Advances in Robot Kinematics, Softcover reprint of the original 1st ed. 2000

This book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufacturing, automation, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dexterity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw algebra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers and students, in fields of engineering and mathematics related to robot theory, design, control and application. All articles in the book were reported at the seventh international symposium on Advances in Robot Kinematics that was organised in June 2000 in the beautiful ancient Mediterranean town of Piran in Slovenia. The preceding symposia of the series took place in Ljubljana (1988), Linz (1990), Ferrara (1992), Ljubljana (1994), and Piran (1996), and Salzburg (1998).

1. Methods in Kinematics.- Study’s kinematic mapping — A tool for motion design.- Kinestatic analysis of serial and parallel robot manipulators using Grassmann-Cayley algebra.- Unit quaternion and CRV: Complementary non-singular representations of rigid-body orientation.- Numerically stable methods for converting rotation matrices to Euler parameters.- Geometry of homokinematic spatial Cardan shafts by dual methods.- A concise Bézier clipping technique for solving inverse kinematics problems.- Geometric calibration of robots using multiple plane constraints.- 2. Kinematic Synthesis.- On isotropic sets of points in the plane. Application to the design of robot architectures.- Fourier methods for synthesis of coupled serial chain mechanisms.- Dimensional synthesis of spatial RR robots.- Approximate motion synthesis via parametric constraint manifold fitting.- Designing linkages with symmetric motions: The spherical case.- Kinematic synthesis of planar platforms with RPR, PRR, and RRR chains.- 3. Force Analysis.- Impact analysis as a design tool for the legs of mobile robots.- Vehicle wheel-ground contact angle estimation: with application to mobile robot traction control.- The Melbourne hand.- Active force closure for multiple objects.- SCALPP: A 6-dof robot with a non-spherical wrist for surgical applications.- A framework for multi-contact multi-body dynamic simulation and haptic display.- On the dynamics of a class of parallel robots.- 4. Kinematic Redundancy.- A simplified criterion for the repeatability of redundant manipulators.- An intuitive interface for nullspace teaching of redundant robots.- Methods for resolving velocity degeneracies of joint-redundant manipulators.- Novel kinematics for continuum robots.- The optimum quality index for a spatial redundant4–8 in-parallel manipulator.- Fuzzy inverse kinematics for underwater vehicle-manipulator systems.- 5. Parallel Mechanisms and Workspace Analysis.- Symmetries in workspace densities of discretely actuated manipulators.- Workspace characterization of planar three-legged platforms with holonomic higher pairs.- Estimating the controllable workspace of tendon-based Stewart platforms.- The chord method for the determination of non-convex workspaces of planar parallel platforms.- Elasto-kinematic design tools for parallel mechanisms.- Kinematic analysis of a new parallel machine tool: the orthoglide.- Optimal trajectory planning of a 5-axis machine-tool based on a 6-axis parallel manipulator.- 6. Analysis and Application of Parallel Mechanisms.- A 4-dof parallel mechanism simulating the movement of the human sternum-clavicle-scapula complex.- Parallel mechanisms applied to the human knee passive motion simulation.- A geometric model for cylinder-cylinder impact with application to vertebrae motion simulation.- Architecture singular parallel manipulators and their self-motions.- Architectural shakiness or architectural mobility of platforms.- Möbius mechanisms.- 7. Parallel Mechanisms and Screw Algebra.- Direct kinematics of the double-triangular manipulator: An exercise in geometric thinking.- A three-dof tripod for generating spherical rotation.- Kinematical analysis and simulation of a new parallel mechanism for robotics’ application.- Early studies in screw theory.- On deriving infinitesimal twists and velocity screws from finite displacement screws.- Synthesis by screw algebra of translating in-parallel actuated mechanisms.- Author Index.