a1 - CSE4421/5324: Assignment 1 Burton Ma Posted: Jan 21,...

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CSE4421/5324: Assignment 1 Burton Ma Posted: Jan 21, 2012 Due: Feb 03, 2012 1. Find the 4 × 4 homogeneous transformation matrix (showing the numeric values for all 16 elements) T 0 1 where: (a) { 1 } has the same orientation as { 0 } and the origin of { 1 } is translated relative to the origin of { 0 } by d 0 1 = ± 5 - 5 10 ² T . (b) The origin of { 1 } is coincident with the origin of { 0 } , and ˆ x 0 1 = - ˆ z 0 0 , ˆ y 0 1 = - ˆ x 0 0 , and ˆ z 0 1 = ˆ y 0 0 . (c) The origin of { 1 } is translated relative to the origin of { 0 } by d 0 1 = ± 0 0 - 10 ² T , and the orientation of { 1 } relative to { 0 } is the same as in part (b). (d) The origin of { 0 } is translated relative to the origin of { 1 } by d 1 0 = ± 0 0 - 10 ² T , and the orientation of { 1 } relative to { 0 } is ˆ x 0 1 = ± 0 . 9971 - 0 . 0292 - 0 . 0705 ² T , ˆ y 0 1 = ± - 0 . 0292 0 . 7083 - 0 . 7053 ² T , and ˆ z 0 1 = ± 0 . 0705 0 . 7053 0 . 7053 ² T . Explain how you derived the solution for part (d). 2. Find the missing elements of the following rotation matrices. Show your work, or explain your rea- soning. It may be the case that there is no unique solution, in which case you should find all possible solutions. (a) · 1 0 · 0 0 · 0 - 1 (b) · 3 / 2 0 · 0 1 3 / 2 · 0 (c) 0 0 1 · · 0 · · 0 1
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3. Consider the following 4 × 4 homogeneous transformation matrices: R x,a : rotation about x by an angle a R y,a : rotation about y by an angle a R z,a : rotation about z by an angle a D x,a : translation along x by a distance a D y,a : translation along y by a distance a D z,a : translation along z by a distance a Write the matrix product giving the overall transformation for the following sequences (do not perform the actual matrix multiplications): (a) The following rotations all occur in the moving frame. i. Rotate about the current
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This note was uploaded on 02/13/2012 for the course CSE 4421 taught by Professor Burton during the Winter '11 term at York University.

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a1 - CSE4421/5324: Assignment 1 Burton Ma Posted: Jan 21,...

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