On the Self-Mobility of Point-Symmetric Hexapods

In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.

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

[2]  Josef Schicho,et al.  Pentapods with Mobility 2 , 2014, ArXiv.

[3]  Georg Nawratil.  Introducing the Theory of Bonds for Stewart Gough Platforms With Self-Motions , 2014 .

[4]  Jean-Pierre Merlet,et al.  Singular Configurations of Parallel Manipulators and Grassmann Geometry , 1988, Int. J. Robotics Res..

[5]  Adolf Karger.  Architecturally singular non-planar parallel manipulators , 2008 .

[6]  Josef Schicho,et al.  Bond Theory and Closed 5R Linkages , 2012, ARK.

[7]  Georg Nawratil.  Planar Stewart Gough platforms with a type II DM self-motion , 2011 .

[8]  Leah Blau,et al.  Computational Line Geometry , 2016 .

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

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

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

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

[13]  Manfred L. Husty,et al.  Classification of all self-motions of the original Stewart-Gough platform , 1998, Comput. Aided Des..

[14]  G. Nawratil.  CONGRUENT STEWART GOUGH PLATFORMS WITH NON-TRANSLATIONAL SELF-MOTIONS , 2014 .

[15]  Georg Nawratil.  Self-Motions of Planar Projective Stewart Gough Platforms , 2012, ARK.

[16]  Georg Nawratil.  A new approach to the classification of architecturally singular parallel manipulators , 2009 .

[17]  H. Stachel,et al.  On the flexibility and symmetry of overconstrained mechanisms , 2014, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[18]  Georg Nawratil.  On Stewart Gough manipulators with multidimensional self-motions , 2014, Comput. Aided Geom. Des..

[19]  Manfred L. Husty,et al.  Half-turns and line symmetric motions , 2011 .

[20]  John Stillwell,et al.  Symmetry , 2000, Am. Math. Mon..

[21]  Manfred Husty,et al.  Kinematik und Robotik , 1997 .

[22]  Georg Nawratil.  Review and Recent Results on Stewart Gough Platforms with Self-Motions , 2012 .

[23]  Josef Schicho,et al.  Bond theory for pentapods and hexapods , 2014, ArXiv.

[24]  P. Dietmaier.  Forward Kinematics and Mobility Criteria of One Type of Symmetric Stewart-Gough Platforms , 1996 .

[25]  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 .

[26]  Georg Nawratil.  On equiform Stewart Gough platforms with self-motions , 2013 .

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

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