Geometrical and Kinematical Control Functions for a Cartesian Robot Structure (original) (raw)
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Design of robot manipulators based on kinematic analyses
Robotics and Computer-Integrated Manufacturing, 1988
Kinematic analysis represents an important tool for the functional design of robot applications. It facilitates the determination of layout arrangements for the production cell, the selection of suitable machines and equipment, the design of task specifications and robot paths and the performance of all the tasks required by new robot manipulators.
2018
The kinematic modeling of a mechanical system with n degrees of freedom, involves an impressive volume of computational or differential calculus. There are algorithms dedicated to this task developed in the literature. Applying of algorithms allows a detailed, numerical and / or graphical analysis of kinematics for a mechanical structure, regardless of its type and complexity. The results obtained with algorithms are essential in optimal design, dimensional and energetically, but also to simulate the kinematical and dynamic behavior of the mechanical structures of the robots.
Geometric Control of a Robot's Tool
2021
The goal of this paper is to present a rigorous and intrinsic formulation of a riemannian PD-regulator of the robot’s tool, The first one is based upon the Lasalle’s invariance principle, we use it to control the tool’s position in the workspace under the assumption of absence of singularities in configuration space, The second method deals with geometrical constraints on the trajectory of the robot’s tool with the same assumption, we construct a unique orthogonal force that is viewed as a gravitational force that keeps the tool constrained, We also present a variation of the first method in the case of double pendulum based on the Lyapunov stability theorem. With this modification, we control the tool and the difference between the two angles, we did simulations on a two-link manipulator that shows the efficiency of the presented methods.
Point-based Jacobian formulation for computational kinematics of manipulators
Mechanism and Machine Theory, 2006
Computational kinematic analysis of mechanisms is a promising tool for the development of new classes of manipulators. In this paper, the authors present a velocity equation to be compiled by general-purpose software and applicable to any mechanism topology. First, the approach to model the mechanism is introduced. The method uses a set of kinematic restrictions applied to characteristic points of the mechanism. The resultant velocity equation is not an input-output equation, but a comprehensive one. In addition, the Jacobian characterizing the equation is dimensionless hence extremely useful for singularity and performance indicators. The motion space of the manipulator is obtained from the velocity equation. Angular velocities are compiled out of three non-collinear point velocities. The procedure is applied to a 3-DoF parallel manipulator to illustrate.
Kinematics of common industrial robots
Robotics and Autonomous Systems, 1988
An approach to finding the solution equations for simple manipulators is described which enhances the well known method of Paul, Renaud, and Stevenson, by explicitly making use of known decouplings in the manipulator kinematics. This reduces the set of acceptable equations from which we obtain relationships for the joint variables. For analyzing the Jacobian, such decoupling is also useful since it manifests itself as a block of zeros, which makes inversion much easier. This zero lock can be used to obtain a concise representation for the forward and inverse Jacobian computations. The decoupling also simplifies the calculations sufficiently to allow us to make good use of a symbolic algebra program (MACSYMA) in obtaining our results. Techniques for using MACSYMA in this way are described. Examples are given for several industrial manipulators.
2018
A robot manipulator is a movable chain of links interconnected by joints. One end is fixed to the ground, and a hand or end effector that can move freely in space is attached at the other end. This book begins with an introduction to the subject of robot manipulators. Next, it describes about a forward and reverse analysis for serial robot arms. Most of the text focuses on closed form solution techniques applied to a broad range of manipulator geometries, from typical industrial robot designs. A unique feature is its detailed analysis of 3R mechanisms. Case studies show how the techniques described in the book are used in real engineering applications. The book will be useful to both graduate students and engineers working in the field of robotics.
Kinematic control of constrained robotic systems
Sba: Controle & Automação Sociedade Brasileira de Automatica, 2011
Este artigo considera o problema de controle de postura para sistemas robóticos com restrições cinemáticas. A ideia principal é considerar as restrições cinemáticas dos mecanismos a partir de suas equações estruturais, ao invés de usar explicitamente a equação de restrição. Um estudo de caso para robôs paralelos e robôs cooperativos é discutido baseado nos conceitos de cinemática direta, cinemática diferencial, singularidades e controle cinemático. Resultados de simulação, obtidos a partir de um mecanismo F our-Bar linkage, uma plataforma de Gough-Stewart planar e dois robôs cooperativos, ilustram a aplicabilidade e versatilidade da metodologia proposta.