The Gantry-Tau parallel kinematic machine-kinematic and elastodynamic design optimisation

Pubished version of an article in the journal: Meccanica. Also available from the publisher at: http://dx.doi.org/10.1007/s11012-010-9394-9One of the main advantages of the Gantry-Tau machine is a large accessible workspace/footprint ratio compared to many other parallel machines. The optimal kinematic, elastostatic and elastodynamic design parameters of the machine are still difficult to calculate and this paper introduces an optimisation scheme based on the geometric and functional dependencies to define the workspace and first resonance frequency. This method assumes that each link and universal joint can be described by a mass-spring-damper model and calculates the transfer function from a Cartesian force or torque to Cartesian position or orientation. The evolutionary algorithm based on the complex search method is compared to the gradient-based search function in Matlab integrated optimisation toolbox. Kinematic design obtained by optimisation according to this paper gives a 2D workspace/footprint ratio more than 1.66 and first resonance frequency is more than 50 Hz with components of an existing lab prototype at the University of Agder, Norway

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

Three-Stage Design Analysis and Multicriteria Optimization of a Parallel Ankle Rehabilitation Robot Using Genetic Algorithm

This paper describes the design analysis and optimization of a novel 3-degrees of freedom (DOF) wearable parallel robot developed for ankle rehabilitation treatments. To address the challenges arising from the use of a parallel mechanism, flexible actuators, and the constraints imposed by the ankle rehabilitation treatment, a complete robot design analysis is performed. Three design stages of the robot, namely, kinematic design, actuation design, and structural design are identified and investigated, and, in the process, six important performance objectives are identified which are vital to achieve design goals. Initially, the optimization is performed by considering only a single objective. Further analysis revealed that some of these objectives are conflicting, and hence these are required to be simultaneously optimized. To investigate a further improvement in the optimal values of design objectives, a preference-based approach and evolutionary-algorithm-based nondominated sorting algorithm (NSGA II) are adapted to the present design optimization problem. Results from NSGA II are compared with the results obtained from the single objective optimization and preference-based optimization approaches. It is found that NSGA II is able to provide better design solutions and is adequate to optimize all of the objective functions concurrently. Finally, a fuzzy-based ranking method has been devised and implemented in order to select the final design solution from the set of nondominated solutions obtained through NSGA II. The proposed design analysis of parallel robots together with the multiobjective optimization and subsequent fuzzy-based ranking can be generalized with modest efforts for the development of all of the classes of parallel robots

Industrial Robotics

This book covers a wide range of topics relating to advanced industrial robotics, sensors and automation technologies. Although being highly technical and complex in nature, the papers presented in this book represent some of the latest cutting edge technologies and advancements in industrial robotics technology. This book covers topics such as networking, properties of manipulators, forward and inverse robot arm kinematics, motion path-planning, machine vision and many other practical topics too numerous to list here. The authors and editor of this book wish to inspire people, especially young ones, to get involved with robotic and mechatronic engineering technology and to develop new and exciting practical applications, perhaps using the ideas and concepts presented herein

Motion/Force transmission analysis of axis-symmetric parallel mechanisms with closed-loop sub-chains

 This thesis presents several results regarding the kinematic performance analysis of axis-symmetric parallel mechanisms with closed-loop sub-chains. Screw theory based methods have been utilised to generate new indices, along with a formal procedure, enabling the systematic and complete singularity and motion/force transmission analysis of parallel mechanisms with these closed-loop sub-chains

MATLAB

This excellent book represents the final part of three-volumes regarding MATLAB-based applications in almost every branch of science. The book consists of 19 excellent, insightful articles and the readers will find the results very useful to their work. In particular, the book consists of three parts, the first one is devoted to mathematical methods in the applied sciences by using MATLAB, the second is devoted to MATLAB applications of general interest and the third one discusses MATLAB for educational purposes. This collection of high quality articles, refers to a large range of professional fields and can be used for science as well as for various educational purposes

