What is the rotation matrix for a rotation of 30 about the OZ axis, followed by...

 

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What is the rotation matrix for a rotation of 30° about the OZ axis, followed by a rota- tion of 60° about the OX axis, followed by a rotation of 90° about the OY axis? 2.2 What is the rotation matrix for a rotation of angle about the OX axis, followed by a rotation of angle about the OW axis, followed by a rotation of angle about the OY axis? 2.3 Find another sequence of rotations that is different from Prob. 2.2, but which results in the same rotation matrix. 2.4 Derive the formula for sin ( + 0) and cos ( + 0) by expanding symbolically two rotations of and using the rotation matrix concepts discussed in this chapter. 2.5 Determine a T matrix that represents a rotation of a angle about the OX axis, followed by a translation of b unit of distance along the OZ axis, followed by a rotation of o angle about the OV axis. 2.6 For the figure shown below, find the 4 x 4 homogeneous transformation matrices ¹-¹A; and A, for i = 1, 2, 3, 4, 5. 20 Yo Z3 3 21 X3 X1 ¥2 What is the rotation matrix for a rotation of 30° about the OZ axis, followed by a rota- tion of 60° about the OX axis, followed by a rotation of 90° about the OY axis? 2.2 What is the rotation matrix for a rotation of angle about the OX axis, followed by a rotation of angle about the OW axis, followed by a rotation of angle about the OY axis? 2.3 Find another sequence of rotations that is different from Prob. 2.2, but which results in the same rotation matrix. 2.4 Derive the formula for sin ( + 0) and cos ( + 0) by expanding symbolically two rotations of and using the rotation matrix concepts discussed in this chapter. 2.5 Determine a T matrix that represents a rotation of a angle about the OX axis, followed by a translation of b unit of distance along the OZ axis, followed by a rotation of o angle about the OV axis. 2.6 For the figure shown below, find the 4 x 4 homogeneous transformation matrices ¹-¹A; and A, for i = 1, 2, 3, 4, 5. 20 Yo Z3 3 21 X3 X1 ¥2 What is the rotation matrix for a rotation of 30° about the OZ axis, followed by a rota- tion of 60° about the OX axis, followed by a rotation of 90° about the OY axis? 2.2 What is the rotation matrix for a rotation of angle about the OX axis, followed by a rotation of angle about the OW axis, followed by a rotation of angle about the OY axis? 2.3 Find another sequence of rotations that is different from Prob. 2.2, but which results in the same rotation matrix. 2.4 Derive the formula for sin ( + 0) and cos ( + 0) by expanding symbolically two rotations of and using the rotation matrix concepts discussed in this chapter. 2.5 Determine a T matrix that represents a rotation of a angle about the OX axis, followed by a translation of b unit of distance along the OZ axis, followed by a rotation of o angle about the OV axis. 2.6 For the figure shown below, find the 4 x 4 homogeneous transformation matrices ¹-¹A; and A, for i = 1, 2, 3, 4, 5. 20 Yo Z3 3 21 X3 X1 ¥2

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