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    THẠC SĨ 3-Axis and 5-Axis Machining with Stewart Platform

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  6. 3-Axis and 5-Axis Machining with Stewart Platform

    i










    Declaration

    I hereby declare that this thesis is my original work and it has been written by me
    in its entirety. I have duly acknowledged all
    the sources of information which have been used in the thesis.

    This thesis has also not been submitted for any degree in any university previously.




    Ng Chee Chung
    30 July 2012

    Acknowledgements
    ii

    Acknowledgements

    The author would like to express his sincere gratitude to Prof. Andrew Nee
    Yeh Ching and Assoc. Prof. Ong Soh Khim for their assistance, inspiration and
    guidance throughout the duration of this research project.

    The author is also grateful to his fellow postgraduate students, Mr.
    Vincensius Billy Saputra, Mr. Bernard Kee Buck Tong, Miss Wong Shek Yoon,
    Mr. Stanley Thian Chen Hai and professional officer, Mr. Neo Ken Soon and Mr.
    Tan Choon Huat for their constant encouragement and suggestions. Furthermore,
    he is also grateful to Laboratory Technologist Mr. Lee Chiang Soon, Mr. Au Siew
    Kong and Mr. Chua Choon Tye for their help in the fabrication of the components
    and their advice in the design of the research project.

    In addition, the author would like to acknowledge the assistance given by
    the technical staff of the Advanced Manufacturing Laboratory, Mr. Wong Chian
    Long, Mr. Simon Tan Suan Beng, Mr. Ho Yan Chee and Mr. Lim Soon Cheong.

    Last but not least, the author would also like to acknowledge the financial
    assistance received from National University of Singapore for the duration of the
    project, and to thank all those who, directly or indirectly, have helped him in one
    way or another. Table of Contents
    iii

    Table of contents
    Declaration i
    Acknowledgements . ii
    Table of contents iii
    Summary iv
    List of Tables vi
    List of Figures . vii
    List of Symbols xiii
    Chapter 1 Introduction 1
    Chapter 2 Kinematics of Stewart Platform . 13
    Chapter 3 Fundamentals of Machining . 39
    Chapter 4 Three-Axis Machining 50
    Chapter 5 Five-axis machining . 76
    Chapter 6 Five-axis machining post-processor . 91
    Chapter 7 Calibration of Stewart Platform 110
    Chapter 8 Control interface . 124
    Chapter 9 3-DOF modular micro Parallel Kinematic Manipulator for machining
    . 130
    Chapter 10 Conclusions and Recommendations . 160
    References . 166
    Appendices 172
    Appendix A: NC Code tables 172
    Appendix B: Coordinate of circular arc in NC program . 175
    Appendix C: Sensors installation methods . 184
    Appendix D: Image processing . 200
    Appendix E: Interval time calculation 219 Summary
    iv

    Summary

    There is an increasing trend of interest to implement the Parallel
    Kinematics Platforms (Stewart Platforms) in the fields of machining and
    manufacturing. This is due to the capability of the Stewart Platforms to perform
    six degrees-of-freedom (DOF) motions within a very compact environment,
    which cannot be achieved by traditional machining centers.

    However, unlike CNC machining centers which axes of movements can be
    controlled individually, the movement of a Stewart Platform requires a
    simultaneous control of the six individual links to achieve the final position of the
    platform. Therefore, the available commercial CNC applications for the
    machining centers are not suitable for use to control a Stewart Platform. A
    specially defined postprocessor has to be developed to achieve automatic
    conversion of CNC codes, which have been generated from commercial CAM
    packages based on the CAD models, to control and manipulate a Stewart Platform
    to achieve the machining purposes. Furthermore, a sophisticated control interface
    has been developed so that users can perform machining with a Stewart Platform
    based on CNC codes.

