Topic
Kinematics equations
About: Kinematics equations is a research topic. Over the lifetime, 1775 publications have been published within this topic receiving 34617 citations.
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Book•
22 Mar 1994
TL;DR: In this paper, the authors present a detailed overview of the history of multifingered hands and dextrous manipulation, and present a mathematical model for steerable and non-driveable hands.
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
6,592 citations
Book•
01 Jan 1989
TL;DR: This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control, providing background material on terminology and linear transformations and examples illustrating all aspects of the theory and problems.
Abstract: From the Publisher:
This self-contained introduction to practical robot kinematics and dynamics includes a comprehensive treatment of robot control. Provides background material on terminology and linear transformations, followed by coverage of kinematics and inverse kinematics, dynamics, manipulator control, robust control, force control, use of feedback in nonlinear systems, and adaptive control. Each topic is supported by examples of specific applications. Derivations and proofs are included in many cases. Includes many worked examples, examples illustrating all aspects of the theory, and problems.
3,736 citations
Book•
01 Jan 1965
TL;DR: In this article, the Lagrange Equations are used to model the dynamics of a rigid body and a system of parts of a particle system with respect to the velocity of a single particle.
Abstract: 1. Introductory Concepts. 2. Kinematics of a Particle. 3. Dynamics of a Particle. 4. Dynamics of a System of Particles. 5. Orbital Motion. 6. Lagrange's Equations. 7. Basic Concepts and Kinematics of Rigid Body Motion. 8. Dynamics of a Rigid Body. 9. Vibration Theory. Appendices: Inertial Properties of Homogeneous Bodies. Answers to Selected Problems. Index.
773 citations
Book•
07 Apr 2011
TL;DR: In this paper, the authors propose an algebraic synthesis of spherical chains for solving constraint equations in the plane, based on the analysis of Spherical linkages and spherical trigonometry.
Abstract: Introduction.- Analysis of Planar Linkages.- Graphical Synthesis in the Plane.- Planar Kinematics.- Algebraic Synthesis of Planar Chains.- Analysis of Spherical Linkages.- Spherical Kinematics.- Algebraic Synthesis of Spherical Chains.- Analysis of Spatial Chains.- Spatial Kinematics.- Algebraic Synthesis of Spatial Chains.- Platform Manipulators.- Graphical Constructions.- Solving Constraint Equations.- Spherical Trigonometry.- Operations with Dual Numbers.- Kinematics Equations.- References.- Index.
540 citations
TL;DR: In this work, the inverse kinematics problem is approached through nonlinear programming techniques and has been successfully used since 1988 in the spatial constraint system within Jack, a human figure simulation system and proves to be satisfactorily efficient, controllable, and robust.
Abstract: An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straight forward to compute figure configurations given joint angles (forward kinematics), it is more difficult to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed several different approaches. However, when we try to follow these approaches in an interactive animation system where the object on which to operate is as highly articulated as a realistic human figure, they fail in either generality or performance. So, we approach this problem through nonlinear programming techniques. It has been successfully used since 1988 in the spatial constraint system within Jack, a human figure simulation system developed at the University of Pennsylvania, and proves to be satisfactorily efficient, controllable, and robust. A spatial constraint in our system involves two parts: one constraint on the figure, the end-effector, and one on the spatial environment, the goal. These two parts are dealt with separately, so that we can achieve a neat modular implementation. Constraints can be added one at a time with appropriate weights designating the importance of this constraint relative to the others and are always solved as a group. If physical limits prevent satisfaction of all the constraints, the system stops with the (possibly local) optimal solution for the given weights. Also, the rigidity of each joint angle can be controlled, which is useful for redundant degrees of freedom.
401 citations