Theory of Parallel Mechanisms

Grübler-Kutzbach Criterion.-  3.2.2 Mobility Open Issue.-  3.3 Mobility Principle based on Reciprocal Screw.-  3.3.1 Mechanism Can Be Expressed as a Screw System.-  3.3.2. Development of Our Unified Mobility Principle.-  3.3.3 The Modified G-K Formulas.-  3.4 Constraint Analysis based on Reciprocal Screw.-  3.4.1 The Common Constraint.-  3.4.2 Parallel Constraint.-  3.4.3. Over-constraint.-  3.4.4. The Generalized Kinematic Pair.-  3.5 Mobility Property Analyses.-  3.5.1 Translation and Rotation.-  3.5.2 Rotational Axis.-  3.5.3 Instantaneous Mobility and Full-cycle Mobility.-  3.5.4 Full-field Mobility.-  3.5.5 Parasitic Motion.-  3.5.6 Self-motion.-  References.-  Chapter 4 Mobility Analysis Part 2.- 4.1  Mobility analysis of simple mechanisms.-  4.1.1  Open Chain linkage.-  4.1.2  Roberval mechanism.-  4.1.3  RUPUR mechanism.-  4.1.4  Hervé 6.bar mechanism.-  4.1.5  Spatial 4P mechanism.-  4.1.6  Delassus H-H-H-H Mechanism.-  4.1.7  Hervé's CCC Mechanism.-  4.2  Mobility Analysis of classical mechanisms.-  4.2.1  Bennett mechanism.-  4.2.2  Five-bar Goldberg Linkage.-  4.2.3  Six-bar Goldberg linkage.-  4.2.4  Myard linkage with symmetrical plane.-  4.2.5  Bricard with symmetrical plane.-  4.2.6  Altmann Abb.34 Mechanism.-  4.2.7  Altmann six-bar linkage.-  4.2.8  Waldron six-bar linkage.-  4.3  Mobility Analysis of Modern Parallel Mechanisms.-  4.3.1  4-DOF 4-URU Mechanism.-  4.3.2  3-CRR mechanism.-  4.3.3  Zlatanov and Gosselin's Mechanism.-  4.3.4  Carricato's mechanism.-  4.3.5  Delta mechanism.-  4.3.6  H4 manipulator.-  4.3.7  Yang's mechanism.-  4.4  Mobility analysis of Hoberman Switch-pitch ball.-  4.4.1 Structure analysis.-  4.4.2 Three-link chain.-  4.4.3 Eight-link loop.-  4.4.4 Double loop.-  4.4.5 Three-loop chain.-  4.4.6  The whole mechanism.-  4.5  Six-hole cubiform mechanism.-  4.5.1 Double-hole linkage.-  4.5.2 Four-hole linkage.-  4.5.3 five-hole linkage.-  4.5.4 The whole six-hole mechanism.-  References.-  Chapter 5  Kinematic Influence Coefficient and Kinematics Analysis.-  5.1 Concept of KIC.-  5.2 KIC and Kinematic Analysis of Serial Chains.-  5.2.1 Position Analysis.-  5.2.2 First-Order KIC.-  5.2.3 Second-Order KIC.-  5.3 Kinematic Analysis of Parallel Mechanism.-  5.3.1 First-Order KIC and Mechanism Velocity Analysis.-  5.3.2 Second-Order KIC and Mechanism Accelerations.-  5.4 Virtual Mechanism Principle of Lower-Mobility Parallel Mechanisms.-  5.4.1 Virtual Mechanism Principle.-  5.4.2 Kinematic Analysis Based on Virtual Mechanism Principle.-  Fig. 5.7 A virtual limb.-  References.-  Chapter 6   Full-Scale Feasible Instantaneous Screw Motion.-  6.1. Introduction.-  6.2. Determination of Principal Screws.-  6.2.1 The Representation of pitch and axes.-  6.2.2 Principal screws of a third-order screw system.-  6.3. Full-Scale Feasible Instantaneous Screws of the 3-RPS mechanism.-  6.3.1. Virtual Mechanism and Jacobian Matrix.-  6.3.2 Upper platform is parallel to the base.-  6.3.3 The upper platform rotates by an angle about line a2a3.-  6.3.4 General configuration of the 3-RPS mechanism.-  6.4. Full-Scale Feasible Instantaneous Screw of a 3-UPU mechanism.-  6.4.1 Mobility analysis.-  6.4.2 First-order influence matrices and kinematic analysis.-  6.4.3. Initial configuration.-  6.4.4 The second configuration.-  6.5 Full-Scale Feasible Instantaneous Screw of a 3-RPS Pyramid mechanism.-  6.5.1 First-order influence coefficient matrix (Jacobian matrix).-  6.5.2  Principal screws and full-scale feasible motions.-  6.6 A 3-DOF Rotational Parallel Manipulator without Intersecting Axes.-  6.6.1 An Open Problem of the PMs with Intersecting Axes.-  6.6.2 A 3-D revolute mechanism without intersecting axes.-  6.3.3 The Orientation Workspace.-  6.6.4  Examples.-  6.6.5 Discussions about the differences between the SPMs and the 3-RPS Cubic PM.