Showing papers on "Kinematics equations published in 2011"

Geometric Design of Linkages

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.

Dynamics of the 6-6 Stewart parallel manipulator

Abstract: Recursive matrix relations in kinematics and dynamics of the 6-6 Stewart-Gough parallel manipulator having six mobile prismatic actuators are established in this paper. Controlled by six forces, the manipulator prototype is a spatial six-degrees-of-freedom mechanical system with six parallel legs connecting to the moving platform. Knowing the position and the general motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each manipulator's link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Finally, compact matrix relations and graphs of simulation for the input velocities and accelerations, the input forces and powers are obtained.

Kinematic analysis of a novel 3-DOF actuation redundant parallel manipulator using artificial intelligence approach

Abstract: Kinematic analysis is one of the key issues in the research domain of parallel kinematic manipulators. It includes inverse kinematics and forward kinematics. Contrary to a serial manipulator, the inverse kinematics of a parallel manipulator is usually simple and straightforward. However, forward kinematic mapping of a parallel manipulator involves highly coupled nonlinear equations. Therefore, it is more difficult to solve the forward kinematics problem of parallel robots. In this paper, a novel three degrees-of-freedom (DOFs) actuation redundant parallel manipulator is introduced. Different intelligent approaches, which include the Multilayer Perceptron (MLP) neural network, Radial Basis Functions (RBF) neural network, and Support Vector Machine (SVM), are applied to investigate the forward kinematic problem of the robot. Simulation is conducted and the accuracy of the models set up by the different methods is compared in detail. The advantages and the disadvantages of each method are analyzed. It is concluded that @n-SVM with a linear kernel function has the best performance to estimate the forward kinematic mapping of a parallel manipulator.

Learning inverse kinematics with structured prediction

Abstract: Learning inverse kinematics of robots with redundant degrees of freedom (DoF) is a difficult problem in robot learning. The difficulty lies in the non-uniqueness of the inverse kinematics function. Existing methods tackle non-uniqueness by segmenting the configuration space and building a global solution from local experts. The usage of local experts implies the definition of an oracle, which governs the global consistency of the local models; the definition of this oracle is difficult. We propose an algorithm suitable to learn the inverse kinematics function in a single global model despite its multivalued nature. Inverse kinematics is approximated from examples using structured output learning methods. Unlike most of the existing methods, which estimate inverse kinematics on velocity level, we address the learning of the direct function on position level. This problem is a significantly harder. To support the proposed method, we conducted real world experiments on a tracking control task and tested our algorithms on these models.

Dynamics and control of a 5-DOF manipulator based on an H-4 parallel mechanism

Abstract: This paper presents a design of a unique hybrid five-degree-of-freedom manipulator based on an H-4 family parallel mechanism with three translational movements and one rotational movement (orientation angle) together with a single axis rotating table. Forward or direct kinematics, inverse kinematics, and Jacobian are derived in details as well as the dynamic model. The dynamic model is derived from the Lagrangian formulation and is shown to be suitable in the real-time feedback control. The numerical results of the analysis of kinematics, inverse kinematics, and the dynamic model are compared with the results from a popular commercial software using a virtual modeling data, the ADAMS solver. Friction models obtained from the experiment are used to compensate for the actual friction of the system in the resolve acceleration control strategy. The inverse dynamics is implemented for the first four axis of the chosen configuration to perform feedback linearization. From the experimental results, the tracking performance is satisfied and can be improved by increasing the rigidity of the railway structure and reducing the numerical truncation error.

Kinematics and Singularity Analysis of a Parallel Manipulator with Three Rotational and One Translational DOFs

Abstract: This paper addresses kinematics and singularity analysis of a novel symmetrical four degrees of freedom (DOFs) parallel manipulator, known as 4UPS +1PS manipulator. The manipulator consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by five serial chains (legs), four UPS-type active legs, and one PS-type passive leg where P, U, and S stand for prismatic, universal, and spherical joints, respectively. First, the inverse and direct position kinematics of the manipulator are investigated. The direct position kinematics leads to an even twelfth-degree polynomial in a single variable indicating that the manipulator has two sets of at most six assembly configurations which are symmetric with respect to each other. Through a numerical example it is shown that the polynomial is minimal. Then, the inverse and direct velocity kinematics problems are solved and singularity of the manipulator is analyzed using Jacobian matrices. Also the number and type of addition...

