Problem 2 In terms of the xs, ŷs, 2s coordinates of a fixed space frame {s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its y-axis pointing in the direction (-1,0,0), and frame {b} has its x-axis pointing in the direction (1,0,0) and its ŷ₁-axis pointing in the direction (0,0,−1). The origin of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}. (a) Draw by hand a diagram showing {a} and {b} relative to {s}. (b) Write down the rotation matrices Rsa and Rsb and the transformation matrices Tsa and Tsb.

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Chapter1: Units, Trigonometry. And Vectors
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Problem 2 In terms of the xs, ŷ, 2s coordinates of a fixed space frame
{s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its ŷ₂-axis
pointing in the direction (-1,0, 0), and frame {b} has its x-axis pointing in the
direction (1, 0, 0) and its y-axis pointing in the direction (0, 0, -1). The origin
of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}.
(a) Draw by hand a diagram showing {a} and {b} relative to {s}.
(b)
Write down the rotation matrices Rsa and Rsb and the transformation
matrices Tsa and Tsb.
(c Calculate the matrix exponential corresponding to the exponential coordi-
nates of rigid-body motion S0 = (0, 1, 2, 3, 0, 0). Draw the corresponding
frame relative to {s}, as well as the screw axis S.
Transcribed Image Text:Problem 2 In terms of the xs, ŷ, 2s coordinates of a fixed space frame {s}, frame {a} has its x-axis pointing in the direction (0, 0, 1) and its ŷ₂-axis pointing in the direction (-1,0, 0), and frame {b} has its x-axis pointing in the direction (1, 0, 0) and its y-axis pointing in the direction (0, 0, -1). The origin of {a} is at (3, 0, 0) in {s} and the origin of {b} is at (0, 2, 0) in {s}. (a) Draw by hand a diagram showing {a} and {b} relative to {s}. (b) Write down the rotation matrices Rsa and Rsb and the transformation matrices Tsa and Tsb. (c Calculate the matrix exponential corresponding to the exponential coordi- nates of rigid-body motion S0 = (0, 1, 2, 3, 0, 0). Draw the corresponding frame relative to {s}, as well as the screw axis S.
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