(Turning a robot hand) The robot produces any 3 by 3 rotation A from plane rotations
Chapter 9, Problem 14(choose chapter or problem)
(Turning a robot hand) The robot produces any 3 by 3 rotation A from plane rotations around the x, y, z axes. Then Q32Q31 Q21A = R, where A is orthogonal so R is I! The three robot turns are in A = Q"2l Q-:;l Q-:;i. The three angles are "Euler angles" and det Q = 1 to avoid reflection. Start by choosing cos e and sin e so that Q21A = [~~:; - ~~: ~ ~] ~ [-; -i ;] is zero in the (2, 1) position.
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