Showing papers on "Degrees of freedom published in 1985"
01 Mar 1985
TL;DR: In this article, a recursive cellular representation for configuration space is presented along with an algorithm for searching that space for collision-free paths for polygonal obstacles and a moving object with two translational and one rotational degrees of freedom.
Abstract: A recursive cellular representation for configuration space is presented along with an algorithm for searching that space for collision-free paths. The details of the algorithm are presented for polygonal obstacles and a moving object with two translational and one rotational degrees of freedom.
416 citations
01 Mar 1985
TL;DR: An iterative solution is presented that is suitable for any class of robots having rotary or prismatic joints, with any arbitrary number of degrees of freedom, including both standard and kinematically redundant robots.
Abstract: The kinematic transformation between task space and joint configuration coordinates is nonlinear and configuration dependent. A solution to the inverse kinematics is a vector of joint configuration coordinates that corresponds to a set of task space coordinates. For a class of robots closed form solutions always exist, but constraints on joint displacements cannot be systematically incorporated in the process of obtaining a solution. An iterative solution is presented that is suitable for any class of robots having rotary or prismatic joints, with any arbitrary number of degrees of freedom, including both standard and kinematically redundant robots. The solution can be obtained subject to specified constraints and based on certain performance criteria. The solution is based on a new rapidly convergent constrained nonlinear optimization algorithm which uses a modified Newton-Raphson technique for solving a system nonlinear equations. The algorithm is illustrated using as an example a kinematically redundant robot.
325 citations
TL;DR: In this article, a new plane-stress triangular element is derived using the free formulation of Bergan and Nygard, which possesses nine degrees of freedom: six corner translations and three corner normal rotations.
307 citations
TL;DR: In this paper, the relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier-Stokes attractor was investigated.
Abstract: Research on the abstract properties of the Navier–Stokes equations in three dimensions has cast a new light on the time-asymptotic approximate solutions of those equations. Here heuristic arguments, based on the rigorous results of that research, are used to show the intimate relationship between the sufficient number of degrees of freedom describing fluid flow and the bound on the fractal dimension of the Navier–Stokes attractor. In particular it is demonstrated how the conventional estimate of the number of degrees of freedom, based on purely physical and dimensional arguments, can be obtained from the properties of the Navier–Stokes equation. Also the Reynolds-number dependence of the sufficient number of degrees of freedom and of the dimension of the attractor in function space is elucidated.
213 citations
202 citations
TL;DR: In this paper, pathintegral techniques are used to study the quantum effects on the translational degrees of freedom of both liquid water at 300 K and small clustrs (n = 1,2,3) at 100 K.
114 citations
71 citations
TL;DR: Emphasis has been placed on the geometry of the resulting potential-energy hypersurface for the system as a whole to explain temperature dependence of short-range order, and to characterize bistable degrees of freedom that dominate low-temperature properties in this, and other, amorphous solids.
Abstract: Molecular-dynamics computer simulations have been carried out to study the liquid and amorphous solid states for a system comprising 120 Ni and 30 P atoms. This study utilized additive central pair potentials to model the interactions. Emphasis has been placed on the geometry of the resulting potential-energy hypersurface for the system as a whole to explain temperature dependence of short-range order, and to characterize bistable degrees of freedom that dominate low-temperature properties in this, and other, amorphous solids. A small collection of transition states and associated reaction coordinates for such degrees of freedom has been numerically constructed. The corresponding atomic motions tend to be localized mainly on a small subset of the atoms, but are diverse insofar as which chemical species are involved, in barrier height and asymmetry, and in the nonlinearity of the collective reaction coordinate.
70 citations
TL;DR: In this paper, the escape rate of an impulsive collisional (BGK) model and the Fokker-Planck frictional (Kramers) model is evaluated analytically for arbitrary potentials and any number of degrees of freedom in the low collision or low friction limit.
Abstract: The escape rate constant out of a metastable well for an impulsive collisional (BGK) model and the Fokker–Planck frictional (Kramers) model is evaluated analytically for arbitrary potentials and any number of degrees of freedom in the low collision or low friction limit. Completely statistical behavior of the collisionless dynamical system is assumed. The rate constants increase dramatically with the number of degrees of freedom. The result of the weak collision Kramers model allows us to evaluate the collision efficiency βc without adjustable parameters. It is argued that some reactions could be described by a non‐Markovian Kramers model with an appropriate number of degrees of freedom.
68 citations
TL;DR: In this article, two families of elementary one-particle potentials of n degrees of freedom which are separable in elliptical-spherical coordinates or in generalized elliptic coordinates were found.
55 citations
TL;DR: The use of a constrained-restrained least-squares procedure has proven to be extremely useful in refining macromolecular structures, especially when the initial model has severe errors.
