Showing papers on "Degrees of freedom published in 1990"

On Ranking Opportunity Sets in Terms of Freedom of Choice

Abstract: The paper explores the notion of freedom of choice which is of considerable importance in welfare economics and the theory of social choice. Three plausible axioms are introduced for ranking alternative opportunity sets in terms of the degrees of freedom that they offer to the agent making choices. It is shown that, under these axioms, judgements about degrees of freedom of choice have to be based on the naive principle of simply counting the number of available options.

A robust quadrilateral membrane finite element with drilling degrees of freedom

Abstract: A quadrilateral membrane finite element with drilling degrees of freedom is derived from variational principles employing an independent rotation field. Both displacement based and mixed approaches are investigated. The element exhibits excellent accuracy characteristics. When combined with a plate bending element, the element provides an efficient tool for linear analysis of shells.

Force reflecting hand controller

Abstract: A universal input device for interfacing a human operator with a slave machine such as a robot or the like includes a plurality of serially connected mechanical links extending from a base. A handgrip is connected to the mechanical links distal from the base such that a human operator may grasp the handgrip and control the position thereof relative to the base through the mechanical links. A plurality of rotary joints is arranged to connect the mechanical links together to provide at least three translational degrees of freedom and at least three rotational degrees of freedom of motion of the handgrip relative to the base. A cable and pulley assembly for each joint is connected to a corresponding motor for transmitting forces from the slave machine to the handgrip to provide kinesthetic feedback to the operator and for producing control signals that may be transmitted from the handgrip to the slave machine. The device gives excellent kinesthetic feedback, high-fidelity force/torque feedback, a kinematically simple structure, mechanically decoupled motion in all six degrees of freedom, and zero backlash. The device also has a much larger work envelope, greater stiffness and responsiveness, smaller stowage volume, and better overlap of the human operator's range of motion than previous designs.

Solving Maxwell equations in a closed cavity, and the question of 'spurious modes'

Abstract: It is pointed out that for a closed cavity should not be solved by the 'vectorial' analog of the classical finite-element method (that is, with node-based finite elements). It is suggested that there are good reasons to use edge-elements instead. Such elements (whose degrees of freedom correspond to the edges of the mesh, not its nodes) not only guarantee the right kind of continuity for fields like h and e, but also prevent the appearance of unwanted, unphysical divergent solutions in the problem of eigenmodes, the so-called spurious modes. >

Solving geometric constraint systems

Abstract: Finding the configurations of a set of rigid bodies that satisfy a set of geometric constraints is a problem traditionally solved by reformulating the geometry and constraints as algebraic equations which are solved symbolically or numerically But many such problems can be solved by rea soning symbolically about the geometric bodies themselves using a new technique called degrees of freedom analysis In this approach, a sequence of actions is devised to satisfy each constraint incrementally, thus monotonically decreasing the system's remaining degrees of freedom This sequence of actions is used metaphorically to solve, in a maximally decoupled form, the equations resulting from an algebraic representation of the problem Degrees of freedom analysis has significant computational advantages over conventional algebraic approaches The utility of the technique is demonstrated with a program that assembles and kinematically simulates mechanical linkages

Correlation between the energy and structure of grain boundaries in b.c.c. metals. II. Symmetrical tilt boundaries

Abstract: The correlation between the structure and zero-temperature energy of symmetrical tilt grain boundaries (STGBs) in b.c.c. metals is investigated using a many-body potential of the Finnis-Sinclair type for Mo and Johnson's pair potential spline-fitted for α-Fe. As in free surfaces, the misorientation phase space associated with these simple planar defects consists of only two macroscopic degrees of freedom, namely those defining the grain-boundary (GB) plane normal. In a novel approach, the two-dimensional phase space is investigated in terms of a stereographic triangle and not in terms of the usual three parameters associated with the boundary misorientation. A comparison with similar calculations for free surfaces demonstrates the importance of the translational (microscopic) degrees of freedom in grain boundaries, while the comparison with STGBs in f.c.c. metals elucidates the important role played by the GB plane.

