangulations.
Abstract: The coordinate systems of each of the Galilean satellites are defined and coordinates of features seen in the Voyager pictures of these satellites are presented. The control nets of the satellites were computed by means of single block analytical triangulations. The normal equations were solved by the conjugate iterative method which is convenient and which converges rapidly as the initial estimates of the parameters are very good.
TL;DR: In this paper, the behavior of the directional singularities of a family of Weyl solutions is examined by examining the space-time in a different coordinate system, and the singular points are actually extended hypersurfaces which have been collapsed to a point by an improper choice of coordinates.
Abstract: The behavior of the directional singularities of a family of Weyl solutions is examined. By examining the space-time in a different coordinate system, the directional singularities are understood. The singular points are actually extended hypersurfaces which have been collapsed to a point by an improper choice of coordinates. The singular structure is examined in the new coordinate system. The coordinate system shows the space-time to be geodesically incomplete. A completion of the symmetry axis is described.
TL;DR: In this article, a site-centred coordinate system is considered for site-interaction molecular fluids, yielding an angle-dependent site-site correlation function Gss(r,Ω).
TL;DR: Kraitchman's method for the determination of the substitution (or r s ) coordinates of an atom in a rotating molecule (asymmetric rotor) from the two sets of three principal moments of inertia of the common isotope of the molecule and the species where the particular atom has been isotopically substituted, has been extended to include the complete coordinate transformation between the principal axis systems of both molecular species.
TL;DR: Very simple stability bounds for spinning finned missiles with spin rates well above resonance as well as for a gyroscopically stable shell are given in this article, but the motion of slowly spinning missiles should be numerically computed.
Abstract: Lloyd and Brown have shown that constant horizontal and vertical side forces and moments applied to a spinning projectile can result in dynamic instability. This instability arises from the nonlinear terms in the fixedplane coordinate system spin that appear in the equations of motion. By the use of the fixed-plane system (rather than Lloyd and Brown's nonrolling system) simpler relations can be developed, the full effects of gravity, drag and roll damping obtained, and the limitation to large gyroscopic stability factors removed. Very simple stability bounds are given for spinning finned missiles with spin rates well above resonance as well as for a gyroscopically stable shell. Exact solutions are given for finned missiles with zero spin but the motion of slowly spinning missiles should be numerically computed.
TL;DR: In this article, local coordinate systems are introduced into open sets of topological spaces, defined for the nuclear configuration space R of polyatomic nuclear systems, and the open sets are directly related to common chemical concepts, such as chemical structure, reaction mechanism, and stability of reaction paths.
Abstract: Local coordinate systems are introduced into open sets of topological spaces, defined for the nuclear configuration space R of polyatomic nuclear systems. The open sets are directly related to common chemical concepts, such as chemical structure, reaction mechanism, and stability of reaction paths. A topological model of molecules and chemical reactions is a generalization of the geometrical model, and is particularly suitable to account for the nonrigid nature of chemical structures. The coordinate neighborhoods defined on R and on its submanifolds represent the extent and natural limits for partial analyses of multidimensional potential surfaces.
Patent•
22 Dec 1981
TL;DR: In an optical digitizer, a cursor is movable on a plane surface having coordinate axis as discussed by the authors, which includes a source of light that is scanned across the coordinate system, and a detector receiving light from the angle to which the beam is instantaneously directed.
Abstract: In an optical digitizer, a cursor is movable on a plane surface having coordinate axis. The cursor includes a source of light that is scanned across the coordinate system, and a detector receiving light from the angle to which the beam is instantaneously directed. The coordinate system has curved mirrors at the origin and point spaced from the origin along the axis thereof, and plane mirrors extending along the axis. A calculator determines the position of the cursor in the coordinate system by triangulation. Alternatively, the cursor may be a curved mirror, with rotating light sources and detectors positioned at determined points in the coordinate system.
TL;DR: A method of image reconstruction from projections is described which processes the data in polar rather than rectangular coordinates and which does not require back projection.
Abstract: A method of image reconstruction from projections is described which processes the data in polar rather than rectangular coordinates and which does not require back projection. It is based on the decomposition of the object and its shadow (set of projections) into circular harmonics or radial modulators of angular Fourier components. The radial modulators of the object may be reconstructed from those of the shadow using a space-variant system which becomes space-invariant under a coordinate transformation. Experiments using digital and optical implementations are described.
TL;DR: In this paper, the problems of scattering of acoustic, electromagnetic, and elastic SH plane waves by a penetrable elliptic cylinder embedded in an infinite medium of different properties are discussed, and the solution of each problem is reduced to that of two simultaneous Fredholm integral equations of the first kind which are solved when the wave lengths in the two media are large as compared with the distance between the two foci of elliptical coordinate systems.
Abstract: We discuss here the problems of scattering of acoustic, electromagnetic, and elastic SH plane waves by a penetrable elliptic cylinder embedded in an infinite medium of different properties. Following usual Green’s function approach, the solution of each problem is reduced to that of two simultaneous Fredholm integral equations of the first kind which are solved when the wave lengths in the two media are large as compared with the distance between the two foci of elliptical coordinate systems. Approximate expressions for the external and internal fields, the farfield scattering amplitude, and the scattering cross section of the elliptic cylinder are derived.
TL;DR: In this article, an analysis has been developed to predict transonic potential flow about three-dimensional objects including inlet, duct and body geometries using finite-differences and line relaxation.
Abstract: An analysis has been developed t o predict transonic potential flow about three-dimensional objects including inlet, duct and body geometries. Finite-differences and line relaxation are used t o solve the complete potential flow equation. The coordinate system is independent of body geometry and hence places n o restrictions on body shape. Cylindrical coordinates have been used for the computer code. The analysis has been programmed for the Control Data Corporation CYBER 203 vector computer with this programming oriented t o take advantage of the vector processing capabilities of the computer. Comparisons of c o m p ~ ~ t e d results with experimental measurements are presented to verify the analysis.
01 Jan 1981
TL;DR: In this article, the authors present and collect some important classical results and concepts from the theories of tensor analysis and differential geometry, and use the presented results in devising differential models for generating coordinates in arbitrarily bounded regions.
Abstract: : The two main objectives of this monograph are, (1) to present and collect at one place some important classical results and concepts from the theories of tensor analysis and differential geometry, and (2) to use the presented results in devising differential models for generating coordinates in arbitrarily bounded regions. Though most of the discussions on tensors and differential geometry are in the context of curvilinear coordinate generation, the first two parts can profitably be used for applied problems in various branches of engineering both by students and researchers. The last part of the monograph is concerned with the development of two methods, based on differential equations, for the generation of coordinates. The selected models are based on elloptic partial differential equations which can be solved on a computer to provide smooth differentiable coordinate curves in the region of interest.