@henrik,
by intermediate experiments I meanwhile came upon another problem about the claw:
how would you define, if an object has to be gripped by the claw's finger tips (e.g., a chess piece) or by the "full hand", e.g. to grab a bottle?
Addionally, the yaw, pitch+roll orientation of the claw should be possible to be defined for FK and IK, e.g. to pick a chess piece at the top from above, a bottle horizontally from either side, or a slanted object from a diagonal position.
as to float vs. double, as stated before, single-float is surely precise enough for FK; but I was meanwhile recalling issues about floats in matrix determinats which leaded to false values (falsely positive instead of actually zero in some cases) which then leaded to false, invalid inverted matrices, even with nans.
So as to det and Inverted matrices to IK, double fp is probably indispensible.