In the science fiction novels The Mote in God's Eye and The Gripping Hand by Larry Niven and Jerry Pournelle, the gripping hand is literally the strongest of the three asymmetrical arms of the aliens called "Moties". Most of the species of Motie have two weaker arms with better fine control on one side, and a single much stronger arm on the other side.
Figuratively, it was typically used when presenting a third choice or fact after two others, usually after the second had been presented with the phrase "on the other hand...". Thus, a discussion of choices could follow the typical English pattern of saying "We could do this, but on the other hand we could do that," followed by what would in conventional English be a non sequitur, "but on the gripping hand, there's another alternative". In keeping with the idea that this represents the strongest arm, the last fact is often one that is most unpleasant or difficult to deal with, in some way.
Some of the more devoted fans of Niven and Pournelle will sometimes slip into this metaphor in regular speech, often resulting in some confusion from the listener.
