Showing papers on "Kinematics published in 1994"

A Mathematical Introduction to Robotic Manipulation

Abstract: INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

The PHANToM Haptic Interface: A Device for Probing Virtual Objects

Abstract: 1. Abstract This paper describes the PHANToM haptic interface - a device which measures a user’s finger tip position and exerts a precisely controlled force vector on the finger tip. The device has enabled users to interact with and feel a wide variety of virtual objects and will be used for control of remote manipulators. This paper discusses the design rationale, novel kinematics and mechanics of the PHANToM. A brief description of the programming of basic shape elements and contact interactions is also given.

A modal approach to hyper-redundant manipulator kinematics

Abstract: This paper presents novel and efficient kinematic modeling techniques for "hyper-redundant" robots. This approach is based on a "backbone curve" that captures the robot's macroscopic geometric features. The inverse kinematic, or "hyper-redundancy resolution," problem reduces to determining the time varying backbone curve behavior. To efficiently solve the inverse kinematics problem, the authors introduce a "modal" approach, in which a set of intrinsic backbone curve shape functions are restricted to a modal form. The singularities of the modal approach, modal non-degeneracy conditions, and modal switching are considered. For discretely segmented morphologies, the authors introduce "fitting" algorithms that determine the actuator displacements that cause the discrete manipulator to adhere to the backbone curve. These techniques are demonstrated with planar and spatial mechanism examples. They have also been implemented on a 30 degree-of-freedom robot prototype. >

Rigid Body Collisions of Planar Kinematic Chains with Multiple Contact Points

Abstract: This article deals with the rigid body collisions of planar, kinematic chains with an external surface while in contact with other surfaces. Two solution procedures that cast the impact equations in dierential and algebraic forms are developed to solve the general problem. The dierential formulation can be used to obtain three sets of solutions based on the kinematic, kinetic, and the energetic denitions of the coecient of restitution. Whereas the algebraic formulation can be used to obtain solutions based on the approaches presented in Whittaker (1904) and Brach (1990). A specic example of a planar, three-link chain with two contact points is studied to compare the outcomes predicted by each approach. A particular emphasis is placed on the energy loss that results from the application of each solution scheme. The circumstances where various methods lead to identical or distinct outcomes are investigated. Most importantly, the study elaborates on the rebounds at the non-colliding ends, a phenomenon that is observed only in multi-contact collisions. The interaction of the chain with the contact surfaces at the non-colliding contact points is examined and the dierences in the prediction of rebounds that arise from using various methods are investigated.

The agile eye: a high-performance three-degree-of-freedom camera-orienting device

Abstract: This paper presents some results obtained in the development of a three-degree-of-freedom camera-orienting device. The agile eye, as it is referred to, is capable of an orientation workspace larger than that of the human eye. The miniature camera mounted on the end-effector can be pointed within a cone of 140 degrees opening with plus or minus 30 degrees in torsion. The mechanical architecture of the orienting device is based on a spherical three-degree-of-freedom parallel manipulator which leads to high-performance dynamics. A kinematic optimization has been performed in order to determine the dimensional parameters of the prototype which would provide the best overall accuracy. A complete dynamical model of the manipulator has also been derived and programmed, and simulation results have guided the mechanical design. Finally, a prototype has been built and experimented with. >

Efficient inverse kinematics for general 6R manipulators

Abstract: In this paper, we present an algorithm and implementation for efficient inverse kinematics for a general six-revolute (6R) manipulator. When stated mathematically, the problem reduces to solving a system of multivariate equations. We make use of the algebraic properties of the system and the symbolic formulation used for reducing the problem to solving a univariate polynomial. However, the polynomial is expressed as a matrix determinant and its roots are computed by reducing to an eigenvalue problem. The other roots of the multivariate system are obtained by computing eigenvectors and substitution. The algorithm involves symbolic preprocessing, matrix computations and a variety of other numerical techniques. The average running time of the algorithm, for most cases, is 11 milliseconds on an IBM RS/6000 workstation. This approach is applicable to inverse kinematics of all serial manipulators. >

Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator

Abstract: The goal of this paper is to present experimental results on the implementation of the damped least-squares method for the six-joint ABB IRb2000 industrial robot manipulator. A number of inverse kinematics schemes are reviewed which allow robot control through kinematic singularities. The basic scheme adopts a damped least-squares inverse of the manipulator Jacobian with a varying damping factor acting in the neighborhood of singularities. The effect of a weighted damped least-squares solution is investigated to provide user-defined accuracy capabilities along prescribed end-effector space directions. An online estimation algorithm is employed to measure closeness to singular configurations. A feedback correction error term is introduced to ensure algorithm tracking convergence and its effect on the joint velocity solution is discussed. Computational aspects are discussed in view of real-time implementation of the proposed schemes. Experimental case studies are developed to investigate manipulator performance in the case of critical end-effector trajectories passing through and near the shoulder and wrist singularities of the structure. >