Forward kinematics analysis of offset 6-RRCRR parallel manipulators

Abstract: A methodology for the numerical solution of the forward kinematics problem of 6-RRCRR parallel manipulators with orthogonal non-intersecting RR-joint configuration is presented in this article. The inverse and forward kinematics solutions of such robots compared with that of parallel robots with orthogonal intersecting RR-joint or universal joint configurations are much more complicated due to the existence of dependent joint variables. The constraints of RR-joints are analysed and the numerical algorithm for the forward kinematics solution is assessed. Numerical results for the solution of the forward kinematics of 6-RRCRR parallel robot under study are provided to confirm the accuracy and efficiency of the procedure.

Inverse kinematics of modular Cable-driven Snake-like Robots with flexible backbones

Abstract: A Cable-driven Snake-like Robot (CSR) with a flexible backbone possesses a number of promising advantages over the conventional rigid-link manipulators, such as lightweight mechanical structure, large reachable workspace, high dexterity, and high maneuverability. In general, a CSR is a hyper-redundant manipulator that consists of a large number of identical or similar segments. A modular design approach is employed in this paper in order to simplify the CSR design, analysis, and control to a manageable level. As the basic building block of CSRs, a 2-DOF cable-driven joint module with a flexible backbone is proposed. Based on the motion characteristics of the 2-DOF joint module, the concept of instantaneous rotation axis in conjunction with the Product-Of-Exponentials (POE) formula is proposed to formulate its kinematic model. However, as the instantaneous rotation axis is unfixed, the Lie Bracket method from the Group theory is employed to derive the instantaneous kinematic model of the joint module. With the joint's kinematics model, a configuration-independent numerical inverse kinematics (NIK) algorithm is formulated for the modular CSRs. The effectiveness of the proposed NIK algorithm is validated through simulation examples.

Closed-form inverse kinematics of 6R milling robot with singularity avoidance

Abstract: For a 6R milling robot, it is necessary to convert the postprocessing cutter locations (CL) into the robot’s revolute joint variables. This paper introduces an algorithm for calculating the forward and inverse kinematics of a 6R robot according to the CL data generated by conventional CAD/CAM systems. A redundant mechanism is analyzed to avoid the singular configurations and joint limits. The Denavit–Hartenberg (D–H) convention is referred to for developing the forward kinematics, and a closed-form solution of the inverse kinematics is presented by means of kinematic decoupling. A fundamental approach with modifying factor for avoiding singularity are developed with regard to three-axis and five-axis CL data. A gap bridging strategy is applied to reduce the jerk motion caused by tool retraction and cut paths connection. Finally, the result is conducted to simulation and machining test to verify the algorithms.

Inverse Kinematics solution of PUMA 560 robot arm using ANFIS

Abstract: One of the problems in robotics field is, finding the solution of Inverse Kinematics (IK) problem. Traditional methods such as iterative, geometric and algebraic are inadequate if the joint structure of the robot is more complex. As the complexity of manipulator increases, solution of IK is difficult and computationally expensive. In this paper, using the ability of Adaptive Neuro-Fuzzy Inference System (ANFIS) to learn from training data, it is possible to create ANFIS with limited mathematical representation of the system. In the proposed method, forward kinematics relations of robot arm are used to obtain the data for training of ANFIS. Simulation is carried out on a PUMA 560 robot arm to show the effectiveness of the approach.

Differential-algebraic equations of programmed motions of Lagrangian dynamical systems

Abstract: We suggest a method for constructing the dynamic equations of manipulator systems in canonical variables. The system of differential dynamic equations has an integral manifold corresponding to the holonomic and nonholonomic constraint equations. The controls are determined so as to ensure the stability of this manifold. We state conditions for the exponential stability of the manifold and for constraint stabilization when solving the dynamic equations numerically by a simplest difference method. We also present the solution of the problem of control of a plane two-link manipulator.

Closed-form Dynamic Equations of the 6-RSS Parallel Mechanism through the Newton-Euler Approach

Abstract: The 6-RSS parallel robot is a parallel manipulator whose mobile platform has 6 DOF. In order to construct a complete dynamic model of 6-RSS parallel manipulator, a serial of coordinates on components were defined with D-H method and a kinematics analysis on a single chain was carried out. As a result, closed-form equations for the inverse kinematics and velocity and acceleration transformations from joint space to task space are given. The dynamics model of 6-RSS parallel mechanism is deduced based on the platform, as an example, the driving moment curves for circumferential translation are drawn. The paper’s work establishes the basis for dynamics analysis of mechanism with this type.

