Kinematics of common industrial robots (original) (raw)
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Symbolically Automated Direct Kinematic Equations Solver for Robotic Manipulators
Robotica, 1989
Solving the direct kinematic problem in a symbolic form requires a laborious process of successive multiplications of the link homogeneous transformation matrices and involves a series of algebraic and trigonometric simplifications. The manual production of such solutions is tedious and error-prone. Due to the efficiency of the Prolog language in symbolic processing, a rule-based Prolog program is developed to automate the creation of the following processes: Link transformation matrices; forward kinematic solutions; and the Jacobian matrix. This paper presents the backward recursive formulation techniques, the trigonometric identity rules, and some heuristic rules for implementing the system. A verification of the system has been demonstrated in case of several industrial robots.
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.
2011 IEEE International Conference on Mechatronics and Automation, 2011
In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator's forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given.
Analysis And Validation Of An Industrial Robot Manipulator
2022
Due to nonlinearity and multiple solutions, it is quite complicated to analyze the inverse kinematics of a 6-DOF industrial robot. There is no distinctive solution for an inverse kinematic; hence a number of predictive approaches are adopted to solve the problem. The conventional method like Jacobin transformation is used to get the closed form solution of joint angles. The ANN and fuzzy logic are applied to a number of models to solve the inverse kinematic problem. The higher degree of polynomial solution does not solve by these methods. To overcome the conventional technique problem, any more optimization approaches are applied. The ANN and fuzzy logic shows more convergence to words the acceptable solution. Here 6-DOF industrial robot is designed and the joint angles are simulated with the robo analyzer method.
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.
International Journal of Advanced Robotic Systems, 2011
In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator's forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given.
Simulation of Industrial Manipulators Based on the UDU T Decomposition of Inertia Matrix
2003
The UDU T-U and D are respectively the upper triangular and diagonal matrices-decomposition of the generalized inertia matrix of an n-link serial manipulator, introduced elsewhere, is used here for the simulation of industrial manipulators which are mainly of serial type. The decomposition is based on the application of the Gaussian elimination rules to the recursive expressions of the elements of the inertia matrix that are obtained using the Decoupled Natural Orthogonal Complement matrices. The decomposition resulted in an efficient order n, i.e., O(n), recursive forward dynamics algorithm that calculates the joint accelerations. These accelerations are then integrated numerically to perform simulation. Using this methodology, a computer algorithm for the simulation of any n degrees of freedom (DOF) industrial manipulator comprising of revolute and/or prismatic joints is developed. As illustrations, simulation results of three manipulators, namely, a three-DOF planar manipulator, and the six-DOF Stanford arm and PUMA robot, are reported in this paper.
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.
Robot Manipulators and Control Systems 2.1 Introduction
This book focuses on industrial robotic manipulators and on industrial manufacturing cells built using that type of robots. This chapter covers the current practical methodologies for kinematics and dynamics modeling and computations. The kinematics model represents the motion of the robot without considering the forces that cause the motion. The dynamics model establishes the relationships between the motion and the forces involved, taking into account the masses and moments of inertia, i.e., the dynamics model considers the masses and inertias involved and relates the forces with the observed motion, or instead calculates the forces necessary to produce the required motion. These topics are considered very important to study and efficient use of industrial robots. Both the kinematics and dynamics models are used currently to design, simulate, and control industrial robots. The kinematics model is a prerequisite for the dynamics model and fundamental for practical aspects like motion planning, singularity and workspace analysis, and manufacturing cell graphical simulation. For example, the majority of the robot manufacturers and many independent software vendors offer graphical environments where users, namely developers and system integrators, can design and simulate their own manufacturing cell projects (Figure 2.1). Kinematics and dynamics modeling is the subject of numerous publications and textbooks [1-4]. The objective here is to present the topics without prerequisites, covering the fundamentals. Consequently, a real industrial robot will be used as an example which makes the chapter more practical, and easier to read. Nevertheless, the reader is invited to seek further explanation in the following very good sources:
A more compact expression of relative Jacobian based on individual manipulator Jacobians
Robotics and Autonomous Systems, 2015
This work presents a re-derivation of relative Jacobian matrix for parallel manipulators, expressed in terms of the individual manipulator Jacobians and multiplied by their corresponding transformation matrices. This is particularly useful when the individual manipulator Jacobians are given, such that one would not need to derive an entirely new expression of a relative Jacobian but will only use the existing manipulator Jacobians and perform the necessary transformations. In this work, the final result reveals a wrench transformation matrix which was not present in previous derivations, or was not explicitly expressed. The proposed Jacobian expression results in a simplified, more compact and intuitive form. It will be shown that the wrench transformation matrix is present in stationary as well as mobile combined manipulators. Simulation results show that at high angular end-effector velocities, the contribution of the wrench transformation matrix cannot be ignored.