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There are only three 6-SPS parallel manipulators with triangular base and platform, i.e., the octahedral, the flagged, and the partially flagged, which are studied in this paper. The forward kinematics of the octahedral manipulator is algebraically intricate, while those of the other two can be solved by three trilaterations. As an additional nice feature, the flagged manipulator is the only parallel platform for which a cell decomposition of its singularity locus has been derived. Here, wedoi:10.1109/tro.2009.2018970 fatcat:lnvc3rxbwjdjxh43nbuucp2b3a