Dynamics modeing and maneuverability analysis of a near-space earth observation platform

Abstract: Near-space autonomous airship represents a unique and promising platform for earth observation and surveillance that involve a long duration airborne presence. In this paper, a six-degrees-of-freedom dynamics model and maneuverability of a near-space earth observation platform are presented. First, the near-space earth observation platform is introduced, including the concept design, configuration, energy sources, propeller and payload. Second, reference frames and motion parameters of the platform are defined, and the kinematics equations describing the platform's dimensional motion are derived. The effects of gravity, buoyancy, added inertia, aerodynamics and thrust on the platform are incorporated into the dynamics analysis, and a dynamics model in vector form of the platform is derived based on Newton-Euler principle. Finally, a simulation program has been developed to implement the dynamics model and applied to analyze the maneuverability of the platform. It is hoped that this work is useful to support the evaluation of maneuverability and the development of control system for the near-space earth observation platform.

Kinematics of a Robot with Crawler Drive

Abstract: In order to describe the kinematics of the robot with crawler drive it is necessary to present kinematics equations. The problem of mathematical description of the kinematics equations of consideration to tracked skidding drive has been presented. In the Matlab–Simulink environment simulation of the robot’s kinematics behaviour has been carried out. Such a mode of computations software have been further discussed in paper [1,7,8]. On the basis of kinematics parameters simulation and comparison of the results have been carried out.

A new 12 DOF biped robot's mechanical design and kinematic analysis

Abstract: This paper decribes the progress of an humanoid biped robot project and mainly focuses on its mechanical design and kinematics analysis. This project, which started in 2009, is aiming at the realization of the lower part of an humanoid biped robot. As the first step to finish the biped robot's overall development, a novel mechanical structure was designed with two legs, two feet and a pelvis. It has 12 degrees of freedom. The robot's body shape and mass distribution is similar to that of an adult with the purpose to get an ideal stable walking movement. In this paper, first we discuss the robot's basic configuration, joints structure, transmitters, and sensors, second an approach to the analysis of one leg's forward kinematics and inverse kinematics is introduced.

Kinematics for the scara and the cylindrical manipulators

Abstract: Kinematics analysis is divided into: forward and inverse kinematics. For- ward kinematics showed how to determine the end-effector position and orientation in terms of the joint variables. The problem of inverse kinematics is tond the joint vari- ables in terms of the end-effector position and orientation. The Jacobian presents the relation between the joint and the end effector position velocities. The paper shows the kinematics of the SCARA robot with four degrees of freedom, the four degrees are dif- ferent from others. The paper shows the kinematics of the cylindrical robot with three degrees of freedom. Keywords: Kinematics, SCARA manipulator, Cylindrical manipulator

Kinematics analysis of a novel 7-DOF humanoid manipulator for table tennis

Abstract: A novel 7-DOF humanoid manipulator used to play table tennis is presented and the kinematics of the manipulator is analyzed according to its architecture. Both the forward kinematics and the inverse kinematics are established and the Jacobian matrix is calculated. Especially, an analytic method for the inverse kinematics which can obtain anthropomorphic solutions is proposed. Motion characteristics of human arms are taken into account in the inverse kinematics and the relationship between the elbow position and the operation space is built up offline using an artificial neural network (ANN). The elbow position can be calculated according to the ANN model when solving the inverse kinematics and thus the anthropomorphic solutions are derived. The method for the inverse kinematics is simple and beneficial to the real-time motion control of the manipulator. The validation and simulation on the kinematics are carried out and the results prove the correctness and feasibility.

Kinematics analysis of a 3-DOF joint for a novel hyper-redundant robot arm

Abstract: In this paper, the kinematics of a joint with three degrees of freedom for a novel hyper-redundant robot arm is investigated. This joint is able to achieve a superposed rotation about two axes (roll and pitch) and a translational motion along one axis as a common prismatic joint. The forward and inverse kinematics of the so-called Multi-Joint will be determined in a closed-form solution. Next, the reachable and suitable workspace will be worked out to determine the solution space of the inverse kinematics. Finally, the differential kinematics to compute the cartesian velocity and statics will be determined.

