DISTANCE-BASED FORMULATIONS FOR THE POSITION ANALYSIS OF KINEMATIC CHAINS

[1]  N. Manolescu,et al.  A method based on Baranov Trusses, and using graph theory to find the set of planar jointed kinematic chains and mechanisms , 1973 .

[2]  Robert Stawell Ball,et al.  The theory of screws: A study in the dynamics of a rigid body , 1876 .

[3]  Clément Gosselin,et al.  Forward displacement analysis of third-class analytic 3-RPR planar parallel manipulators , 2001 .

[4]  Offer Shai,et al.  CHECKING MOBILITY AND DECOMPOSITION OF LINKAGES VIA PEBBLE GAME ALGORITHM , 2011 .

[5]  Carlo Innocenti,et al.  Polynomial solution to the position analysis of the 7-link assur kinematic chain with one quaternary link , 1995 .

[6]  Eldon Hansen,et al.  Global optimization using interval analysis , 1992, Pure and applied mathematics.

[7]  Federico Thomas,et al.  On the Trilaterable Six-Degree-of-Freedom Parallel and Serial Manipulators , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[8]  Youxin Luo,et al.  Forward Displacement Analysis of a Kind of Nine-Link Barranov Truss Based on Hyper-chaotic Newton Downhill Method , 2010, 2010 Second International Conference on Intelligent Human-Machine Systems and Cybernetics.

[9]  Wen-Yeuan Chung,et al.  The position analysis of Assur kinematic chain with five links , 2005 .

[10]  Charles W. Wampler.  Displacement Analysis of Spherical Mechanisms Having Three or Fewer Loops , 2004 .

[11]  G. Gogu.  Mobility of mechanisms: a critical review , 2005 .

[12]  Liao Qi-zheng.  Research on Displacement Analysis of a Kind of Non-Planar Nine-Link Barranov Truss , 2006 .

[13]  J. Sefrioui,et al.  Polynomial solutions for the direct kinematic problem of planar three-degree-of-freedom parallel manipulators , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[14]  Federico Thomas,et al.  A Linear Relaxation Technique for the Position Analysis of Multiloop Linkages , 2009, IEEE Transactions on Robotics.

[15]  Lu Yang,et al.  Solving Spatial Constraints with Global Distance Coordinate System , 2006, Int. J. Comput. Geom. Appl..

[16]  Anoop K. Dhingra,et al.  Closed-form displacement analysis of 8, 9 and 10-link mechanisms , 2000, Mechanism and Machine Theory.

[17]  F. Freudenstein.  Approximate synthesis of four-bar linkages , 1955, Journal of Fluids Engineering.

[18]  Henry Wolkowicz,et al.  Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming , 1999, Comput. Optim. Appl..

[19]  Pin Wang,et al.  Displacement analysis of nine-link Barranov truss , 2007 .

[20]  J. M. Porta,et al.  Box Approximations of Planar Linkage Configuration Spaces , 2007 .

[21]  O. Shai.  Topological Synthesis of All 2D Mechanisms Through Assur Graphs , 2010 .

[22]  Jean-Pierre Merlet,et al.  Direct kinematics of planar parallel manipulators , 1996, Proceedings of IEEE International Conference on Robotics and Automation.

[23]  Carme Torras,et al.  A branch-and-prune algorithm for solving systems of distance constraints , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[24]  E. Allgower,et al.  Introduction to Numerical Continuation Methods , 1987 .

[25]  Carlo Innocenti,et al.  Position analysis in analytical form of the 7-link assur kinematic chain featuring one ternary link connected to ternary links only , 1997 .

[26]  Deepak Kapur,et al.  Comparison of various multivariate resultant formulations , 1995, ISSAC '95.

[27]  R. J. Walker.  Algebraic curves , 1950 .

[28]  Ileana Streinu,et al.  The Number of Embeddings of Minimally Rigid Graphs , 2004, Discret. Comput. Geom..

[29]  C. Galletti,et al.  A note on modular approaches to planar linkage kinematic analysis , 1986 .

[30]  Richard H. Byrd,et al.  A Stochastic/Perturbation Global Optimization Algorithm for Distance Geometry Problems , 1997, J. Glob. Optim..