Efficient gradient projection optimization for manipulators with multiple degrees of redundancy

Abstract: An efficient gradient projection optimization scheme is presented for manipulators with multiple degrees of redundancy. This is an extension of the gradient projection scheme presented by R.B. Dubey et al. (Proc. IEEE Int. Conf. on Robotics and Automation, p.28-36, 1989) for manipulators with one degree of redundancy. The feasibility and effectiveness of this scheme are tested through simulations of the seven-degree-of-freedom NASA Laboratory Telerobotic Manipulator (LTM). Only the position of the LTM end effector is controlled, which requires only three degrees of freedom. The remaining joints, except for the wrist roll joint, which does not contribute to the end-effector linear velocity, provide three degrees of redundancy. >

Decentralized continuous robust controller for mobile robots

Abstract: A composite system model for the wheeled mobile robot is proposed. The overall system can be thought of as a composite of two subsystems; one is the vehicle with m degrees of freedom, and the other is the robot arm with n degrees of freedom. The interconnections between them are unknown interactive forces. To overcome the effects of the unknown interactive forces and some mismatches between the estimated parameter values and the actual ones, a decentralized continuous robust controller is proposed. Conditions are derived for stability when the interconnections are not known. The theoretical analysis and computer simulation results show that the performance of the continuous robust controller is much better than that of the nonrobust controller. An interesting conclusion is that one can choose arbitrarily large weighting gains to decrease the trajectory errors without increasing the magnitude of the physical control torques. >

A five degrees of freedom analysis of vibrations in precision spindles

Abstract: This paper outlines a five degrees of freedom model of a rigid shaft supported by a pair of angular contact ball bearings. The model simulates an existing precision grinding machine tool spindle. It enables the study of various loading arrangements to be carried out.

Self-organized criticality

Abstract: Dissipative dynamical systems with many degrees of freedom naturally evolve to a critical state with fluctuations extending over all length- and time-scales. It is suggested, and supported by simulations on simple toy-model systems, that turbulence, earthquakes, “1/f” noise, and economics may operate at the self-organized critical state.

Lagrangian Formulation of the Equations of Motion for Elastic Mechanisms With Mutual Dependence Between Rigid Body and Elastic Motions: Part I—Element Level Equations

Abstract: Equations of motion are derived using Lagrange's equation for elastic mechanism systems. The elastic links are modeled using the finite element method. Both rigid body degrees of freedom and the elastic degrees of freedom are considered as generalized coordinates in the derivation

A system of one dimensional balls with gravity

Abstract: We introduce a Hamiltonian system with many degrees of freedom for which the nonvanishing of (some) Lyapunov exponents almost everywhere can be established analytically.

Symmetrically actuated double pointing systems: the basis of singularity-free robot wrists

Abstract: An analysis is conducted of symmetrically actuated double pointing systems, which are two spherical pointing systems connected serially with a common center. The double pointing systems have four degrees of freedom interrelated by two constraint functions, reducing the systems to two independent degrees of freedom. Together, these constraint functions result in a symmetry in the motion of corresponding links in each pointing system of the double system. A singularity analysis is presented of a generalized symmetrically actuated double pointing system in order to prove that it and the systems derived from it have maximal singularity-free workspaces. Closed-form solutions to the inverse position and velocity problems are presented along with different types of kinematic arrangements. Any of the double pointing systems presented can serve as the basis of a singularity-free wrist. >

Dimensional analysis of the waking EEG

Abstract: The theory of nonlinear systems has become increasingly useful and relevant to the study of empirical dynamics. When a system produces irregularity in one or more of its variables, it is of interest whether this behavior results from randomness (meaning that the number of degrees of freedom is infinite) or whether a finite, and possibly small, number of degrees of freedom has produced the chaos (meaning that the system is deterministic). Our understanding of deterministic systems was greatly enhanced when Lorenz (1963) discovered that a simple system with as few as three differential equations can generate totally irregular fluctuations of the system’s variables — a phenomenon nowadays generally referred to as deterministic chaos. The prominent features of chaos are unpredictability over extended time periods, and sensitive dependence on initial conditions. Once started with specific initial values, the system’s future might be totally different from what it would have been if it had been started under slightly different initial conditions. Chaos may not be the ultimate description for a system’s irregular dynamic. As outlined by Rossler (1983), more complex structures “beyond chaos” may await discovery.