Biomechanical relationship between center of gravity and center of pressure during standing

Abstract: The relationship between the position of a body's center of gravity (CG) as determined by a whole body kinematic model and that given by 3 CG position estimation techniques using the ground reaction force center of pressure (CP) has been investigated in this study. The CG and CP are related by the Newtonian mechanics equations of motion. Data required to determine directly the center of gravity position, a key variable in posture and locomotion, are usually not obtained in posture or gait trials; rather, force plate data and center of pressure data are often obtained. Consequently, previous studies have developed estimations of CG position history from CP data. The results of 3 CP-based CG estimations methods are here compared with kinematically determined CG positions in humans. The CP position varies about the CG position and has a higher frequency content than the motion of the CG. This observation, based on the authors' data and mechanics theory, provides the basis for the methods considered in this study. All current methods employ a filtering technique to obtain CG position from CP position time histories during standing trials. In most cases the mean square error is less than 0.1 cm/sup 2/. Finite-duration impulse response filters with periods of 1.0 s to 1.50 s gave the best results when compared with the CG position based on kinematic data. A low-pass filter with cutoff frequency of 0.4 Hz to 0.5 Hz provides the best comparison for this approximation method. The accuracy of the methods diminishes as more dynamics are introduced to the trial. The average mean square differences for walking-in-place trials is from 1 to 10 times greater than that for the standing. CG position estimates from CP data must be interpreted cautiously when nonstatic tasks are monitored, especially in unstable patients. >

Proprioceptive coordination of movement sequences: role of velocity and position information

Abstract: 1. Recent studies have shown that the CNS uses proprioceptive information to coordinate multijoint movement sequences; proprioceptive input related to the kinematics of one joint rotation in a move...

Kinematic Dexterity of Robotic Mechanisms

Abstract: In this article we develop a mathematical theory for optimizing the kinematic dexterity of robotic mechanisms and obtain a collection of analytical tools for robot design. The performance criteria we consider are workspace volume and dexterity; by the latter we mean the ability to move and apply forces in arbitrary directions as easily as possible. Clearly, dexterity and workspace volume are intrinsic to a mechanism, so that any mathematical formulation of these properties must necessarily be independent of the particular coordinate representation of the kinematics.By regarding the forward kinematics of a mechanism as defining a mapping between Riemannian manifolds, we apply the coordinate-free language of differential geometry to define natural measures of kinematic dexterity and workspace volume. This approach takes into account the geometric and topolog ical structures of the joint and workspaces. We show that the functional associated with harmonic mapping theory provides a natural measure of the kine...

A search for consensus among model parameters reported for the PUMA 560 robot

Abstract: The PUMA 560 robot is the white rat of robotics research - it has been studied and used in countless experiments over many years and in many laboratories. However, it remains a challenge to assemble the complete data needed for model-based control of the robot. This paper presents a numerical comparison of kinematic, dynamic and electrical parameters for the PUMA 560 robot which have been reported in the literature. For the first time, data from several experiments are presented in a single system of coordinates, which facilitates comparison. Differences in the data and the various methods of measurement are discussed. New data have been gathered and are presented where the record was incomplete. >

Interactive system for simulation and display of multi-body systems in three dimensions

Abstract: Method and apparatus for simulating a multibody system on a computer. The invention provides for inputting into the computer a mathematical description of each body in the multibody system, specifying into the computer a force to act on one of the bodies, formulating a Jacobian matrix, solving kinematics constraints in the computer, graphically displaying a result of the solution of the kinematic constraints from the computer onto an electronic display, whereupon the user can interactively input a change to the multibody system into the computer and graphically display a result of the change to the multibody system from the computer.

Resolving manipulator redundancy under inequality constraints

Abstract: Due to hardware limitations, physical constraints such as joint rate bounds, joint angle limits, and joint torque constraints always exist. In this paper, these constraints are considered in the general formulation of the redundant inverse kinematic problem. To take these physical constraints into account, the computationally efficient compact quadratic programming (QP) method is formed to resolve the constrained kinematic redundancy problem. In addition, the compact-inverse QP method is also formulated to remedy the inescapable singularity problem with inequality constraints. Two examples are given to demonstrate the generality and superiority of these two methods: to eliminate the drift phenomenon caused by self motion and to remedy saturation-type nonlinearity problems. >

Orienting the finger opposition space during prehension movements.