    Calibration of the accuracy of the developed NC postprocessor program
    has been performed based on actual 3-axis and 5-axis machining processes
    performed on the Stewart Platform. A machining frame with a spindle was
    designed and developed, and a feedback system was implemented based on wire Summary
    v

    sensors mounted linearly along the actuators of the platform. Thus, the position
    and orientation of the end-effector can be calibrated based on the feedback of the
    links of the platform. Experimental data was collected during the machining
    processes. The data was analyzed and improvement was made on the
    configuration of the system.

    Alternate machining processes are reviewed with Parallel Kinematic
    Manipulators of different structural designs that have been used for the Stewart
    Platform. The structural characteristics associated with parallel manipulators are
    evaluated. A class of three DOF parallel manipulators is determined. Several types
    of parallel manipulators with translational movement and orientation have been
    identified. Based on the identification, a hybrid 3-.UPU (Universal Joint-
    Prismatic-Universal Joint) parallel manipulator was fabricated and studied.


    List of Tables
    vi

    List of Tables
    Table 3.1 Characteristic of various structure concepts [Reimund, 2000] . 43
    Table 3.2 Comparison of workspace of CNC machine and Stewart Platform 45
    Table 4.1 Coordinate systems . 52
    Table 9.1 Feasible limb configurations for spatial 3-DOF manipulators [Tsai,
    2000] . 133
    Table 9.2 Workspace of mobile platforms with various radii . 137
    Table 9.3 Workspace of the base with various radii . 138
    Table 9.4 Calibration Result of the Micro Stewart Platform with the CMM . 155
    Table 9.5 Calibration Result of the Micro Stewart Platform with the CMM when
    the Platform travels within boundary workspace 157
    Table A1 Address characters [Ken, 2001] 172
    Table A2 G-codes chart [Ken, 2001] 173
    Table A3 Miscellaneous functions (M functions) [Ken, 2001] 174
    Table D1 Difference of displacement value of each actuator corresponding to
    100,000 counts of pulse of the stepper motor . 213
    Table D2 Error of motion along the Z-axis . 215
    Table D3 Coordinate of the calibrated Points . 217
    Table E1 Previous data collected by manually moving the Stewart Platform 222
    Table E2 The time calculation when the velocity is 50000 step/sec and the
    acceleration is 500000 step/sec
    2
    222 List of Figures
    vii

    List of Figures
    Figure 1.1 Serial kinematics chains [Irene and Gloria, 2000] 3
    Figure 1.2 Parallel kinematics manipulator classifications . 5
    Figure 1.3 The standard Stewart Platform [Craig, 1986] 7
    Figure 1.4 Stewart Platform machining center . 9
    Figure 2.1 The Gough-Stewart Platform . 14
    Figure 2.2 Locations of the joints of the platform 16
    Figure 2.3 Locations of the joints of the base . 16
    Figure 2.4 The workspace of Stewart Platform when . 32
    Figure 2.5 The algorithm of the workspace calculation 33
    Figure 2.6 The singularity configuration of Stewart Platform [Yee, 1993] 37
    Figure 3.1 Standard postprocessor sequences . 41
    Figure 3.2 CNC model inputs/outputs schematic representation 42
    Figure 3.3 Comparison of the workspace of Stewart Platform (blue color dots) and
    CNC machine (red color lines) . 44
    Figure 3.4(a) Dexterous workspace (red color box) of the Stewart Platform (Front)
    . 46
    Figure 3.4(b) Dexterous workspace (red color box) of the Stewart Platform (Side)
    . 46
    Figure 4.1 The coordinate system of a Stewart Platform 50
    Figure 4.2 Comparison of the coordinate systems of the cutting tool and the
    Stewart Platform 51
    Figure 4.3 Cutting tool and platform movements during the machining process for
    Stewart Platform 52
    Figure 4.4 Format of an NC program . 56
    Figure 4.5 Flow chart of identification algorithm to evaluate address characters
    and the respective values . 58
    Figure 4.6(a) Flow chart of algorithm to determine maximum number of G code59
    Figure 4.6(b) Flow chart of algorithm to determine maximum number of M code
    . 60
    Figure 4.7 Flow chart of matrix preparation for the corresponding character
    address of an NC program 62
    Figure 4.8 Flow chart of algorithm to assign the value of character addresses of an
    NC program to the respective character addresses matrix array . 63
    Figure 4.9 Flow chart of algorithm to determine the characteristics of the
    coordinate system 65
    Figure 4.10 Flow chart of algorithm to determine the values of X-, Y- and Z-
    coordinates 66
    0 ,0 ,0   
      List of Figures
    viii