[31]  Andrew J. Sommese,et al.  The numerical solution of systems of polynomials - arising in engineering and science , 2005 .

[32]  Ea Evert Dijksman.  Motion Geometry of Mechanisms , 1976 .

[33]  Albert Castellet Llerena.  Solving inverse kinematics problems using an interval method , 1998 .

[34]  C. D. Albert,et al.  Kinematics of machinery , 1931 .

[35]  Federico Thomas,et al.  INVERSE KINEMATICS BY DISTANCE MATRIX COMPLETION , 2005 .

[36]  Enric Celaya,et al.  A Relational Positioning Methodology for Robot Task Specification and Execution , 2008, IEEE Transactions on Robotics.

[37]  A. Castellet,et al.  An Algorithm for the Solution of Inverse Kinematics Problems Based on an Interval Method , 1998 .

[38]  Luis Basañez Villaluenga,et al.  A framework for robotized teleoperated tasks , 2011 .

[39]  Federico Thomas,et al.  Revisiting trilateration for robot localization , 2005, IEEE Transactions on Robotics.

[40]  F. Thomas,et al.  A coordinate-free approach to tracing the coupler curves of pin-jointed linkages , 2011 .

[41]  Günter Hommel,et al.  On the Tangent-Half-Angle Substitution , 1993 .

[42]  Wei Shimin,et al.  Direct position analysis of nine-link Barranov truss based on Dixon resultants , 2006 .

[43]  Josep M. Porta,et al.  CuikSLAM: A Kinematics-based Approach to SLAM , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[44]  Jian S. Dai,et al.  Orientation and Workspace Analysis of the Multifingered Metamorphic Hand—Metahand , 2009, IEEE Transactions on Robotics.

[45]  Q. Liao,et al.  New research of forward displacement analysis of 6-link Assur group , 2010, The 2nd International Conference on Information Science and Engineering.

[46]  Q. Liao,et al.  Research on Position Analysis of a Kind of Nine-Link Barranov Truss , 2008 .

[48]  Abdo Y. Alfakih,et al.  On the uniqueness of Euclidean distance matrix completions , 2003 .

[49]  J. C. Owen,et al.  The non-solvability by radicals of generic 3-connected planar Laman graphs , 2006 .

[50]  Bernard Roth,et al.  Solving the Input/Output Problem for Planar Mechanisms , 1999 .

[51]  Damien Chablat,et al.  Kinematic analysis of a class of analytic planar 3-RPR parallel manipulators , 2009, ArXiv.

[52]  Jon C. Dattorro,et al.  Convex Optimization & Euclidean Distance Geometry , 2004 .

[53]  Bruno Buchberger,et al.  Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..

[54]  Qizheng Liao,et al.  Closed-form displacement analysis for a nine-link Barranov truss or a eight-link Assur group , 2000 .

[55]  Federico Thomas,et al.  Multi-loop Position Analysis via Iterated Linear Programming , 2006, Robotics: Science and Systems.

[56]  Alex. B. W. Kennedy,et al.  The Kinematics of Machinery: Outlines of a Theory of Machines , 2006 .

[57]  C. Innocenti.  Analytical Determination of the Intersections of Two Coupler-Point Curves Generated by Two Four-Bar Linkages , 1993 .

[58]  K. Wohlhart.  Position Analysis of the Rhombic Assur Group , 1995 .

[59]  Francis C. Moon,et al.  Franz Reuleaux: Contributions to 19th century kinematics and theory of machines , 2003 .

[60]  Liao De-gang.  The Research of Newton Iterative Method Based on Chaos Mapping and its Application to Forward Solutions of the 3-RPR Planar Parallel Mechanism , 2007 .

[61]  M. Husty,et al.  On the kinematic constraint surfaces of general three-legged planar robot platforms , 2003 .

[62]  Abel J. P. Gomes,et al.  A Derivative-Free Tracking Algorithm for Implicit Curves with Singularities , 2004, International Conference on Computational Science.

[63]  S. Lösch.  Parallel Redundant Manipulators Based on Open and Closed Normal Assur Chains , 1995 .

