Six legs, six numbers

A Gough–Stewart platform at (0.00, 0.00, 2.40) with a rotation vector of (0.00, 0.00, 0.00). The six leg lengths run from 2.977 to 3.156, and every one of them was computed from the pose by a single subtraction and a square root, with no leg consulting another. Going the other way — six lengths in, one pose out — takes an iterative solve and does not have one answer. The six leg lines span a screw system of order 6; the smallest singular value of the six is 0.0363, which is how far this pose is from a configuration where they become dependent and the platform stops being controllable.