    Figure 4.11 Flow chart of algorithm to determine the cutting plane and the style of
    the cutting path 68
    Figure 4.12(a) Flow chart of algorithm to convert NC program to machine
    trajectory . 69
    Figure 4.12(b) Flow chart of algorithm to convert NC program to the machine
    trajectory . 70
    Figure 4.13 Trajectory path of a Stewart Platform translated from an NC program
    . 71
    Figure 4.14(a) The pocketing machining process: plot outline in MasterCam . 72
    Figure 4.14(b) The pocketing process: MasterCam generate the tool cutting path
    . 72
    Figure 4.14(c) The pocketing process: Simulation of cutting path in MasterCam 73
    Figure4.14(d) The pocketing process: Generate trajectory path . 73
    through MATLAB
    ®
    73
    Figure 4.14(e) The pocketing process: Machine workpiece through the contouring
    process . 74
    Figure 4.15 3D cutting path generated from the NC program created from model
    in MasterCam 75
    Figure 4.16 Outcome of machining on a Stewart Platform 75
    Figure 5.1 Geometric error associated with tolerance between freeform surface
    and designed surface . 77
    Figure 5.2 A constant step over distance in the parametric space does not
    generally yield a constant step over in the Cartesian space [Liang, 2002] . 78
    Figure 5.3 Triangular tessellated freeform surface . 79
    Figure 5.4 Standard triangular representation of STL model . 80
    Figure 5.5 Generation of CC points 83
    Figure 5.6 Determination of the intersection points between the cutting plane and
    the face on the freeform surface 85
    Figure 5.7(a) Flow chart for the generation of CC points . 86
    Figure 5.7(b) Flow chart for the generation of CC points 87
    Figure 5.8 Local Coordinate System (LCS) Setup . 88
    Figure 5.9 Collision between tool and freedom surface . 89
    Figure 5.10 Gouging . 90
    Figure 6.1 Comparison of (a) 5-axis machining center and (b) Stewart Platform 92
    Figure 6.2 Various coordinate systems defined in the Stewart Platform 93
    Figure 6.3 Orientation of mobile platform around Y-axis 95
    Figure 6.4 Relationship between the cutting tool frame LCS and the workpiece
    frame LCS . 97 List of Figures
    ix

    Figure 6.5 Normal Vector of Face intersected with the Cutting Plane . 99
    Figure 6.6 ASCII STL text format 101
    Figure 6.7 The surface model derived from the vertices and faces 101
    Figure 6.8 Tessellated triangular surfaces of the freeform surface . 102
    Figure 6.9 Intersected points with norm (green dot line) along the cutting plane
    . 103
    Figure 6.10 Intersected points of the freeform surface with one cutting plane and
    perpendicular lines (green) are the normal of the intersected points 104
    Figure 6.11 Generation of the intersected points with a series of cutting planes 105
    Figure 6.12 Generation of the intersected points with a series of cutting planes 106
    Figure 6.13 Trajectory path of the Stewart Platform generated based on the LCS
    of the freeform surface 107
    Figure 6.14 Trajectory path of the Stewart Platform with retracted points 107
    Figure 6.15 Simulation of 5-axis machining in MATLAB
    ®
    . 108
    Figure 6.16 5-axis machining result 109
    Figure 7.1 The mounting of the sensors to the sensor holder . 111
    Figure 7.2 The model of the trajectory path of the end-effector based on the
    feedback of the wire sensors while the platform was moving along the Z-axis . 112
    Figure 7.3 The model of the trajectory path of the end-effector based on the
    feedback of the wire sensors while the platform was moving along the Z-axis
    (front view) 113
    Figure 7.4 The model of the trajectory path of the end-effector based on the
    feedback of the wire sensors while the platform was moving along the X-axis . 114
    Figure 7.5 The model of the trajectory path of the end-effector based on the
    feedback of the wire sensors while the platform was moving along the Y-axis . 115
    Figure 7.6 Feedback of actuators stroke position while the platform is . 117
    being manipulated. 117
    Figure 7.7 The corresponding position and orientation of the platform end-effector
    with respect to the strokes of the actuators . 118
    Figure 7.8 The Stewart Platform position and orientation feedback interface . 119
    Figure 7.9 The real time feedback interface of the wire sensor when the platform
    is being manipulated . 120
    Figure 7.10 The tool path generated from the real time position feedback 120
    Figure 7.11 Calibration of workpiece . 121
    Figure 7.12 Comparison of calibrated result of the plotted point (Blue) and the
    ideal point (Red) and the coordinate of the plotted points on the calibration plate
    . 122
    Figure 8.1 Motion control interface 125
    Figure 8.2 Motion control feedback 126 List of Figures
    x