Kinematics analysis and motion planning for a 7-DOF redundant industrial robot manipulator

Abstract: This paper proposes application methods for utilizing a 7-DOF robot manipulator called YH050 in industrial settings. For finding an optimal method to solve the inverse kinematics problem, we propose three methods: numerical approach, geometrical approach and combined approach for inverse kinematics solution. Also, for efficient application of the robot in a work zone, we present motion planning to avoid singularities, obstacles, and to occupy minimal workspace. In this paper, these studies are theoretically explained and then experimentally verified.

Research on kinematics of modular reconfigurable robots

Abstract: This paper mainly focuses on the kinematics of multi-branch modular reconfigurable robots. A method of generating the forward kinematics is proposed. Firstly, the robot is divided into joints and links, which are formed dyads subsequently. Secondly, module frames are defined and attached to each connector of modules. Thirdly, based on screw theory and Lie group and Lie algebra, the initial poses and twists of a multi-branch robot are obtained, and the kinematic equations of the robot are derived. An illustrative example and an experiment are implemented, respectively, and the results show that the method is valid and suitable for both single-open-chain robots and multi-branch robots.

Design and Analysis of a Novel Wall-Climbing Robot Mechanism

Abstract: A novel wall-climbing robot mechanism designed for anti-hijacking task is presented. This mechanism consists of a negative pressure adhesion module, a vacuum suction module and a planetary-gear train. The design of biped-wheel hybrid locomotion mechanism, with the advantages of wheeled robots and legged robots, allows the robot to move fast and cross over obstacles easily. This design qualifies the robot for the motion of moving straight, turning in plane and crossing between inclined surfaces. Then the kinematics equations are derived and the locomotion modes are analyzed. Many experiments have been implemented and the results prove that the robot has such characteristics as rapid speed, excellent transition ability between inclined surfaces and curved surface adaptability. Therefore, this novel wall-climbing mechanism could be used for the application of inspection, surveillance and reconnaissance.

The basic component of computational intelligence for KUKA KR c3 robot

Abstract: In this paper the solution algorithm of inverse kinematics problem for KUKA KR C3 robot is presented. This algorithm may be a basic component of future computational intelligence for theses robots. The problem of computing the joint variables corresponding a specified location of end-effector is called inverse kinematics problem. This algorithm was implemented into the controller of the robot. It allowed controlling these robots by using the vision system, which specifies required location of the end-effector. This required location makes it possible for the end-effector to approach a manipulation object (observed by vision system) and pick it up. These robots are equipped with several manipulator which has 6 links joined by revolute joint. First the location of end-effector in relation to the base of the manipulator were described. Next the position workspace of this robot was illustrated. The example of solutions of the inverse kinematics problem and conclusions were presented in the end of this work. In this example are the multiple solutions for singular configurations of this manipulator.

Estimation of Multibody Kinematics Using Position Measurements

Abstract: A method for the estimation of kinematics of a system of rigid bodies connected by three degrees of freedom rotational joints using position measurements is introduced. In the proposed approach, system kinematics are computed from experimental measurements while preserving important physical and kinematic properties. These properties include system integrity, i.e., preserving interconnections between the bodies, and the entire system dynamic properties, namely, center of mass kinematics and its angular momentum. The computational procedure consists in solving a sequence of optimizations of appropriately formulated objective functions that incorporate the preservation of physical and kinematic properties by employing the penalty function approach. The configuration of the segment kinematics of the system is computed via a quaternion parametrization of orientation that leads to an efficient computation procedure. The sequence of optimization problems is solved using an embedded iteration process. Two studies are presented to demonstrate the performance of the proposed approach: estimations of the kinematics of a simulated three-link model and of an experimentally measured 3D motion of human body during flight phase of a jump. The results of the two studies indicate fast convergence of the algorithm to an optimal solution while accurately satisfying the imposed the constraints.

