The (true) Stewart platform has 12 configurations

D. Lazard, J.-P. Merlet
Proceedings of the 1994 IEEE International Conference on Robotics and Automation  
We consider a Stewart platform and show that it 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.
doi:10.1109/robot.1994.350969 dblp:conf/icra/LazardM94 fatcat:a5lzxcpnendnrgpfrqylfyd4gi