Abstract: Publisher Summary The CORELS (COnstrained-REstrained Least-Squares) program is developed for proteins and nucleic acids to take advantage of the intrinsic rigid groups found in the molecules and to overcome the relatively low resolution of the X-ray data from their crystals. CORELS combines Scheringer's rigid groups constraints, extended to allow for variable torsion angles, with distance restraints to maintain stereochemistry between groups within a specified error limit. Even though allowing variable internal dihedral angles introduces torsional degrees of freedom within the otherwise constrained group, it can reduce the total number of structural parameters in the structure by decreasing the number of groups. The advantages of this approach include a large increase in the data-to-parameter ratio over the restrained refinement methods; automatic maintenance of group stereochemistry: within the group, all bond lengths and bond angles are constrained. The use of a constrained-restrained least-squares procedure has proven to be extremely useful in refining macromolecular structures, especially when the initial model has severe errors. This method inherently has many fewer degrees of freedom than restrained refinement procedures and therefore is applicable at extremely low resolution with a very large radius of convergence.
Patent•
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23 Sep 1985
TL;DR: In this paper, an industrial robot with six degrees of freedom and a work envelope which is substantially free of dead spaces is described. And a system is provided in which embedded microprocessors are interconnected with a signal transmitter (ST) located at the body free end and receivers fixed in their positions on the stationary base of the body.
Abstract: An industrial robot (15) is disclosed which has a flexible frame or body and is constructed so as to have six degrees of freedom and a work envelope which is substantially free of dead spaces. A free end of the body includes an end effector (27) for performing a task. To determine the position of the end effector (27) within the work envelope and to displace the end effector (27) according to the task requirements, a system is provided in which embedded microprocessors are interconnected with a signal transmitter (ST) located at the body free end (23) and receivers (R1, R2, R3) fixed in their positions on the stationary base (16) of the body. Continual monitoring of the end effector location is possible and adjustment in position may be made immediately. A remote computer linked to the microprocessors provides instructions for the operation and displacement of the robot. The degrees of freedom for the body are movement about a vertical axis, a horizontal axis and within a plane oriented so as to be in-line with the vertical axis and perpendicular to the horizontal axis. Actuating mechanisms are provided for effecting movement of the flexible body either sequentially or simultaneously about the two axes and within the plane. Movement by the flexible body within the plane is accomplished hydraulically with bladder actuators positioned along the length of the segmented body and connected for fluid communication between each other.
TL;DR: In this article, the tracking problem for a robotic manipulator with n controlled degrees of freedom and uncertain dynamics is considered, and a class of continuous feedback control is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood σ of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect σ.
Abstract: The tracking problem for a robotic manipulator withn controlled degrees of freedom and uncertain dynamics is considered. Based on the deterministic theory of Refs. 1–15 and requiring only knowledge of bounds on the system uncertainty, a classC of continuous feedback controls (adapted from Ref. 11) is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood σ of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect to σ. The theory is illustrated in a numerical example of a robot with two degrees of freedom.
19 Jun 1985
TL;DR: In this paper, a general eigenvalue assignment (EA) control problem for linear multivariable systems is formulated and solved within the framework of parametric eigenstructure assignment.
Abstract: A general eigenvalue assignment (EA) control problem for linear multivariable systems is formulated and solved within the framework of parametric eigenstructure assignment. It is shown that EA control is achievable by means of a family of classes of state feedback EA controllers. The number of classes is equal to the number of admissable Jordan forms of the closed-loop system. Each class is characterised by a specific minimum number N of free parameters (degrees of freedom) in the parametric form of the feedback gain matrix. The class of EA controllers with the greatest value of N is specified.
TL;DR: In this article, normal forms suitable for the neighbourhood of such an, instability were developed, and at this approximation, the bifurcation from the periodic orbit of a family of invariant two-dimensional tori was demonstrated.
Abstract: In an autonomous Hamiltonian system with three or more degrees of freedom, a family of periodic orbits may become unstable when two pairs of characteristic multipliers coallesce on the unit circle at points not equal to ±1, and then move off the unit circle. This paper develops normal forms suitable for the neighbourhood of such an, instability, and, at this approximation, demonstrates the bifurcation from the periodic orbit of a family of invariant two-dimensional tori. The theory is illustrated with numerical computations of orbits of the planar general three-body problem.
TL;DR: A new formulation for solving the three dimensional eddy current problem was introduced at the last COMPUMAG meeting, and a package CARMEN has since been developed, giving an indication of the possible applications of the package.
Abstract: A new formulation for solving the three dimensional eddy current problem was introduced at the last COMPUMAG meeting [1], which promised to be an optimal solution in terms of the number of degrees of freedom required. A package CARMEN has since been developed based on that formulation, and results for some test cases are presented, giving an indication of the possible applications of the package. A study of possible methodologies that could further reduce the number of degrees of freedom required in conducting regions is also included, with details of one such formulation.
01 Dec 1985
TL;DR: Grasps by a robot hand in the absence of friction shows that if the degrees of freedom of the hand are restricted to correspond to a hand built by Hanafusa and Asada, stable grips on a polygon cannot in general be achieved.
Abstract: We study grasps by a robot hand in the absence of friction. In two dimensions, a hand with three spring-loaded fingers and five degrees of freedom can achieve an equilibrium grasp on any object described by a polygon. Furthermore, the grasp is stable, that is, at a local minimum of the potential energy function defined by the springs of the fingers. In three dimensions, the hand can grasp any cylinder. In contrast, if the degrees of freedom of the hand are restricted to correspond to a hand built by Hanafusa and Asada, stable grips on a polygon cannot in general be achieved.