Smooth Inverse Kinematics Algorithms for Serial Redundant Robots

Abstract: The inverse kinematics of a robot is the mapping that, given a goal position, calculates a set of joint positions so as to place the robot’s end effector in the specified goal. As this is a relevant issue to move the robot, there has been a lot of work about obtaining a fast and robust inverse kinematic algorithm. In this work we present the main concerns on finding an inverse kinematics algorithm for a serial redundant manipulator. We firstly comment on our motivation, the state of the art and set our objectives, to later briefly expose some necessary concepts. Then the work is divided into two parts: the first one, describing analytical methods for solving inverse kinematics, and the second one about control-based methods. In the analytical methods, we will see how difficult it may be to have a closed analytical form, in particular for redundant manipulators, and we will try to solve, not always with success, the inverse kinematics of some robots. Then we will move into control-based algorithms, which are iterative methods using the Jacobian matrix of a robot, and we will firstly discuss the concerns of these methods, which mainly are: • Convergence: Achieving the specified goal from a given starting position. • Joint limit avoidance: Given the valid interval for each joint, the algorithm should not give a solution which cannot be reached due to the joints physical limitations. • Robustness: When a singularity occurs, the algorithm must be capable of not getting stuck or become chaotic. • Cost: The time it takes to find a solution. We will present a survey on the most used existing control-based algorithms. We point out the drawbacks of each one of them, to later propose a new way of numerically filtering the Jacobian matrix, and also a new method to avoid step-depending convergence issues, while respecting joint limits, to have a very smooth and robust algorithm. All these methods have been implemented using Matlab to solve the inverse kinematics of some robots. The results of two of them, a 4R planar robot and the Barrett’s WAM arm, are shown so as to draw conclusions. To end up, we discuss the convergence of these methods, and the global use of them. The algorithm we propose has the advantadge of successfully respecting joint limits and its convergence is not being step-dependent makes it more robust. Nevertheless, we also discuss the need of, when the goal is far from the starting position, add path planning methods to approach the target.

Direct position kinematics of a three revolute- prismatic-spherical parallel manipulator

Abstract: In this work, the direct position kinematics of a 3 degree-of-freedom parallel manipulator with three identical limbs, type revolute-prismatic-spherical (RPS), is analyzed. In contrast to the previous studies on this class of manipulators, the revolute joints of the proposed manipulator are actuated rather than the prismatic joints. Direct position kinematics of the manipulator leads to a system of three nonlinear equations in three unknowns that are reduced to a univariate polynomial of degree eight and two quadratic equations in sequence using Sylvester dialytic elimination method. In addition, to show the efficiency of the presented method a numerical example is provided.

Kinematics and workspace of 3-RUU parallel manipulator

Abstract: Kinematics design of a lower-DOF parallel robot parallel, a 3-UUR pure rotational parallel manipulator, is presented. We first analyzed the instantaneous motions of 3-RUU parallel robot at initial configuration by reciprocal screw, after the inverse kinematics and forward kinematics are analyzed. At the basis on the kinematics, the workspace of parallel robot is presented in the paper. The main influences for the workspace of parallel robot consist of circumscribed circle radius of fixed platform Ra, circumscribed circle radius of moving fixed platform R b , length of connecting rod l and the angles Θ among connecting rod. The performances of such 3-RUU mechanisms are very different for different configurations. The curve of simulation which prove the academic analysis is given by Adams.

Research on Planar Six-bar Mechanism's Kinematics Simulation System

Abstract: The paper established the kinematics model of the planar six-bar mechanism of shaper by closed-volume method.On the basis,using MATLAB/GUI toolbox,a kinematics simulation system applied to planar six-bar mechanism was developed by means of MATLB programming.And it was used for the kinematics simulation and animation display of shaper,furthermore,simulated the figure of angle,angular velocity and angular acceleration of link and the figure of position,velocity and acceleration of slider and ram.The result proves that this system can be used to analyze institutions conveniently and intuitionally and the change of mechanism kinematics characteristics is achieved by changing parameters.

Analysis on Workspace and Influence Coefficients of a Proposed Palletizing Robot

Abstract: The kinematic equations for a proposed palletizing robot are established using Denavit-Hartenberg (D-H) method.When considering some constraint conditions,its kinematics equations are solved by using numerical methods and its three-dimensional workspace maps and coordinate plane projection maps are derived.On this basis,the concept of influence coefficient on robot workspace is brought forward and defined.Finally,the influence coefficients curves about the length and rotation angle of links are obtained and quantitatively analyzed in detail,and its structural optimization and design from kinematic view is provided.