Conditions for line-based singularities in spatial platform manipulators

In this paper, we consider singular configurations of a robotic system that can be modeled as a platform supported by serial robotic chains. The goal is to determine the conditions under which these singular configurations depend purely on the geometry of lines associated with each supporting chain. These conditions are satisfied by many manipulator systems, particularly those based on the Stewart platform. A geometric classification of these ‘‘line-based’’ singularities is presented. Q 1998 John Wiley &

[1]  E. J. F. Primrose.  Analytic Geometry of Three Dimensions, Vol. II. By G. Salmon. Pp. xvi, 334. $4.95. 1965. (Chelsea, New York) , 1967 .

[2]  Vijay Kumar,et al.  Instantaneous Kinematics of Parallel-Chain Robotic Mechanisms , 1992 .

[3]  Alain Dandurand.  The Rigidity of Compound Spatial Grids , 1984 .

[4]  K. H. Hunt,et al.  Geometry of screw systems1Screws: Genesis and geometry , 1990 .

[5]  K. H. Hunt,et al.  Geometry of screw systems—2: classification of screw systems , 1990 .

[6]  Joseph Duffy,et al.  Classification of screw systems—II. Three-systems , 1992 .

[7]  Joseph Duffy,et al.  Classification of screw systems—I. One- and two-systems , 1992 .

[8]  John J. Craig Zhu,et al.  Introduction to robotics mechanics and control , 1991 .

[9]  Joseph Duffy,et al.  The Elliptic Polarity of Screws , 1985 .

[10]  R. Paul.  Robot manipulators : mathematics, programming, and control : the computer control of robot manipulators , 1981 .

[11]  Curtis L. Collins,et al.  The singularity analysis of an in-parallel hand controller for force-reflected teleoperation , 1995, IEEE Trans. Robotics Autom..

[12]  E F Fichter,et al.  A Stewart Platform- Based Manipulator: General Theory and Practical Construction , 1986 .

[13]  D. John Sanger,et al.  Redundant grasps, redundant manipulators, and their dual relationships , 1992, J. Field Robotics.

[14]  Jean-Pierre Merlet.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1989, Int. J. Robotics Res..

[15]  J. D. Everett.  A Treatise on the Theory of Screws , 1901, Nature.

[16]  J. Michael McCarthy,et al.  Introduction to theoretical kinematics , 1990 .

[17]  D. Stewart,et al.  A Platform with Six Degree of Freedom , 1965 .

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

[19]  C. M. Jessop,et al.  A Treatise on the Line Complex , 2022 .

[20]  Joseph Duffy,et al.  A Direct Determination of the Instantaneous Kinematics of Fully Parallel Robot Manipulators , 1985 .

[21]  Jack Phillips,et al.  Freedom in Machinery: Volume 1, Introducing Screw Theory , 1985 .