Showing papers on "Kinematics published in 1990"

Biomechanics and Motor Control of Human Movement

Abstract: Preface to the Fourth Edition. 1 Biomechanics as an Interdiscipline. 1.0 Introduction. 1.1 Measurement, Description, Analysis, and Assessment. 1.2 Biomechanics and its Relationship with Physiology and Anatomy. 1.3 Scope of the Textbook. 1.4 References. 2 Signal Processing. 2.0 Introduction. 2.1 Auto- and Cross-Correlation Analyses. 2.2 Frequency Analysis. 2.3 Ensemble Averaging of Repetitive Waveforms. 2.4 References. 3 Kinematics. 3.0 Historical Development and Complexity of Problem. 3.1 Kinematic Conventions. 3.2 Direct Measurement Techniques. 3.3 Imaging Measurement Techniques. 3.4 Processing of Raw Kinematic Data. 3.5 Calculation of Other Kinematic Variables. 3.6 Problems Based on Kinematic Data. 3.7 References. 4 Anthropometry. 4.0 Scope of Anthropometry in Movement Biomechanics. 4.1 Density, Mass, and Inertial Properties. 4.2 Direct Experimental Measures. 4.3 Muscle Anthropometry. 4.4 Problems Based on Anthropometric Data. 4.5 References. 5 Kinetics: Forces and Moments of Force. 5.0 Biomechanical Models. 5.1 Basic Link-Segment Equations-the Free-Body Diagram. 5.2 Force Transducers and Force Plates. 5.3 Bone-on-Bone Forces During Dynamic Conditions. 5.4 Problems Based on Kinetic and Kinematic Data. 5.5 References. 6 Mechanical Work, Energy, and Power. 6.0 Introduction. 6.1 Efficiency. 6.2 Forms of Energy Storage. 6.3 Calculation of Internal and External Work. 6.4 Power Balances at Joints and Within Segments. 6.5 Problems Based on Kinetic and Kinematic Data. 6.6 References. 7 Three-Dimensional Kinematics and Kinetics. 7.0 Introduction. 7.1 Axes Systems. 7.2 Marker and Anatomical Axes Systems. 7.3 Determination of Segment Angular Velocities and Accelerations. 7.4 Kinetic Analysis of Reaction Forces and Moments. 7.5 Suggested Further Reading. 7.6 References. 8 Synthesis of Human Movement-Forward Solutions. 8.0 Introduction. 8.1 Review of Forward Solution Models. 8.2 Mathematical Formulation. 8.3 System Energy. 8.4 External Forces and Torques. 8.5 Designation of Joints. 8.6 Illustrative Example. 8.7 Conclusions. 8.8 References. 9 Muscle Mechanics. 9.0 Introduction. 9.1 Force-Length Characteristics of Muscles. 9.2 Force-Velocity Characteristics. 9.3 Muscle Modeling. 9.4 References. 10 Kinesiological Electromyography. 10.0 Introduction. 10.1 Electrophysiology of Muscle Contraction. 10.2 Recording of the Electromyogram. 10.3 Processing of the Electromyogram,. 10.4 Relationship between Electromyogram and Biomechanical Variables. 10.5 References. 11 Biomechanical Movement Synergies. 11.0 Introduction. 11.1 The Support Moment Synergy. 11.2 Medial/Lateral and Anterior/Posterior Balance in Standing. 11.3 Dynamic Balance during Walking. 11.4 References. APPENDICES. A. Kinematic, Kinetic, and Energy Data. Figure A.1 Walking Trial-Marker Locations and Mass and Frame Rate Information. Table A.1 Raw Coordinate Data (cm). Table A.2( a ) Filtered Marker Kinematics-Rib Cage and Greater Trochanter (Hip). Table A.2( b ) Filtered Marker Kinematics-Femoral Lateral Epicondyle (Knee) and Head of Fibula. Table A.2( c ) Filtered Marker Kinematics-Lateral Malleolus (Ankle) and Heel. Table A.2( d ) Filtered Marker Kinematics-Fifth Metatarsal and Toe. Table A.3( a ) Linear and Angular Kinematics-Foot. Table A.3( b ) Linear and Angular Kinematics-Leg. Table A.3( c ) Linear and Angular Kinematics-Thigh. Table A.3( d ) Linear and Angular Kinematics-1/2 HAT. Table A.4 Relative Joint Angular Kinematics-Ankle, Knee, and Hip. Table A.5( a ) Reaction Forces and Moments of Force-Ankle and Knee. Table A.5( b ) Reaction Forces and Moments of Force-Hip. Table A.6 Segment Potential, Kinetic, and Total Energies-Foot, Leg, Thigh, and1/2 HAT. Table A.7 Power Generation/Absorption and Transfer-Ankle, Knee, and Hip. B. Units and Definitions Related to Biomechanical and Electromyographical Measurements. Table B.1 Base SI Units. Table B.2 Derived SI Units. Index.