TL;DR: The concentration of image degrees of freedom to produce a resolution enhancement in the object reconstruction is demonstrated for suitable types of prior knowledge.
Abstract: Prior knowledge and image data are combined to produce an object reconstruction, using the best-linear-estimate technique. It is shown how this technique is related to the minimum norm method and the singular function method. How prior knowledge influences the object reconstruction is examined in detail. The concentration of image degrees of freedom to produce a resolution enhancement in the object reconstruction is demonstrated for suitable types of prior knowledge.
TL;DR: In this paper, the authors define l'existence et l'unicite des estimations du maximum de vraisemblance for la distribution d'echelle du khi-deux non center a zero degre de liberte.
Abstract: On etablit l'existence et l'unicite des estimations du maximum de vraisemblance pour la distribution d'echelle du khi-deux non centre a zero degre de liberte
TL;DR: Comments on the literature concerning the nearest-neighbour technique are offered only to prevent the confusion caused to one of us (RS) and to preclude the necessity for other workers to negotiate the tortuous path through the literature established by another (SDW).
Abstract: As noted above Thompson (1956) shows that the nearest-neighbour statistic is distributed as x2 with 2Nn degrees of freedom. Southwood (1966, 1978) states that the statistic has 2N degrees of freedom, which is only true for the first nearest-neighbour i.e. when n is 1. Wratten and Fry (1980) incorrectly use 2Nn; n relates to the 1st, 2nd, 3rd, ...nth nearest-neighbour and therefore has a considerable effect on the number of degrees of freedom and hence the interpretation of the empirically derived value of X2. These comments on the literature concerning the nearest-neighbour technique are offered only to prevent the confusion caused to one of us (RS) and to preclude the necessity for other workers to negotiate the tortuous path through the literature established by another (SDW). References
TL;DR: In this paper, the concept of structural inconsistency in systems of equations was generalized to systems in which the number of equations is not necessarily equal to that of unknowns, and efficient algorithms for detecting it are established.
Patent•
27 Feb 1985
TL;DR: In this article, a wall mounted hair dryer has an outlet for dispensing heated air which is movable to multiple positions and in multiple directions, including translational and rotational degrees of freedom.
Abstract: A wall mounted hair dryer has an outlet for dispensing heated air which is movable to multiple positions and in multiple directions. The degrees of movement include translational and rotational degrees of freedom. Translational movements are provided by the outlet itself while an extension tube may be provided to permit additional translational degrees of freedom of movement as well as a rotational degree of movement. The translational degrees of freedom of movement permit the position of the outlet to be proximate the head of the person whose hair is being dried; the rotational degree of freedom of movement permits the selection of the direction in which the heated air is directed. The person whose hair is being dried may accomplish collateral tasks as his hair is being dried.
TL;DR: A new learning algorithm is proposed that permits one to construct an 'ordered' spin glass and therefore to memorise an exponential number of hierarchically ordered images.
Abstract: Recent developments in the theory of spin glasses due to the discovery of the hierarchical structure of different degrees of freedom are used for the construction of Ising spin memory models. A new learning algorithm is proposed. This algorithm permits one to construct an 'ordered' spin glass and therefore to memorise an exponential number of hierarchically ordered images.
TL;DR: In this article, the existence of RCF for nonholonomic systems with k degrees of freedom was studied and the RCF method was shown to be applicable in a widened configuration space.
TL;DR: In this article, a method is described to analyze observed conformations for molecular fragments with more than three torsional degrees of freedom, which is an adaption of statistical cluster analysis to multidimensional, symmetric, periodic distributions of data points.
Abstract: A method is described to analyze observed conformations for molecular fragments with more than three torsional degrees of freedom. The method is an adaption of statistical cluster analysis to multidimensional, symmetric, periodic distributions of data points. Application to the molecular fragment M(PPh3)2 with eight torsional degrees of freedom reveals a model of conformational interconversion. The model implies gearing motion of the two PC3 fragments alternating with stepwise inversions of the helicities of the PPh3-propellers.
TL;DR: The physics of systems with many degrees of freedom often differs in crucial ways from what we understand for simple systems as mentioned in this paper, which is a challenge common to all areas of physics is to understand the properties of systems having large or infinite numbers of degrees offreedom in terms of known underlying interactions.
Abstract: One of the fundamental challenges common to all areas of physics is to understand the properties of systems having large or infinite numbers of degrees of freedom in terms of known underlying interactions. Simply knowing the Schrodinger equation and Coulomb's law, for example, is not sufficient to let us understand the chain through which atoms form molecules, which, in turn, beget macromolcules, which eventually aggregate into a biological object with a life of its own. Nor has knowledge of the Lagrangian for quantum chromodynamics yet yielded an understanding of hadrons. The physics of systems with many degrees of freedom often differs in crucial ways from what we understand for simple systems.