[64]  Jonathan D. Hauenstein,et al.  Software for numerical algebraic geometry: a paradigm and progress towards its implementation , 2008 .

[65]  Rohitash Chandra,et al.  On solving the forward kinematics of 3RPR planar parallel manipulator using hybrid metaheuristics , 2011, Appl. Math. Comput..

[66]  Jan Verschelde,et al.  Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation , 1999, TOMS.

[67]  Paul J. Zsombor-Murray,et al.  Unified Kinematic Analysis of General Planar Parallel Manipulators , 2004 .

[68]  Federico Thomas,et al.  Distance Constraints Solved Geometrically , 2004 .

[69]  Luo You-xin,et al.  Forward solutions of the 3-RPR planar parallel mechanism with Wu′s method , 2004 .

[70]  Lydia E. Kavraki,et al.  Randomized path planning for linkages with closed kinematic chains , 2001, IEEE Trans. Robotics Autom..

[71]  Juan Jesús Pérez,et al.  Complete maps of molecular‐loop conformational spaces , 2007, J. Comput. Chem..

[72]  J. O'Rourke.  Art gallery theorems and algorithms , 1987 .

[73]  A. Ampere.  Essai sur la philosophie des sciences, ou, Exposition analytique d'une classification naturelle de toutes les connaissances humaines / , 1856 .

[74]  J. Hauenstein,et al.  Mechanism mobility and a local dimension test , 2011 .

[75]  Timothy F. Havel.  Some Examples of the Use of Distances as Coordinates for Euclidean Geometry , 1991, J. Symb. Comput..

[76]  B. Roth,et al.  Synthesis of Path-Generating Mechanisms by Numerical Methods , 1963 .

[77]  Manfred Husty,et al.  Non-singular assembly mode change in 3-RPR-parallel manipulators , 2009 .

[78]  Federico Thomas,et al.  The Forward Kinematics of 3-R$\underline{P}$R Planar Robots: A Review and a Distance-Based Formulation , 2011, IEEE Transactions on Robotics.

[79]  Sebti Foufou,et al.  Using Cayley-Menger determinants for geometric constraint solving , 2004, SM '04.

[80]  Jean-Pierre Merlet,et al.  Parallel Robots , 2000 .

[81]  Iulian Popescu,et al.  Position analysis in polynomial form of planar mechanisms with Assur groups of class 3 including revolute and prismatic joints , 2003 .

[82]  Carlo Innocenti,et al.  Analytical-form position analysis of the 7-link assur kinematic chain with four serially-connected ternary links , 1994 .

[83]  Youxin Luo,et al.  Forward Displacement Analysis of 25th Nine-Link Barranov Truss Based on Chaos Least Square Method , 2010, 2010 Second International Conference on Computer Modeling and Simulation.

[84]  Federico Thomas,et al.  On closed-form solutions to the position analysis of Baranov trusses , 2012 .

[85]  Han Lin,et al.  Closed-Form Displacement Analysis of a Planar Fifth-Class Group with Lower Pairs , 2010 .

[86]  C. Collins,et al.  Forward kinematics of planar parallel manipulators in the Clifford algebra of P2 , 2002 .

[87]  Anoop K. Dhingra,et al.  Closed-form displacement and coupler curve analysis of planar multi-loop mechanisms using Gröbner bases , 2001 .

[88]  J. Lambert.  Numerical Methods for Ordinary Differential Systems: The Initial Value Problem , 1991 .

[89]  J. Michael McCarthy,et al.  Kinematics, Polynomials, and Computers—A Brief History , 2011 .

[90]  K. Wohlhart.  Position analyses of normal quadrilateral Assur groups , 2010 .

[91]  Thomas R. Hagedorn.  General Formulas for Solving Solvable Sextic Equations , 2000 .

[92]  Federico Thomas,et al.  Distance-based position analysis of the three seven-link Assur kinematic chains , 2011 .

[93]  Damien Chablat,et al.  Degeneracy study of the forward kinematics of planar 3-RPR parallel manipulators , 2007, ArXiv.

[94]  Marco Ceccarelli,et al.  Burmester and Allievi: A Theory and Its Application for Mechanism Design at the End of 19th Century , 2008 .