Singularity analysis of closed-loop kinematic chains

Abstract: The different kinds of singularities encountered in closed-loop kinematics chains are analyzed. A general classification of these singularities in three main groups, which is based on the properties of the Jacobian matrices of the chain, is described. The identification of the singular configurations is particularly relevant for hard automation modules or robotic devices based on closed kinematic chains, such as linkages and parallel manipulators. Examples are given to illustrate the application of the method to these mechanical systems. >

Head stabilization during various locomotor tasks in humans. I. Normal subjects.

Abstract: Head kinematics were studied in ten normal subjects while they executed various locomotor tasks The movement of the body was recorded with a video system which allowed a computer reconstruction of motion of joint articulations and other selected points on the body in three dimensions Analyses focus on head translation along the vertical axis and rotation in the sagittal plane This was done by recording the displacement of a line approximating the plane of horizontal semi-circular canals (the Frankfort plane: F-P) Four conditions were studied: free walking (W) walking in place (WIP) running in place (R) and hopping (H) In the 4 experimental conditions, amplitude and velocity of head translation along the vertical axis ranged from 1 cm to 25 cm and 015 m/s to 18 m/s In spite of the disparities in the tasks regarding the magnitude of dynamic components, we found a significant stabilization of the F-P around the earth horizontal Maximum amplitude of F-P rotation did not exceed 20° in the 4 situations Vertical angular velocities increased from locomotion tasks to the dynamic equilibrium task although the maximum values remained less than 140°/s Predominant frequencies of translations and rotations in all the tasks were within the range 04–35 Hz and harmonics were present up to 6–8 Hz During walking in darkness, mean head position is tilted downward, with the F-P always below the earth horizontal Darkness did not significantly influence the amplitude and velocity of head angular displacement during W, WIP and R, but during H the amplitude decreased by 37% Residual head angular displacement is found to compensate for head translation during the 4 conditions Our study emphasizes the importance of head stabilization as part of the postural control system and described as a basis for inertial guidance

Introduction to Theoretical Kinematics

Abstract: "Introduction to Theoretical Kinematics" provides a uniform presentation of the mathematical foundations required for studying the movement of a kinematic chain that makes up robot arms, mechanical hands, walking machines, and similar mechanisms It is a concise and readable introduction that takes a more modern approach than other kinematics texts and introduces several useful derivations that are new to the literature The author employees a unique format, highlighting the similarity of the mathematical results for planar, spherical, and spatial cases by studying them all in each chapter rather than as separate topics For the first time, he applies to kinematic theory two tools of modern mathematics--the theory of multivectors and the theory of Clifford algebras--that serve to clarify the seemingly arbitrary nature of the construction of screws and dual quaternions The first two chapters formulate the matrices that represent planar, spherical, and spatial displacements and examine a continuous set of displacements which define a continuous movement of a body, introducing the "tangent operator" Chapter 3 focuses on the tangent operators of spatial motion as they are reassembled into six-dimensional vectors or screws, placing these in the modern setting of multivector algebra Clifford algebras are used in chapter 4 to unify the construction of various hypercomplex "quaternion" numbers Chapter 5 presents the elementary formulas that compute the degrees of freedom, or mobility, of kinematic chains, and chapter 6 defines the structure equations of these chains in terms of matrix transformations The last chapter computes the quaternion form ofthe structure equations for ten specific mechanisms These equations define parameterized manifolds in the Clifford algebras, or "image spaces," associated with planar, spherical, and spatial displacements McCarthy reveals a particularly interesting result by showing that these parameters can be mathematically manipulated to yield hyperboloids or intersections of hyperboloids

Kinematic control of redundant robot manipulators: A tutorial

Abstract: In this paper, we present a tentatively comprehensive tutorial report of the most recent literature on kinematic control of redundant robot manipulators. Our goal is to lend some perspective to the most widely adopted on-line instantaneous control solutions, namely those based on the simple manipulator's Jacobian, those based on the local optimization of objective functions in the null space of the Jacobian, those based on the task space augmentation by additional constraint tasks (with task priority), and those based on the construction of inverse kinematic functions.