Abstract: Two experiments are reported that examined the act of prehension when subjects were asked to grasp with their thumb and index finger pads an elongated object resting horizontally on a surface and placed at different orientations with respect to the subject. In Experiment 1, the pad opposition preferences were determined for the six angles of orientation examined. For angles of 90 degrees (object parallel to frontal plane) or less, no rotation of the wrist (pronation) was used; for angles 110 degrees or greater, pronation was systematically employed to reorient the finger opposition space. Only one angle, 100 degrees , produced any evidence of ambiguity in how to grasp the object: Approximately 60% of these grasps involved pronation and 40% did not. Using the foregoing grasp preference data, in Experiment 2 we examined the kinematics of the wrist and elbow trajectories during prehension movements directed at an object in different orientations. Movement time, time to peak acceleration, velocity, and deceleration were measured. No kinematic differences were observed when the object orientation either required (110 degrees ) or did not require (80 degrees ) a pronation. By contrast, if the orientation was changed at the onset of the movement, such that an unpredicted pronation had to be introduced to achieve the grasp, kinematics were affected: Movement time was increased, and the time devoted to deceleration was lengthened. These data are interpreted as evidence that when natural prehension occurs, pronation can be included in the motor plan without affecting the movement kinematics. When constraints are imposed on the movement execution as a consequence of a perturbation, however, the introduction of a pronation component requires kinematic rearrangement.

Four-bar linkage prosthetic knee mechanisms: Kinematics, alignment and prescription criteria

Abstract: Introduction Four-bar linkage knee mechanisms for the trans-femoral amputee are widely available, but although they may offer functional advantages to certain amputees, they are fitted in a limited number of cases. It may be assumed that one reason for this is that persons responsible for prescription and fitting may not be familiar with the kinematic characteristics and possible advantages of such mechanisms and are reluctant to use a device which they do not understand completely. This paper will describe the kinematics of several types of four-bar mechanisms, and discuss the differences and prescription criteria for three different classes of four-bar linkage mechanisms currently available for fitting to amputees. Before beginning the discussion of four-bar prosthetic knees, it will be helpful to review some fundamental concepts.

A Biomechanical Analysis of the Last Stride, Touchdown, and Takeoff Characteristics of the Men's Long Jump

Abstract: This study was concerned with the measurement of performance variables from competitors in the men's long jump final of the World Student Games held in Sheffield, England, in July 1991. Several performances of 10 finalists were recorded on cine film at 100 Hz. Resulting sagittal plane kinematic data were obtained for the last stride, touchdown, and takeoff for a total of 27 jumps. It was confirmed that takeoff velocity was a function of touchdown velocity, and that there was an increase in vertical velocity at the expense of a reduction of horizontal velocity. It was concluded that there was evidence for mechanisms which may be termed mechanical, biomechanical, and muscular. The former relates to the generation of vertical velocity by the body pivoting over the base of support during the compression phase, and a lifting of the arms and free leg during the lift phase; the second is the elastic reutilization of energy; and the third is the contribution by concentric muscular contraction.

On a Representation of Friction in Configuration Space

Abstract: This article provides a geometric representation of friction for a rigid planar part with two translational and one rotational degrees of freedom. The article constructs a generalized friction cone by imbedding into the part's configuration space the force constraints that define the classic Coulomb friction cone in real space. The resulting representation provides a simple geometric method for determining the possible motions of a part subjected to an applied force and torque. The representation has been used both for simulating part motions and for planning assem bly operations. The approach generalizes to the six-dimensional configuration space of a three-dimensional part.

Calibration of a parallel robot using multiple kinematic closed loops

Abstract: A method is presented for autonomous kinematic calibration of a 3-DOF redundant parallel robot. Multiple closed loops are used in a least squares optimization method. Ill-conditioning, column scaling of the gradient matrix, and observability indices for the best pose set of robot calibration configurations are discussed. Experimental results are presented and compared with the results using an external calibration device. >

Multisensory Training of Standing Balance in Older Adults: II. Kinematic and Electromyographic Postural Responses

Abstract: BACKGROUND The purpose of this study was to analyze the electromyographic and kinematic characteristics of postural responses of 24 healthy older adults both prior to and immediately after a multisensory balance training period. It was hypothesized that the muscle and movement characteristics of postural responses would be optimized in the group after training. METHODS Balance was tested by determining muscle and kinematic response characteristics used in compensating for support surface displacements. Twenty-four subjects were randomly assigned to a training group or a control group. The training group received a multisensory balance training program during a 15-day training period (described in the companion article). RESULTS The results showed that the training (a) significantly shortened the onset latency of the neck flexor muscle (p < .05); (b) showed a trend toward decreasing the response frequency of antagonist muscles; (c) showed a trend toward increasing the response frequency of the trunk flexor muscles; and (d) showed a trend toward decreasing the maximal excursion of the first-trial of the ankle joint rotation. CONCLUSIONS From these results and those of the companion article, it was concluded that the multisensory balance training program had an effect in optimizing the muscle and movement characteristics of postural response in the training group older adults.

Singularity analysis of mechanisms and robots via a velocity-equation model of the instantaneous kinematics

Abstract: This paper presents a new generalized approach to the singularity analysis of a general mechanism (arbitrary kinematic chain), considered as a non-redundant input-output device with equal number of inputs and outputs. The instantaneous kinematics of a mechanism is described by means of a velocity equation, explicitly including not only the input and output velocities but also the passive-joint velocities. A precise definition of singularity of a general mechanism is provided. On the basis of the six types of singular configurations introduced in the paper singularity classifications are proposed. >