Dynamic isotropy in 3-DOF Gantry Tau robots - An analytical study

3-DOF Gantry Tau is a type of parallel robot, consisting of six struts configured in three clusters, which provides three translational DOFs. It has increasing industrial use in applications where large workspace and high stiffness are required. In fact, the concept of dynamic isotropy, where all the natural frequencies of a system are equal, can be employed in order to effectively optimize the geometry of robots. However, no study on dynamic isotropy of Gantry Tau robots has yet been reported in the literature. In this paper, the problem of dynamic isotropy in 3-DOF Gantry Tau robots is analytically addressed. Firstly, the kinematics is established based on a general approach with 36 geometric variables. Jacobian and stiffness matrices are also investigated where the struts are considered to be axially flexible. Subsequently, analytical solutions to obtain both a decoupled stiffness matrix and a complete dynamic isotropy are presented. Finally, as an example, dynamically isotropic geometries of a Gantry Tau robot are calculated, for a reference platform, using the developed analytical method

Vibrations and Dynamic Isotropy in Hexapods - Analytical Studies

The present work was initiated based on an industrial demand for designing a high-bandwidth hexapod of an advanced large optical telescope. In this dissertation, we have generalized this industrial problem to fully-parametric models of the hexapod vibrations as well as analytical studies on dynamic isotropy in parallel robots, which can be directly used in any hexapod application. Hexapods (also known as Gough-Stewart Platforms, GSPs), being the most widely used type of 6-DOF parallel robots, are employed in numerous modern applications. This work firstly establishes a comprehensive and fully-parametric model for the vibrations in hexapods at symmetric configurations. We have developed three models presenting the Cartesian-space formulation and the joint-space formulation of the hexapod vibrations as well as a refined model taking also the inertia of the struts into account. It is noteworthy that such complete analytical models were not available in the literature prior to the present work. In particular, it is for the first time that the inertia of the struts is being taken into account with a full-analytical approach. Kinematics and accordingly the Jacobian of hexapods are developed parametrically. The equations of motion are formulated and linearized based on a Lagrangian dynamics approach. Inertia, stiffness and damping matrices are also parametrically formulated. The eigenvectors and eigenfrequencies are then established in both the Cartesian and joint spaces. By introducing the inertia of the struts, despite the apparent symmetric geometry, the equivalent inertia matrix in the Cartesian space turns out to be a non-diagonal matrix. In addition, the decoupled vibrations are analytically investigated where it is shown that the consideration of the strut inertia may lead to significant changes of the decoupling conditions. Furthermore, for a reference hexapod, the vibrational behavior with respect to different design variables are systematically studied. The problem of dynamic isotropy, as an optimal design solution for hexapods, is also addressed in this dissertation. Dynamic isotropy is a condition in which all eigenfrequencies of a robot are equal. This is a powerful tool in order to obtain dynamically optimized architectures for parallel robots. We analytically present the conditions of dynamic isotropy in hexapods with and without the consideration of the strut inertia. Dynamic isotropy in hexapods is bound to a constraint related to the inertia properties (classical isotropic constraint), which makes it practically impossible to obtain dynamic isotropy by the standard hexapod architecture. To overcome this limitation, we have extended our study on hexapods to a general study on platforms supported elastically by three nodal joints in 6 DOFs. This method establishes dynamically isotropic solutions for kinematic designs with 3-2-1 and 2-2-2 arrangements. We have shown how effectively this method can be used for obtaining a generalized class of hexapods in order to eliminate the classical isotropic constraint. Accordingly, we have proposed a novel architecture of a generalized hexapod which is dynamically isotropic for a wide range of inertia properties. Finally, we have further extended our work on dynamic isotropy to analytical studies which are not necessarily limited to hexapods. Firstly, we have shown how dynamic isotropy can be achieved with the same approach in other parallel robots. A 3-DOF Gantry Tau robot is presented as an example. Then, the following two novel concepts in dynamic isotropy are introduced and developed in this dissertation: • Analytical index of dynamic isotropy: the analytical index of dynamic isotropy is a measure that mathematically combines all the eigenfrequencies and analytically represents the closeness of a robot to complete dynamic isotropy. It is a powerful tool in order to obtain dynamically isotropic architectures. Furthermore, when there exist geometrical/inertial constraints that make it impossible to accomplish complete dynamic isotropy, this analytical index can also be used for obtaining near-dynamic-isotropy design solutions. • Optimal dynamic isotropy: the presented results show that dynamically isotropic architectures are not unique in hexapods. Therefore, we have mathematically introduced a novel concept in order to find an optimal dynamically isotropic architecture