    Figure 8.3 Wire sensor interface . 127
    Figure 8.4 NC program Interface 128
    Figure 8.5 OpenGL Interface 129
    Figure 9.1(a)(b) 6-Legged Micro Stewart Platform and 3-Legged Micro Stewart
    Platform (c) PSU Micro Stewart Platform 135
    Figure 9.2 Comparison of Workspace of 3-legged (red) and 6-legged (blue)
    Parallel Manipulator 136
    Figure 9.3 Workspace VS radius of Mobile Platform . 137
    Figure 9.4 Workspace vs Radius of Base . 138
    Figure 9.5 The workspace comparison between Passive Joint angle of 20º and 45º
    . 140
    Figure 9.6 The M-235.5 DG Actuator and Hephaist Seiko Spherical Joint . 142
    Designs of the Micro Parallel Manipulator . 142
    Figure 9.7 Parallel Manipulator system fabricated using the same modular
    components (Prismatic Actuator, Spherical Joints, Universal Joints and Variable
    Links) 143
    Figure 9.8 (a) Pure Translational Platform, (b) Pure Rotational Platform 146
    Figure 9.9 Hybrid UPU Parallel Kinematic Manipulator . 147
    Figure 9.10 Schematic Diagram of the Parallel Kinematics Platform (PKM) 148
    Figure 9.11 Calculation of the actual stroke of the link 149
    Figure 9.12 Denavit-Hartenberg Representation 150
    Figure 9.13 The UPU Modified Stewart Platform with a passive prismatic middle
    link 151
    Figure 9.14 The Relationship between the Surface Point and the spherical joint152
    Figure 9.15 Workspace of the Surface Point of the Hybrid PKM 153
    Figure 9.16 Accuracy Calibration of the Micro Stewart Platform with CMM . 154
    Figure 9.17 Displacement and Rotational Error Analysis 156
    Figure 9.18 Integration of the hybrid 3-DOF PKM into 3-axis machining center
    . 159
    Figure 9.19 The machined workpiece . 159
    Figure 10.1 The theodolites system based on the principle of triangulation 164
    Figure B1 Generic circular arc motion of the machining point in one plane 176
    Figure B2 Clockwise circular arc motion with angle of starting point θ smaller
    than angle of ending point β with respect to reference point 178
    Figure B3 Clockwise circular arc motion with angle of ending point smaller than
    angle of starting point with referred to reference point . 178
    Figure B4 Clockwise circular arc motion with starting point at the right side and
    ending point at the left side of the reference point 179 List of Figures
    xi