[95]  Carme Torras,et al.  A branch-and-prune solver for distance constraints , 2005, IEEE Transactions on Robotics.

[96]  Z. Lan,et al.  Kinematic decomposition of coupler plane and the study on the formation and distribution of coupler curves , 2002 .

[97]  Iulian Popescu,et al.  Position analysis in polynomial form of class-three Assur groups with two or three prismatic joints , 2008 .

[98]  Irina Voiculescu,et al.  Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms , 2009 .

[99]  Yasutoshi Yajima,et al.  Positive semidefinite relaxations for distance geometry problems , 2002 .

[100]  Jian S. Dai,et al.  Forward displacement analysis of the general 6–6 Stewart mechanism using Gröbner bases , 2009 .

[101]  Alfonso Hernández,et al.  Position analysis of planar mechanisms with R-pairs using a geometrical–iterative method , 2004 .

[102]  Leonard M. Blumenthal,et al.  Distance Geometries, a Study of the Development of Abstract Metrices , 1938 .

[103]  A. N. Almadi,et al.  Closed-form displacement analysis of 10-link 1-DOF mechanisms: Part 2 – polynomial solutions , 2001 .

[104]  K. H. Hunt,et al.  Structural Kinematics of In-Parallel-Actuated Robot-Arms , 1983 .

[105]  Karl Menger,et al.  New Foundation of Euclidean Geometry , 1931 .

[106]  Robert Willis,et al.  Principles of Mechanism , 2007 .

[107]  Huiping Shen,et al.  Configuration analysis of complex multiloop linkages and manipulators , 2000 .

[108]  Charles W. Wampler,et al.  Solving the Kinematics of Planar Mechanisms by Dixon Determinant and a Complex-Plane Formulation , 2001 .

[109]  Andreas Müller,et al.  Generic mobility of rigid body mechanisms , 2009 .

[110]  A Closed-Form Approach to Coupler-Curves of Multi-Loop Mechanisms , 2000 .

[111]  Pin Wang,et al.  Closed-form displacement analysis of a kind of non-planar nine-link Barranov truss , 2008, 2008 IEEE International Conference on Automation and Logistics.

[112]  Ileana Streinu,et al.  The Number of Embeddings of Minimally Rigid Graphs , 2002, SCG '02.

[113]  L Burmester,et al.  Lehrbuch der Kinematik , 1888 .

[114]  Lu Zhen.  Displacement Analysis of a Nine-Link Barranov Truss , 2009 .

[115]  K. Menger.  Untersuchungen über allgemeine Metrik , 1928 .

[116]  Leonidas J. Guibas,et al.  Inverse Kinematics in Biology: The Protein Loop Closure Problem , 2005, Int. J. Robotics Res..

[117]  Robert Michael Lewis,et al.  Molecular Embedding via a Second Order Dissimilarity Parameterized Approach , 2009, SIAM J. Sci. Comput..

[118]  Ferdinand Freudenstein.  On the Variety of Motions Generated by Mechanisms , 1962 .

[119]  H. Scheraga,et al.  Exact analytical loop closure in proteins using polynomial equations , 1999 .

[120]  Karl Wohlhart,et al.  Position analyses of open normal assur groups A (3.6) , 2009, 2009 ASME/IFToMM International Conference on Reconfigurable Mechanisms and Robots.

[121]  C. Galletti.  On the position analysis of Assur's groups of high class , 1979 .

[122]  Francis C. Moon,et al.  Robert Willis and Franz Reuleaux: pioneers in the theory of machines , 2003, Notes and Records of the Royal Society of London.

[123]  Offer Shai,et al.  Combinatorial characterization of the Assur graphs from engineering , 2008, Eur. J. Comb..

[124]  Abdo Y. Alfakih,et al.  On the uniqueness of Euclidean distance matrix completions: the case of points in general position , 2005 .

[125]  Anoop K. Dhingra,et al.  Closed-form displacement analysis of 8, 9 and 10-link mechanisms , 2000 .

[126]  Federico Thomas,et al.  Solving geometric constraints by iterative projections and backprojections , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[127]  Gordon R. Pennock,et al.  A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage , 2002 .