Reducing uncertainty of objects by robot pushing

Abstract: A sensorless manipulation task eliminating geometrical uncertainty is proposed. It involves a two-fingered tool attached to a robot end effector. The object is assumed to be a convex polyhedron, although this assumption is later relaxed. Assuming that position and orientation are approximately known prior to operation, the initial position of the tool and the direction of movement are chosen. As the tool advances it strikes the object. If the trajectory is chosen properly, the fingers will contact the object with its corner between them. It is shown that such a configuration of contact points uniquely constrains the position of an object in all degrees of freedom. >

Time-scales and degrees of freedom operating in the evolution of continental ice-sheets

Abstract: Comprehensible explanations of the operation of earth climate systems should consist of descriptions of the operation of a few degrees of freedoms. Qualitative interpretations of results from large-scale numerical models generally follow this principle, but do not render formal definitions of the precise nature of such degrees of freedom.At its simplest, ice-sheet kinematics requires knowledge of the evolving height and span. Rheology and surface mass-balance impose different requirements upon the co-evolution of these variables, meaning a two-degree of freedom model is over-prescribed. By means of a perturbation expansion about the analytic similarity solution for viscous spreading, eigenfunctions corresponding to degrees of freedom in the ice-sheet profile are obtained, and are used to decompose mass-balance distributions. Only a few eigenfunctions are needed to replicate numerical models, implying that ice-sheets in plane flow may operate with fewer than ten degrees of freedom.Unstable evolution of ice-sheets can occur, when the operation of a very large number of degrees of freedom can be manifested. Previous work is reviewed and new results for the unstable transformation of valley glaciers into ice-sheets are presented. Phasing of initiation may be an unpredictable phenomenon.

Chapter 2 Control of Human Jaw and Multi-Joint Arm Movements

Abstract: We present models based on the equilibrium point (EP) hypothesis for planar human jaw and arm movements. According to this hypothesis, central commands control the EP of the system by setting motoneuron recruitment thresholds (λs). In multiple muscle systems, these commands control the λs of many muscles in concert. We posit basic central commands which control specific motor functions via various combinations of λs. One command is associated with the level of co-activation of all muscles and other commands are associated with motions in specific degrees of freedom. Both models include two degrees of freedom either distributed across joints (arm) or located at a single joint (jaw). We suggest that arm motions are planned in equilibrium coordinates corresponding to the position of the hand in space whereas jaw motions are planned in equilibrium coordinates associated with rotation and translation of the jaw. In both cases, we argue that the nervous system need only specify the direction and rate of change of the EP (i.e., equilibrium velocity vector). In the absence of special constraints, we propose that the EP is simply, shifted at a constant velocity. We show that the models can, account for experimental kinematic and electrornyographic records, in speech, mastication, and reaching movements.

Quantum stochastic flows with infinite degrees of freedom and countable state Markov processes

Abstract: Quantum stochastic flows are constructed for infinite degrees of freedom. The theory is then used to show that a classical countable state Markov process can be looked upon as one such commutative stochastic flow.

Higher Order Elements and Element Enhancement by Combined Regular and Hypersingular Boundary Integral Equations

Abstract: The direct, collocation boundary element method is used with both the regular and tangent derivative equation to formulate boundary elements with additional degrees of freedom. Use of the tangent derivative equation allows collocation at the same nodes as the regular constraint equation when the derivatives are continuous at the collocation points. Nonconforming elements with degrees of freedom corresponding to tangent derivatives of the primary function are introduced into both equations through Hermitian shape functions. The formulation is given for potential problems in two dimensions with a verification example.