A global human walking model with real-time kinematic personification

Abstract: Presents a human walking model built from experimental data based on a wide range of normalized velocities. The model is structured on two levels. On the first level, global spatial and temporal characteristics are generated. On the second level, a set of parameterized trajectories produce both the position of the body in space and the internal body configuration. This is performed for a standard structure and an average configuration of the human body. The experimental context corresponding to the model is extended by allowing a continuous variation of global spatial and temporal parameters according to the motion rendition expected by the animator. The model is based on a simple kinematic approach designed to keep the intrinsic dynamic characteristics of the experimental model. Such an approach also allows a personification of the walking action in an interactive real-time context in most cases. A correction automata of such motion is then proposed

Mechanics of Forward Flight in Bumblebees: I. Kinematics and Morphology

Abstract: Using high-speed cinematography, bumblebees in free flight were filmed over a range of forward airspeeds. A detailed description of the wing tip and body kinematics was obtained from a three-dimensional reconstruction of the twodimensional film image. A technique for determining quantitatively the angle of attack of the wing was developed. Kinematic parameters found to vary consistently with airspeed were body angle, stroke plane angle, geometrical angle of attack, and rotational angles of the wings at the ends of half-strokes. Results of a morphological analysis of the wings and bodies of thoseinsects filmed in free flight are presented for use in later calculations of the lift and power requirements of forward flight.

DELTA: a simple and efficient parallel robot

Abstract: The DELTA parallel robot, designed by an EPFL (Ecole Polytechnique Federale de Lausanne) research team, is a mechanical structure which has the advantage of parallel robots and ease of serial robots modeling. This paper presents solutions for a complete modeling of the DELTA parallel robot (direct and inverse kinematics, inverse statics, inverse dynamics), with few arithmetic and trigonometric operations. Our method is based on a satisfactory choice of kinematic parameters and on a few restricting hypotheses for the static and dynamic models. We give some details of each model, we present some computation results and we put the emphasis on some particular points, showing the capabilities of this mechanical structure.

Kinematic modeling for feedback control of an omnidirectional wheeled mobile robot

Abstract: We have introduced a methodology for the kinematic modeling of wheeled mobile robots. In this paper, we apply our methodology to Uranus, an omnidirectional wheeled mobile robot which is being developed in the Robotics Institute of Carnegie Mellon University. We assign coordinate systems to specify the transformation matrices and write the kinematic equations-of-motion. We illustrate the actuated inverse and sensed forward solutions; i.e., the calculation of actuator velocities from robot velocities and robot velocities from sensed wheel velocities. We apply the actuated inverse and sensed forward solutions to the kinematic control of Uranus by: calculating in real-time the robot position from shaft encoder readings (i.e., dead reckoning); formulating an algorithm to detect wheel slippage; and developing an algorithm for feedback control.

The kinematics and dynamics of space manipulators: the virtual manipulator approach

Abstract: 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.

Dynamic simulation of autonomous legged locomotion

Abstract: Accurate simulation of Newtonian mechanics is essential for simulating realistic motion of joined figures. Dynamic simulation requires, however, a large amount of computation when compared to kinematic methods, and the control of dynamic figures can be quite complex. We have implemented an efficient forward dynamic simulation algorithm for articulated figures which has a computational complexity linear in the number of joints. In addition, we present a strategy for the coordination of the locomotion of a six-legged figure - a simulated insect - which has two main components: a gait controller which sequences stepping, and motor programs which control motions of the figure by the application of forces. The simulation is capable of generating gait patterns and walking phenomena observed in nature, and our simulated insect can negotiate planar and uneven terrain in a realistic manner. The motor program techniques should be generally applicable to other control problems.

