Self-Motions of Planar Projective Stewart Gough Platforms

In this paper, we study self-motions of non-architecturally singular parallel manipulators of Stewart Gough type, where the planar platform and the planar base are related by a projectivity. By using mainly geometric arguments, we show that these manipulators have either so-called elliptic self-motions or pure translational self-motions. In the latter case, the projectivity has to be an affinity a+Ax, where the singular values s 1 and s 2 of the 2×2 transformation matrix A with 0

[1]  Georg Nawratil.  On the Degenerated Cases of Architecturally Singular Planar Parallel Manipulators , 2008 .

[2]  Adolf Karger.  Architecture singular planar parallel manipulators , 2003 .

[3]  Jadran Lenarčič,et al.  Advances in Robot Kinematics , 2000 .

[4]  Georg Nawratil.  Special Cases of Schönflies-Singular Planar Stewart Gough Platforms , 2010 .

[5]  Carme Torras,et al.  Singularity-Invariant Leg Rearrangements in Stewart–Gough Platforms , 2010 .

[6]  A. Karger.  Singularities and self-motions of equiform platforms , 2001 .

[7]  Karl Wohlhart,et al.  From higher degrees of shakiness to mobility , 2010 .

[8]  Adolf Karger.  Parallel Manipulators with Simple Geometrical Structure , 2009 .

[9]  David B. Peakall,et al.  References and Acknowledgements , 1968 .

[10]  Jadran Lenarčič,et al.  Advances in Robot Kinematics: Theory and Applications , 2013 .

[11]  Otto Röschel,et al.  Characterisation of Architecturally Shaky Platforms , 1998 .

[12]  Georg Nawratil.  Non-existence of Planar Projective Stewart Gough Platforms with Elliptic Self-Motions , 2014 .

[13]  G. Nawratil.  Types of self-motions of planar Stewart Gough platforms , 2013 .

[14]  ON ELLIPTIC SELF-MOTIONS OF PLANAR PROJECTIVE STEWART–GOUGH PLATFORMS , 2013 .

[15]  Adolf Karger.  Singularities and Self-Motions of a Special Type of Platforms , 2002 .

[16]  Jadran Lenarčič,et al.  Advances in Robot Kinematics: Analysis and Control , 1998 .

[17]  M. Husty.  An algorithm for solving the direct kinematics of general Stewart-Gough platforms , 1996 .

[18]  Carme Torras,et al.  Singularity-invariant leg rearrangements in doubly-planar Stewart-Gough platforms , 2010, Robotics: Science and Systems.

[19]  Manfred Husty.  E. Borel’s and R. Bricard’s Papers on Displacements with Spherical Paths and their Relevance to Self-motions of Parallel Manipulators , 2000 .

[20]  Guo Sheng,et al.  The DOF Degeneration Characteristics of Closed Loop Over-Constrained Mechanisms. Transactions of the Canadian Society for Mechanical Engineering , 2012 .

[21]  Clement M. Gosselin,et al.  SELF MOTIONS OF STEWART-GOUGH-PLATFORMS An overview , 2002 .