The (true) Stewart platform has 12 configurations

We consider a Stewart platform and show that its forward kinematics has at most 12 solutions. A first geometrical demonstration is provided which uses the concept of circularity and in a second proof we show that this problem is equivalent to find a system of two planar parallel manipulators with each 6 solutions to the forward kinematic problem. A geometrical construction is provided to construct such a system and a Stewart platform with 12 configurations is exhibited.<<ETX>>

[1]  D. Stewart,et al.  A platform with 6 degrees of freedom , 1966 .

[2]  C. Innocenti,et al.  A novel numerical approach to the closure of the 6-6 Stewart platform mechanism , 1991, Fifth International Conference on Advanced Robotics 'Robots in Unstructured Environments.

[3]  J. Merlet.  Manipulateurs paralleles, 4eme partie : mode d'assemblage et cinematique directe sous forme polynomiale , 1990 .

[4]  C. Innocenti,et al.  Forward Displacement Analysis of Parallel Mechanisms: Closed Form Solution of PRR-3S and PPR-3S Structures , 1992 .

[5]  Vincenzo Parenti-Castelli,et al.  Echelon form solution of direct kinematics for the general fully-parallel spherical wrist , 1993 .

[6]  D. Lazard,et al.  On the Representation of Rigid-Body Motions and its Application to Generalized Platform Manipulators , 1993 .

[7]  Carlo Innocenti,et al.  Direct position analysis of the Stewart platform mechanism , 1990 .

[8]  Felice Ronga,et al.  Stewart platforms without computer , 1995 .

[9]  Shin-Min Song,et al.  Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions , 1992, J. Field Robotics.

[10]  Wei Lin,et al.  Forward Displacement Analyses of the 4-4 Stewart Platforms , 1992 .

[11]  Shin-Min Song,et al.  Forward kinematics of a class of parallel (Stewart) platforms with closed-form solutions , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[12]  D. Stewart.  A Platform with Six Degrees of Freedom , 1965 .

[13]  C. Gosselin,et al.  Solutions polynomiales au probleme de la cinematique directe des manipulateurs paralleles plans a trois degres de liberte , 1992 .

[14]  K. H. Hunt,et al.  Assembly configurations of some in-parallel-actuated manipulators , 1993 .

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