[128]  N. Kazarinoff.  Ruler and the Round: Classic Problems in Geometric Constructions , 2011 .

[129]  S. Y. Ku,et al.  Computing polynomial resultants: Bezout's determinant vs. Collins' reduced P.R.S. algorithm , 1969, CACM.

[130]  D. G. Sotiropoulos,et al.  Optimal centers in branch-and-prune algorithms for univariate global optimization , 2005, Appl. Math. Comput..

[131]  Charles W. Wampler,et al.  Solving the Kinematics of Planar Mechanisms , 1999 .

[132]  T. Koetsier,et al.  From kinematically generated curves to instantaneous invariants: Episodes in the history of instantaneous planar kinematics , 1986 .

[133]  M. Laurent.  A connection between positive semidefinite and euclidean distance matrix completion problems , 1998 .

[134]  Zhu Yu-feng.  Displacement Analysis of a Kind of Nine-Link Barranov Truss , 2006 .

[135]  Karl Wohlhart,et al.  Robots Based on Assur Group A (3.5) , 2008 .

[136]  Q. Liao,et al.  A method for position analysis of a kind of nine-link Barranov truss , 2007 .

[137]  Chen Nai-chao.  Position analysis of planar complex mechanisms using triangular vector loop method , 2005 .

[138]  Jack E. Graver,et al.  Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures , 2001 .

[139]  Konstantinos-Dionysios Bouzakis,et al.  Position analysis in polynomial form of planar mechanism with an Assur group of class 4 including one prismatic joint , 2004 .

[140]  Offer Shai.  The correction to Grubler criterion for calculating the Degrees of Freedoms of Mechanisms , 2011 .

[141]  Federico Thomas,et al.  A Robust Forward Kinematics Analysis of 3-RPR Planar Platforms , 2010 .

[142]  K. H. Hunt,et al.  Kinematic geometry of mechanisms , 1978 .

[143]  R. Gregorio,et al.  Polynomial solution to the position analysis of two Assur kinematic chains with four loops and the same topology , 2009 .

[144]  Symmetrical Coupler Curve and Singular Point Classification in Planar and Spherical Swinging-Block Linkages , 2006 .

[145]  Joseph Duffy,et al.  A vector analysis of robot manipulators , 1985 .

[146]  Leonard M. Blumenthal,et al.  Theory and applications of distance geometry , 1954 .

[147]  McCarthy,et al.  Geometric Design of Linkages , 2000 .

[148]  S. Roberts.  On Three‐bar Motion in Plane Space , 1875 .

[149]  Youxin Luo,et al.  Forward Displacement Analysis of Non-Plane Two Coupled Degree Nine-Link Barranov Truss Based on Hyper-Chaotic Newton Downhill Method , 2010 .

[150]  Federico Thomas,et al.  Closed-Form Solution to the Position Analysis of Watt–Baranov Trusses Using the Bilateration Method , 2011 .

[151]  Han Lin,et al.  Wus Method for Forward Displacement Analysis of the Planar Parallel Mechanisms , 1998 .

[152]  Gordon R. Pennock,et al.  Curvature theory for the double flier eight-bar linkage , 2004 .

[153]  Damien Chablat,et al.  Non-Singular Assembly-mode Changing Motions for 3-RPR Parallel Manipulators , 2008, ArXiv.

[154]  A. N. Almadi,et al.  A Gröbner-Sylvester Hybrid Method for Closed-Form Displacement Analysis of Mechanisms , 2000 .

[155]  Lu Zhen.  Displacement Analysis of Non-Planar Nine-Link Barranov Truss , 2008 .

[156]  C. Gosselin,et al.  The direct kinematics of planar parallel manipulators: Special architectures and number of solutions , 1994 .

[157]  Paul J. Zsombor-Murray,et al.  Solving the Forward Kinematics of a Planar Three-Legged Platform With Holonomic Higher Pairs , 1999 .

[158]  Gordon R. Pennock,et al.  Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot , 1992 .

[159]  H Nolle,et al.  Linkage coupler curve synthesis: A historical review—II. Developments after 1875☆ , 1974 .