On homogeneous transforms, quaternions, and computational efficiency

Abstract: Three-dimensional modeling of rotations and translations in robot kinematics is most commonly performed using homogeneous transforms. An alternate approach, using quaternion-vector pairs as spatial operators, is compared with homogeneous transforms in terms of computational efficiency and storage economy. The conclusion drawn is that quaternion-vector pairs are as efficient as, more compact than, and more elegant than their matrix counterparts. A robust algorithm for converting rotational matrices into equivalent unit quaternions is described, and an efficient quaternion-based inverse kinematics solution for the Puma 560 robot arm is presented. >

Target tracking problems subject to kinematic constraints

Abstract: Filtering problems with kinematic constraints which may arise in target tracking problems are considered. A novel approach which treats kinematic constraints as additional fictitious or pseudomeasurements is proposed. A numerical example is provided to show the technical feasibility of the proposed idea for target tracking problems. This example shows that the proposed method can improve estimation accuracy significantly for velocity and acceleration states in the tracking problem. However, it is noted that the tracking performance may be deteriorated if the constraints do not properly represent the target characteristics and a small R/sub c/ is chosen. >

3-D motion estimation using a sequence of noisy stereo images: models, estimation, and uniqueness results

Abstract: A kinematic model-based approach for the estimation of 3-D motion parameters from a sequence of noisy stereo images is discussed The approach is based on representing the constant acceleration translational motion and constant precession rotational motion in the form of a bilinear state-space model using standard rectilinear states for translation and quaternions for rotation Closed-form solutions of the state transition equations are obtained to propagate the quaternions The measurements are noisy perturbations of 3-D feature points represented in an inertial coordinate system It is assumed that the 3-D feature points are extracted from the stereo images and matched over the frames Owing to the nonlinearity in the state model, nonlinear filters are designed for the estimation of motion parameters Simulation results are included The Cramer-Rao performance bounds for motion parameter estimates are computed A constructive proof for the uniqueness of motion parameters is given It is shown that with uniform sampling in time, three noncollinear feature points in five consecutive binocular image pairs contain all the spatial and temporal information Both nondegenerate and degenerate motions are analyzed A deterministic algorithm to recover motion parameters from a stereo image sequence is summarized from the constructive proof >

Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems

Abstract: W e clearly elucidate the kinematic constraints, and the corresponding kinematic indeterminacy of part of the deviatoric stress tensor, in a rigid-viscoplastic single crystal lacking five independent slip systems. The indeterminate stress component is a Lagrange multiplier enforcing the kinematic constraint, and it must be determined from equilibrium considerations. A simple polycrystalline model is constructed which precisely satisfies local kinematic constraints as well as global compatibility. Volume-average global stresses are obtained by approximating the local constraint stress as the corresponding projection of the (to-be-determined) global stress. Applications of the model to hexagonal crystals without pyramidal slip, and to large deformation and texturing of orthorhombic polycrystalline materials (olivine; HDPE) are made.

A complete and parametrically continuous kinematic model for robot manipulators

Abstract: A kinematic modeling convention for robot manipulators is proposed. The kinematic model is named for its completeness and parametric continuity (CPC) properties. Parametric continuity of the CPC model is achieved by adopting a singularity-free line representation consisting of four line parameters. Completeness is achieved through adding two link parameters to allow arbitrary placement of link coordinate frames. The transformations from the world frame to the base frame and from the last link frame to the tool frame can be modeled with the same modeling convention used for internal link transformations. Since all the redundant parameters in the CPC model can be systematically eliminated, a linearized robot error model can be constructed in which all error parameters are independent and span the entire geometric error space. The focus is on model construction, mappings between the CPC model and the Denavit-Hartenberg model, the study of the model properties, and its application to robot kinematic calibration. >

On the kinematics of wheeled mobile robots

Abstract: A wheeled mobile robot is here modelled as a planar rigid body that rides on an arbitrary number of wheels. The relationship between the rigid body motion of the robot and the steering and drive rates of wheels is developed. In particular, conditions are obtained that guarantee that rolling without skidding or sliding can occur. Explicit differential equations are derived to describe the rigid body motions that arise in such ideal rolling trajectories. The simplest wheel configuration that permits access of arbitrary rigid-body motions is determined. Then the question of slippage due to misalignment of the wheels is investigated by minimization of a nonsmooth convex dis­sipation functional that is derived from Coulomb’s Law of friction. It is shown that this minimization principle is equivalent to the construction of quasi-static motions. Examples are presented to illustrate the models.