-  References.-  Chapter 7  special configuration of Mechanisms.-  7.1. Introduction.-  7.2. Classification of the Special Configuration.-  7.2.1 Singular kinematics classification.-  7.2.2 Classification of the Singularity via a Linear Complex.-  7.3. Singular Kinematic Principle.-  7.4. Singularity Loci of 3/6-Stewart For special orientations.-  7.4.1 Typical Singularity Structures of 3/6-SP.-  7.4.2 Hyperbolic Singularity Equation Derived in an Oblique Plane.-  7.4.3 Singularity Equation Derived in 3D Space.-  7.4.4 Singularity Distribution in 3D Space.-  7.5. Structure and Property of THE Singularity Loci of 3/6-Stewart for General Orientations ( ).-  7.5.1. Singularity Equation Based on Theorem 3 for General Orientations.-  7.5.2  Singularity Analysis Using Singularity-Equivalent-Mechanism.-  7.5.3. General Case.-  7.5.4 Five Special Cases of the Singularity Equation.-  7.6. Structure and Property of the Singularity Loci of the 6/6-Stewart.-  7.6.1 Jacobian Matrix.-  7.6.2 Singularity Analysis in 3D Space.-  7.6.3 Singularity Analysis in Parallel Principal-Sections.-  7.7 Singularity of a 3-RPS Manipulator.-  7.7.1  3-RPS Mechanism.-  7.7.2. Singularity and Its spatial distribution.-  7.7.3. Geometry and Constraint Analysis.-  References.-  Appendix A.-  Chapter 8  Dynamic Problems of Parallel Mechanisms.-  8.1 Over-determine inputs.-  8.1.1 Influence coefficient matrices and inertia forces.-  8.1.2 The Accordant Equation for over-determinate Inputs.-  8.1.3 Optimization of Over-Determinate Input.-  8.1.4 The Weight Distribution of the input Torques.-  8.2  Kinetostatic Analysis of 4-UPU Parallel Mechanisms.-  8.2.1 Main-pair reaction Forces.-  8.2.2 Numerical Example.-  8.3 Kinetostatic Analysis of 4-R(CRR) Parallel Manipulator.-  8.3.1 4-R(CRR) Parallel Manipulator.-  8.3.2. Main-pair reaction.-  8.3.3 Active moments and reactions of other pairs in limbs.-  8.3.4 Numerical example.-  8.3.5. Discussion.-  References.-  Chapter 9 Constraint screw-based method for type synthesis.-  9.1 Description of constraints acting on a rigid body.-  9.2 Limb twist and limb constraint systems.-  9.2.1 Limb twist system.-  9.2.2 Limb constraint system.-  9.3 Platform twist and platform constraint systems.-  9.3.1 Platform twist system.-  9.3.2 Platform constraint system and classification of lower-mobility PMs.-  9. 4 Constraint-screw based synthesis method.-  9.4.1 Procedure of the constraint-screw based synthesis method.-  9.4.2 Generation of different architectures of PM.-  9.4.3 Discrimination for instantaneous PMs.-  9.5 Examples.-  9.5.1 Type synthesis of a 3R2T 5-DOF PM.-  9. 5. 2 Type synthesis of 2R3T 5-DOF PMs.-  9. 5. 3 Type synthesis of 1R3T 4-DOF PMs.-  9. 5. 4 Type synthesis of 3R1T 4-DOF PMs.-  9. 5. 6 Type synthesis of a 2R1T 3-DOF PM.-  9. 5. 7 Type synthesis of a 3T 3-DOF PM.-  9. 5. 8 Type synthesis of a 3R 3-DOF PM.-  9. 5. 9 Type synthesis of a 1R2T 3-DOF PM.-  References.-  Chapter 10   Digital Topology Theory of Kinematic Chains and Atlas Database.-  10-1 Topology Modeling of Mechanisms.-  10.1.1 Modeling of simple joint kinematic chains.-  10.1.2  Modeling of multiple joint kinematic chains.-  10.1.3  Modeling of geared (cam) kinematic chains.-  10.2  Loop operation algebra of kinematic chains.-  10.2.1 Loop and its representation.-  10.2.2  " " Operation of Loops.-  10.2.3  " " Operation of Loops.-  10.2.5  Loop analysis.-  10.2.6  Edge-based operations of loops.-  10.3  Isomorphism identification.-  10.3.1  Perimeter topological graph.-  10.3.2  Canonical perimeter topological graph.-  10.3.3  Characteristic perimeter topological graph.-  10.3.4  Examples of isomorphism identification.-  10.3.5  Analysis of computational complexity.-  10.4  Detection of rigid sub-chains.-  10.5  Digital atlas database and synthesis.-  References.- Index.