    Figure B5 Clockwise circular arc motion with starting point at the left side and
    ending point at the right side of the reference point 180
    Figure B6 Clockwise circular arc motion with starting point and ending point at
    the left side of the reference point with angle theta larger than angle beta . 181
    Figure B7 Clockwise circular arc motion with starting point and ending point at
    the left side of the reference point with angle theta smaller than angle beta 182
    Figure C1 The developed Stewart Platform and the Epsilon wire sensor . 184
    Figure C2 The MATLAB® simulation of the forward kinematics calibration
    system 186
    Figure C3 The laser pointer calibration system diagram 187
    Figure C4 The MATLAB® simulation of the laser platform calibration system 189
    Figure C5 The wire sensor calibration system diagram 191
    Figure C6 Cartesian Coordinate of the vector points 193
    Figure C7 The calibration setup for wire sensor . 195
    Figure C8 Graph of Comparison between theoretical data and actual data from
    Multimeter . 196
    Figure C9 Graph of Actual Length vs Voltage of the wire sensor 197
    Figure C10 Wire sensor interface . 198
    . 198
    Figure C11 The Sampled Wave Signal of the wire sensors 198
    Figure D1 The original image with marked points . 200
    Figure D2 Black and white image . 201
    Figure D3 the Image is rotated into the position so that it is in line with the
    horizontal level 202
    Figure D4 Calibrated points of the image in terms of red color for the printed
    point and blue color highlighted dots for the points marked by the pen . 202
    Figure D5 the tilted line (in green) plotted with respected to the marked points in
    the middle of the graph . 203
    Figure D6a All three sets of coordinates of the Printed Points (Red), Marked
    Points (Blue) and Modified Points (Green) 204
    Figure D6b All three sets of coordinates without background image . 205
    Figure D7 the errors of calibrated points along the X-axis . 206
    Figure D8 the errors of calibrated points along the Y-axis . 207
    Figure D9(a) the distance between two adjacent points along the X-axis 208
    Figure D9(b) the distance between two adjacent points along the Y-axis 209
    Figure D10 The unevenness of the points motion even though it is moving 210
    in the X-direction 210 List of Figures
    xii

    Figure D11 The corresponding error resulting from the ratio of actuator movement
    over the counter of 100,000 steps from the controller 212
    Figure D12 The LVDT-like device . 214
    Figure D13 Calibrated Workpiece 216
    Figure D14 The comparison of coordinates between the actual calibrated points
    and the theoretical points 218
    Figure E1 Distance, Velocity and Acceleration Diagram . 220
    Figure E2 Flow chart of the interval time control . 223 List of Symbols
    xiii

    List of Symbols

    F e The effective DOF of the assembly or mechanism

    The DOF of the space in which the mechanism operates

    L Number of links

    j Number of joints

    f i Degree-of Freedom of i-th joint

    I d Idle or passive Degrees-Of-Freedom

    X p , Y p , Z P The Origin of Platform

    X B , Y B , Z B The Origin of Base

    P i Platform attachment joints, spherical joints, i = 1, 2 , 6

    B i Base attachment joints, universal joints, i = 1, 2 , 6

    σ i The magnitude of the links vector, , i = 1, 2 , 6

    W The force that act on the platform

    A The area of the platform, m
    2

    Υ The Poisson’s Ratio

    I Inertia


    Leg vector

    R Rotational matrix

    S Sine

    C Cosine

    V Matrix of Cartesian Velocities

    W Matrix of Joint Velocities

    D, d Euclidean distance between the two vectors

    i
    l
    List of Symbols
    xiv


    NaN Not a Numerical number

    Rot 3x3 3 x 3Rotation matrix of Stewart Platform

    Tr 3x1 3 x 1Translational matrix of Stewart Platform

    T Homogeneous Coordinate

    Ξ Tolerance of Error

    t

    Translational Vector

    i
    X


    Matrix of pose vector of Stewart Platform

    G Mapping function of length of actuators to the pose of the
    Stewart Platform

    H Differentiation of Mapping function G with the corresponding
    element of the pose vector of Stewart Platform