A closed-loop inverse kinematic scheme for on-line joint-based robot control *

Abstract: SUMMARY A computationally fast inverse kinematic scheme is derived which solves robot's end-effector (EE) trajectories in terms of joint trajectories. The inverse kinematic problem (IKP) is cast as a control problem for a simple dynamic system. The resulting closed-loop algorithms are shown to guarantee satisfactory tracking performance. Differently from previous first-order schemes which only solve for joint positions and velocities, we propose here new second order tracking schemes which allow the on-line generation of joint position + velocity + acceleration (PVA) reference trajectories for any computed torque-like controller in sensor-based robot applications. The algorithms do explicitly solve the IKP for both EE position and orientation. Simulation results for a six-degree-offreedom PUMA-like geometry demonstrate the effectiveness of the scheme, even near singularities.

Coordinated dynamic hybrid position/force control for multiple robot manipulators handling one constrained object

Abstract: A cooperative dynamic hybrid control method for multimotion robotic mechanisms handling a single object whose motion is constrained by environment is discussed. This method takes the manipulator dynamics and object dynamics into consideration and is for controlling the motion of the object as well as for controlling the constraint force and the internal force. The following results are obtained: (1) the force and kinematic relations are established for arms grasping and manipulating an object using various types of end effector; and (2) using the first result, a nonlinear state feedback law for the joint driving force that linearizes and decouples the robot system with respect to the object motion, constraint force, and internal force is given. A basic structure of the dynamic hybrid control system with a servo compensator is presented. The effectiveness of the proposed approach has been examined by a simple experiment. These results are useful for the fine manipulation of an object, in the sense that one can specify the controller characteristics independently for the individual specification of the object motion, the interaction between the object and its environment, and the grasping of the object. >

Interactive real-time articulated figure manipulation using multiple kinematic constraints.

Abstract: In this paper, we describe an interactive system for positioning articulated figures which uses a 3D direct manipulation technique to provide input to an inverse kinematics algorithm running in real time. The system allows the user to manipulate highly articulated figures, such as human figure models, by interactively dragging 3D "reach goals." The user may also define multiple "reach constraints" which are enforced during the manipulation. The 3D direct manipulation interface provides a good mechanism for control of the inverse kinematics algorithm and helps it to overcome problems with redundancies and singularities which occur with figures of many degrees of freedom. We use an adaptive technique for evaluating the constraints which allows us to ensure that only a certain user-controllable amount of time will be consumed by the inverse kinematics algorithm at each iteration of the manipulation process. This technique is also sensitive to the time it takes to redraw the screen, so it prevents the frame display rate of the direct manipulation from become too slow for interactive control.

Dexterity indices for planar and spatial robotic manipulators

Abstract: Novel dexterity indices that can be applied to planar and spatial manipulators are presented. These indices are based on the condition number of the Jacobian matrix of the manipulators, which is known to be a measure of their kinematic accuracy. The formulation of the kinematic equations used leads to dexterity indices that are frame invariant, whereas previous indices are affected by a scaling of the manipulator when both the position and the orientation of the end effector are included in these equations. Two indices are proposed for planar manipulations: the first one is based on a redundant formulation of the velocity equations and the second one on the minimum number of parameters. The corresponding indices are also derived for spatial manipulators. An example is included to demonstrate the invariance of the indices. >

A computational analysis of screw transformations in robotics

Abstract: A computational analysis and a comparison of line-oriented representations of general (ie rotational and translational) spatial displacements of rigid bodies are presented Four mathematical formalisms for effecting a general spatial screw displacement are discussed and analyzed in terms of computational efficiency in performing common operations needed in kinematic analysis of multilinked spatial mechanisms The corresponding algorithms are analyzed in terms of both sequential and parallel execution It is concluded that the dual-unit quaternion representation offers the most compact and most efficient screw transformation formalism but that line-oriented methods in general are not well suited for efficient kinematic computations or real-time control applications Owing to line-based geometry, underlying its definition, screw calculus represents a set of valuable tools in theoretical kinematics However, the mathematical redundancy inherent in Plucker coordinate space representation makes the screw calculus computationally less attractive than the corresponding point-oriented formalisms >