Well, I could have got this more wrong if I had tried --- but not by very much! In fact, it's obviously impossible to grasp a slippery sphere securely at all: there is no mechanism by which (freedom-3) torques around the centre can be countered. As Adam observed, the remaining freedom-3 linear forces are countered by 4 fingers. Thinking about it (late in the day), I've come to the conclusion that the 7-finger minimum applies where the object is slippery but irregular, and actively attempting to escape by generating wrenches / screws (e.g. via attachment to an opponent). But this is all supposition, until somebody can lay hands on a copy of Mishra et al (1987). Of course, a five-fingered primate hand also utilises the palm to assist in grasping: so I wonder, to how many extra fingers might a palm be equivalent? Fred Lunnon On 12/20/10, Adam P. Goucher <apgoucher@gmx.com> wrote:
Fred Lunnon wrote:
There's little light to be cast by screw theory here. Exactly the same analysis applies as to bicycle spokes --- or rather cartwheel spokes, since fingers act
as struts (in compression) rather than ties (in tension). Picking up a slippery sphere requires (at least) 7 fingers. WFL
What? Wouldn't four fingers, positioned at the vertices of a regular tetrahedron, suffice to hold a sphere in position? Or three, if you allow gravity to assist.
Sincerely,
Adam P. Goucher