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Parametric Sweep Search for Parallel Robot Workspace Determination

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Parametric Sweep Search for Parallel Robot Workspace Determination PARAMETRIC SWEEP SEARCH FOR PARALLEL ROBOT WORKSPACE DETERMINATION by CHE ZULKHAIRI ABDULLAH A thesis submitted to The University of Birmingham for the degree of DOCTOR OF PHILOSOPHY School of Mechanical Engineering Collage of Engineering and Physical Sciences The University of Birmingham September 2013 1 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. SYNOPSIS The research presented in this thesis aims to augment the conventional kinematic-based parallel robot workspace determination into an interactive 3D visual system by highlighting the design issue clearly and providing important design information to the user in real-time. The conventional iteration involves heavy computation, high resolution data processing and multiple technical skills set which usually reduce the design option into amending an existing design most related to the requirement. The thesis presents a 3D simulation system that is open and modular and allows for algorithm and technical functional extensions. Following an extensive literature survey on key aspects relating to parallel design development, parallel robot singularity, and search for workspace, five main phases of experimental works were undertaken to develop a strategic search and analysis of parallel robot’s workspace. Phase 1 involves the development of a 3-dimensional simulation system based on Python in order to search for workspace and singularity. The 3-dimensional motions are based on Kinematic, and should integrate easily with various algorithms. The simulation system produces a draft quality result, which is scalable to higher resolutions. Phase 2 involves the development of geometric singularity and Grassmann singularity real-time test. The code should work effortlessly when user redefines the architecture or geometry of the robot. Phase 3 involves the development of Boolean Parametric sweep search strategy that 2 provides an analysis and validation method for the system. The system has to consider various factors such as limit, edge, resolution, and travel direction. This phase involves the integration of 3D and 4D interpolation and extrapolation strategies including Trilinear, L- system fractal, Simplex, adjacency tree and Marching Cube. Phase 4 involves the development of a dynamic grid that is easily integrated into 2D and 3D databases. The haptic engine finds position and orientation information based on this dynamic grid. The grid is tested for a number of concepts such as Simplex, Binary tree and L-system fractal. It was found that the parametric sweep based on Boolean control is applicable in real-time dynamic grid system, where the direction, region and constraint are configurable by either the user or automatically by the system. Phase 5 involves the development of a controller for the Python simulation. This is a multiple Degree-of-Freedom device with two-way motor control for all axes, which is fitted with sensors to provide pre-processed value for distance and orientation on all axes. The controller is a haptic device that provides the user with force-feedback sensation while user operates and manipulates the device. The haptic device provides (i) control for the Python simulation, (ii) processed data to a Matlab and Solid Works system, and (iii) singularity-free control of an associated physical robot. The proposed system is finally verified against a number of applications. 3 ACKNOWLEDGMENTS First of all, I would like to express my deepest gratitude to my supervisor Dr Mozafar Saadat, in the School of Mechanical Engineering, University of Birmingham for his academic supervision, guidance and encouragement over the course of the research. I would like to acknowledge the support from Yayasan Telekom Malaysia and Multimedia University Cyberjaya, Malaysia for providing the opportunity, time and scholarship which enabled this research to be carried out. I would also like to express my heartfelt gratitude to my family (Rodiah Khalid, Aisya Imya and Aileen Fatima Imya) for their understanding and support in providing endless encouragement and motivation. Lastly, I would like to thank my friend Mr Hamid Rakhodaie, Mr Ali Tayebisadrabadi and Mr Nik Farid Che Zainal and colleagues for all their assistance and support, and Mr Hisham bin Jabar for reading through my thesis. 4 TABLE OF CONTENTS SYNOPSIS ............................................................................................................................ 2 ACKNOWLEDGMENTS ................................................................................................... 4 LIST OF FIGURES ............................................................................................................. 9 LIST OF TABLES ............................................................................................................. 11 Chapter 1 : INTRODUCTION ......................................................................................... 12 1.1 Background to the project .................................................................................... 12 1.2 Aims and objectives ............................................................................................. 16 1.3 Thesis layout ........................................................................................................ 17 Chapter 2 : LITERATURE REVIEW ............................................................................ 18 2.1 Challenges in Parallel Robot simulation design .................................................. 18 2.2 Parallel Robot’s Singularity ................................................................................. 19 2.3 Parallel Robot’s workspace .................................................................................. 21 2.4 Haptic Controller .................................................................................................. 22 2.5 Limb rehabilitation strategy ................................................................................. 25 2.6 Cutting path strategy based on Bezier .................................................................. 29 Chapter 3 : KINEMATIC MODEL ................................................................................ 30 3.1 Introduction .......................................................................................................... 30 3.2 Kinematic model .................................................................................................. 30 3.3 Workspace calculations based on inverse kinematic ........................................... 34 3.4 Conclusion ........................................................................................................... 35 Chapter 4 : GRASSMANN ALGEBRA .......................................................................... 36 4.1 Introduction .......................................................................................................... 36 4.2 Grassmann theory................................................................................................. 36 4.3 Weighted value ranking based on Grassmann algebra ........................................ 40 4.4 Results for Grassmann probability experiment .................................................... 44 4.5 Conclusion ........................................................................................................... 45 Chapter 5 : PARAMETRIC SWEEP SEARCH ............................................................ 46 5.1 Introduction .......................................................................................................... 46 5.2 Introduction to parametric sweep ......................................................................... 46 5.3 Condition test theory ............................................................................................ 47 5.4 Parametric Sweep theory...................................................................................... 50 5 5.5 Parametric sweep modelling ................................................................................ 54 5.6 Basic Sweep theory .............................................................................................. 56 5.7 Advanced Parametric Sweep search based on L-system ..................................... 57 5.8 Boolean control for Parametric Sweep search ..................................................... 60 5.9 Test point population theory ................................................................................ 61 5.10 Test point population based on fractal theory .................................................... 63 5.11 Parametric Sweep methodology ......................................................................... 64 5.12 Parametric sweep random fractal generator ....................................................... 65 5.13 Parametric sweep type Hilbert 3D ..................................................................... 66 5.14 Parametric sweep grid extrapolation .................................................................
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