MUSE - a systolic array for adaptive nulling with 64 degrees of freedom, using Givens transformations and wafer-scale integration. Technical report

Abstract: This report describes an architecture for a highly parallel system of computational processors specialized for real-time adaptive antenna nulling computations with many degrees of freedom, which we call MUSE (Matrix Update Systolic Experiment), and a specific realization of MUSE for 64 degrees of freedom. Each processor uses the CORDIC algorithm and has been designed as a single integrated circuit. Ninety-six such processors working together can update the 64-element nulling weights based on 300 new observations in only 6.7 milliseconds. This is equivalent to 2.88 Giga-ops for a conventional processor. The computations are accurate enough to support 50 decibel of signal-to-noise improvement in a sidelobe canceller. The connectivity between processors is quite simple and permits MUSE to be realized on a single large wafer, using restructurable VLSI (Very Large Scale Integration). The complete design of such a wafer is described.

Realtime tracking in five degrees of freedom using two writs-mounted laser range finders

Abstract: The results of experiments in real-time tracking of moving objects using wrist-mounted sensors are presented. Two laser range finders were mounted orthogonal to each other on the wrist of a six-degree-of-freedom PUMA robot. The objective is to have the robot end-effector maintain a constant position and orientation with respect to a flat object moving in 3D space in the field of view of the range finders. Sensory feedback from the range finders is used to servocontrol the robot such that its trajectory is similar to that of the moving object in five degrees of freedom. The algorithms for this application are implemented in C and run on four Motorola MC68020 processors with the Harmony operating system. Tracking is done with maximum linear and angular speeds of the target object being 25 cm/s and 0.5 rad/s, respectively. The robot is capable of maintaining the required pose with respect to the object at these speeds with a small lag due to data-collection time. The acceleration/deceleration and the maximum speed of the robot trajectory are varied depending on the speed of the moving object being tracked to yield different tracking behaviors. A performance study of the tracking experiment is presented. >

A technique for motion specification in computer animation

Abstract: A technique is discussed for the interactive specification and real-time evaluation of the movements of geometrical objects with several degrees of freedom. The technique is a midway between a faithful simulation of the dynamics and kinematics of the object and completely free user control, and as such it is well suited for animated drawings, for example. The method works in two steps: first, the motion of a relevant subobject (the skeleton) is specified interactively in real time. Next, the entire object is deformed and oriented in space such as to match the form of the skeleton. Depending on the complexity of the object, this second step either takes place in real time, or as a batch process. Several forms of geometrical constraints, as well as stretching and squeezing, are supported.

On the Computation of Non-Central Chi-Square Distribution Function

Abstract: The cumulative distribution function of the non-central chi-square is very important in calculating the power function of some statistical tests. On the other hand it involves an integral which is difficult to obtain. In literature some workers discussed the evaluation and the approximation of the c.d.f. of the non-central chi-square [see references (2)]. In the present work two computational formulae for computing the cumulative distribution function of the non-central chi-square distribution are given, the first one deals with the case of any degrees of freedom (odd and even), and the second deals with the case of odd degrees of freedom. Numerical illustrations are discussed.

Toward planning and control of highly redundant manipulators

Abstract: An approach to the path planning of redundant robot manipulators has been developed by exploring paths for a completely flexible manipulator having an infinite number of degrees of freedom. The idealized manipulator is called a continuous curvature model. It is controlled by changing its curvature. The major advantage of the approach is that the complexity of path planning is dependent only on the complexity of the environment, not on the number of degrees of freedom of actual manipulators. A new architecture is not required to map the solutions obtained for the continuous curvature model. A manipulator with 12 ball joints has been chosen as a target hardware architecture and the solution obtained for the continuous curvature model has been mapped to the manipulator, its dynamic simulation has been successfully performed. >