Analytical Method for Determination of Internal Forces of Mechanisms and Manipulators

This paper presents a theory for the analytical determination of internal forces in the links of planar linkage mechanisms and manipulators with statically determinate structures, considering the distributed dynamic loads. Linkage mechanisms and manipulators were divided into elements and joints. Discrete models were created for both the elements and the entire mechanism. The dynamic equations of equilibrium for the discrete model of the elements and the hinged and rigid joints, under the action of longitudinal and transverse distributed dynamic trapezoidal loads, were derived. In the dynamic equations of the equilibrium of the discrete model of the elements and joints, the connections between the components of the force vector in the calculated cross-sections and the geometric, physical, and kinematic characteristics of the element were established for its plane-parallel motion. According to the developed technique, programs were created in the Maple system, and animations of the motion of the mechanisms were produced. The links were constructed with the intensity of transverse- and longitudinal-distributed dynamic loads, bending moments, and shearing and normal forces, depending on the kinematic characteristics of the links.http://dx.doi.org/10.3390/robotics703005

Dynamics of the Orthoglide parallel robot

Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed orientation, which means that the actuating directions are normal to each other. Three identical legs connecting to the moving platform are located on three planes being perpendicular to each other too. Knowing the position and the translation motion of the platform, we develop the inverse kinematics problem and determine the position, velocity and acceleration of each element of the robot. Further, the principle of virtual work is used in the inverse dynamic problem. Some matrix equations offer iterative expressions and graphs for the input forces and the powers of the three actuators

CAD-based approach for identification of elasto-static parameters of robotic manipulators

The paper presents an approach for the identification of elasto-static parameters of a robotic manipulator using the virtual experiments in a CAD environment. It is based on the numerical processing of the data extracted from the finite element analysis results, which are obtained for isolated manipulator links. This approach allows to obtain the desired stiffness matrices taking into account the complex shape of the links, couplings between rotational/translational deflections and particularities of the joints connecting adjacent links. These matrices are integral parts of the manipulator lumped stiffness model that are widely used in robotics due to its high computational efficiency. To improve the identification accuracy, recommendations for optimal settings of the virtual experiments are given, as well as relevant statistical processing techniques are proposed. Efficiency of the developed approach is confirmed by a simulation study that shows that the accuracy in evaluating the stiffness matrix elements is about 0.1%.Comment: arXiv admin note: substantial text overlap with arXiv:0909.146

Dynamic modelling of hexarot parallel mechanisms for design and development

In this research, the kinematics, dynamics, and general closed-form dynamic formulation of the centrifugal high-G hexarot-based manipulators have been developed through the different mathematical modeling techniques. The vibrations of the mechanism have also been investigated

Outils pour l’identification des paramètres de raideur des robots à l’aide d’un logiciel de CAO

This report proposes a CAD-based approach for identification of the elasto-static parameters of the robotic manipulators. The main contributions are in the areas of virtual experiment planning and algorithmic data processing, which allows to obtain the stiffness matrix with required accuracy. In contrast to previous works, the developed technique operates with the deflection field produced by virtual experiments in a CAD environment. The proposed approach provides high identification accuracy (about 0.1% for the stiffness matrix element) and is able to take into account the real shape of the link, coupling between rotational/translational deflections and joint particularities. To compute the stiffness matrix, the numerical technique has been developed, and some recommendations for optimal settings of the virtual experiments are given. In order to minimize the identification errors, the statistical data processing technique was applied. The advantages of the developed approach have been confirmed by case studies dealing with the links of parallel manipulator of the Orthoglide family, for which the identification errors have been reduced to 0.1%ANR COROUSS

Kinematic Modeling, Linearization and First-Order Error Analysis

This chapter deals with a modular method for the kinematic analysis of parallel kinematic machines (PKM) at discrete points within their workspace. Firstly, a modular approach is presented for calculating the forward kinematic transmission function of some widely used parallel kinematic machines. This includes the well-known Stewart-Gough-platforms of general geometry, the Delta-robots, and parallel machines with legs of constant length. The kinematic analysis is based on the kinetostatic method and permits to calculate the position, velocity, and acceleration transmission from the articulated joints towards the moveable platform of the machine. Furthermore, a force transmission is defined based on kinetostatic duality. By means of a simple numerical calculation schema, a comprehensive first-order sensitivity analysis is performed. Finally, it is shown how to set up the stiffness matrix for the aforementioned robots. Computational examples of the proposed algorithms are presented

An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters

Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

Kinematic and dynamic analysis of spatial six degree of freedom parallel structure manipulator

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2003Includes bibliographical references (leaves: 63-69)Text in English; Abstract: Turkish and Englishviii, 86 leavesThis thesis covers a study on kinematic and dynamic analysis of a new type of spatial six degree of freedom parallel manipulator. The background for structural synthesis of parallel manipulators is also given. The structure of the said manipulator is especially designed to cover a larger workspace then well-known Stewart Platform and its derivates. The main point of interest for this manipulator is its hybrid actuating system, consisting of three revolute and three linear actuators.Kinematic analysis comprises forward and inverse displacement analysis. Screw Theory and geometric constraint considerations were the main tools used. While it was possible to derive a closed-form solution for the inverse displacement analysis, a numerical approach was used to solve the problem of forward displacement analysis. Based on the results of the kinematic analysis, a rough workspace study of the manipulator is also accomplished. On the dynamics part, attention has been given on inverse dynamics problem using Lagrange-Euler approach.Both high and lower level software were heavily utilized. Also computer software called .CASSoM. and .iMIDAS. are developed to be used for structural synthesis and inverse displacement analysis. The major contribution of the study to the scientific community is the proposal of a new type of parallel manipulator, which has to be studied extensively regarding its other interesting properties