    R xyz Rotation matrix around X-axis, Y-axis and Z-axis

    Rz,α Rotation matrix around Z axis with rotational angle of α

    Ry,β Rotation matrix around Y axis with rotational angle of β

    Rz,γ Rotation matrix around Z axis with rotational angle of γ

    A z Area of the workspace of Stewart Platform

    V Volume of Workspace

    f bi Force acting on the spherical joint of the mobile platform

    f ai Force acting on the universal joint of the base of Stewart
    Platform

    ω p Angular velocity of the mobile platform

    i
    n i Moment acting on the actuator


    m 1

    Mass of cylinder of actuator

    m 2 Mass of piston of actuator
    List of Symbols
    xv

    e 1i Distance between the center of mass of the cylinder and the
    bottom of the cylinder

    e 2i Distance between the center of mass of the piston and the top of
    the piston

    v 1, v 2 Velocity of the center of mass of the cylinder and piston

    B
    n p Moment about the center of mass of the mobile platform


    i
     Actuating force of the platform


    X_platform,
    Y_platform,
    Z_platform
    Coordinates of mobile platform in local coordinate system

    X_CNC_Code,
    Y_CNC_Code,
    Z_CNC_Code
    Coordinate of XYZ coordinates in NC program

    X abs ,Y abs ,Z abs Absolute coordinate of X, Y and Z position of the mobile
    platform

    X rel ,Y rel ,Z rel Relative coordinate of X, Y and Z position of the mobile
    platform

    C Vector between cutter contact point and normal N of the
    triangular faces of the freeform surface

    N Vector of normal to the face of the triangle in the freeform
    surface

    α c Critical angle of Collision

    α 1 , α 2 Critical angle of gouging

    V mw Vector from milling cutter to workpiece

    N R Magnitude of vector of the normal to the triangle face of the
    freeform surface

    Chapter 1 Introduction
    1
    Chapter 1 Introduction

    Parallel manipulators can be found in many applications in the industry,
    such as vehicle and airplane simulators [Stewart, 1965], adjustable articulated
    trusses [Reinholtz and Gockhale, 1987], mining machines [Arai et al, 1991],
    positioning devices [Gosselin and Hamel, 1994], fine positioning devices, and off-
    shore drilling platforms. Recently, it has also been developed as high precision
    milling machines, namely, a hexapod machining center by Giddings and Lewis in
    1995. A Stewart Platform is a form of manipulator with six degrees of freedoms
    (DOF), which allows one to provide a given position and orientation of the
    surface in the vicinity of any point of the platform on its three Cartesian
    coordinates and projection of the unit of normal vector [Alyushin, 2010].

    The design of parallel manipulators can be dated back to 1962 when
    Gough and Whitehall [Gough, 1962] devised a six-linear jacking system for use as
    a universal tire testing machine. Stewart presented his platform manipulator for
    use as an aircraft simulator in 1965 [Stewart, 1965]. Hunt made a systematic study
    of the parallel manipulator structures [Hunt, 1983]. Since then, parallel
    manipulators have been studied extensively by many other researchers [Tsai,
    1996].

    However, greater interests in the application of these mechanisms in the
    metalworking field have only grown in the last decade. The first CNC-type
    hexapod machine tool prototype (Variax from Giddings & Lewis and the Chapter 1 Introduction
    2
    Octahedral Hexapod from Ingersoll) was presented at the 1994 International
    Machine Tool Show in Chicago. These prototypes were enthusiastically
    welcomed as the new generation of machine tools due to their specific
    characteristics [Irene and Gloria, 2000]:
     Higher payload to weight ratio
     Non-cumulative joint error
     Higher structural rigidity
     Modularity
     Location of the motors close to the fixed base
     Simpler solution of the ‘inverse’ kinematics problem

    However, there are still many disadvantages of the Stewart Platform as
    compared to the serial manipulators, such as a limited workspace and problems in
    singularity configuration. Furthermore, it also has complicated forward kinematics
    due to the closed loop configuration of the system.

    Configuration and classification

    Most of the robots being used in the industries today are serial robots or
    serial manipulators. Manipulators are basically mechanical motion devices,
    generally with two or more DOF. Serial manipulators are normally made up of
    between two to six rigid links with prismatic and/or revolute joints connecting the
    links in an open kinematics chain. Examples of this kind of robots include the
    PUMA 560 series of robot arm and the SCARA type Adept One robot arm [Yee
    1993].

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