A Robust Solution of the Spatial Burmester Problem

The problem of spherical four-bar linkage synthesis is revisited in this paper. The work is aimed at developing a robust synthesis method by taking into account both the formulation and the solution method. In addition, the synthesis of linkages with spherical prismatic joints is considered by treating them as a special case of the linkages under study. A two-step synthesis method is developed, which sequentially deals with equation-solving by a semigraphical approach and branching-detection. Examples are included to demonstrate the proposed method.Copyright © 2010 by ASME

[1]  Manfred Husty,et al.  A NEW METHOD FOR THE SYNTHESIS OF BENNETT MECHANISMS , 2005 .

[2]  Pierre M. Larochelle,et al.  Orientation Order Analysis of Spherical Four-Bar Mechanisms , 2011 .

[3]  Lung-Wen Tsai,et al.  Design of Dyads with helical, cylindrical, spherical, revolute and prismatic joints , 1972 .

[4]  C. H. Chiang,et al.  Kinematics of Spherical Mechanisms , 1988 .

[5]  J. Angeles.  The application of dual algebra to kinematic analysis , 1998 .

[6]  Paul J. Zsombor-Murray,et al.  Solving the burmester problem using kinematic mapping , 2002 .

[7]  Jorge Angeles,et al.  The Synthesis of Robust Spherical Motion Generators , 2004 .

[8]  Jorge Angeles,et al.  A comprehensive solution of the classic Burmester problem , 2008 .

[9]  Bernard Roth,et al.  The Kinematics of Motion Through Finitely Separated Positions , 1967 .

[10]  C. H. Suh,et al.  Kinematics and mechanisms design , 1978 .

[11]  Chintien Huang,et al.  Spatial Generalization of the Planar Path Generation Problem , 2009 .

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

[13]  J. M. McCarthy,et al.  The Design of Spherical 4R Linkages for Four Specified Orientations , 1999 .

[14]  Marco Ceccarelli,et al.  New Trends in Mechanism Science , 2010 .

[15]  G. Forsythe.  Pitfalls in computation, or why a math book isn''t enough , 1970 .

[16]  John R. Zimmerman.  Four-precision-point synthesis of the spherical four-bar function generator , 1967 .

[17]  Willibald Lichtenheldt.  Konstruktionslehre der Getriebe , 1961 .

[18]  B. Roth,et al.  Motion Synthesis Using Kinematic Mappings , 1983 .

[19]  Åke Björck,et al.  Numerical Methods , 1995, Handbook of Marine Craft Hydrodynamics and Motion Control.

[20]  Alba Perez,et al.  Dimensional synthesis of Bennett linkages , 2003 .

[21]  Ian S. Fischer,et al.  Dual-Number Methods in Kinematics, Statics and Dynamics , 1998 .

[22]  F. Freudenstein.  Advanced mechanism design: Analysis and synthesis: Vol. 2, by G. N. Sandor and A. G. Erdman. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1984, 688 p , 1985 .

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

[24]  Leo Joskowicz,et al.  Computational Kinematics , 1991, Artif. Intell..

[25]  Ferdinand Freudenstein,et al.  Kinematic Synthesis of Linkages , 1965 .

[26]  Manfred Husty,et al.  Synthesis of spherical four-bar mechanisms using spherical kinematic mapping , 2006, ARK.

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

[28]  Bernard Roth,et al.  Finite-Position Theory Applied to Mechanism Synthesis , 1967 .

[29]  S. Nash,et al.  Linear and Nonlinear Programming , 1987 .

[30]  Faydor L. Litvin,et al.  Analysis and design of RCCC linkages , 1984 .

[31]  Hikmet Kocabas.  Gripper Design With Spherical Parallelogram Mechanism , 2009 .

[32]  C. Innocenti.  Polynomial Solution of the Spatial Burmester Problem , 1995 .

[33]  Jorge Angeles,et al.  A Robust Solution of the Spherical Burmester Problem , 2010 .

[34]  J. Angeles.  Spatial Kinematic Chains: Analysis ― Synthesis ― Optimization , 1982 .

[35]  J. Michael McCarthy,et al.  21st Century Kinematics: Synthesis, Compliance, and Tensegrity , 2011 .

[36]  David H. Myszka,et al.  Assessing Position Order in Rigid Body Guidance: An Intuitive Approach to Fixed Pivot Selection , 2009 .

[37]  Jorge Angeles,et al.  Fundamentals of Robotic Mechanical Systems , 2008 .

[38]  P. K. Subramanyan.  Kinematics and Mechanisms , 2000 .

[39]  Lung-Wen Tsai,et al.  Incompletely Specified Displacements: Geometry and Spatial Linkage Synthesis , 1973 .

[40]  A. Morgan,et al.  Numerical Continuation Methods for Solving Polynomial Systems Arising in Kinematics , 1990 .

[41]  E. Pennestrì,et al.  Linear algebra and numerical algorithms using dual numbers , 2007 .

[42]  H. Pottmann,et al.  Computational Line Geometry , 2001 .