ME5286CourseNotes03-09 - which deFnes a location (position...

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Position and Orientation of End Effector
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Homogeneous Transformation Matrices Example: Puma 560
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Homogeneous Transformation 4 x 4 Matrix Accounts for body Rotation Translation Columns Specify the directions of the body’s coordinate axes Translation Vector
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Calculation of Position and Orientation in World Coordinates from the Joint Angles: For a manipulator: Base A hand = Base T Hand Origin x Hand Origin A Hand For a six-jointed manipulator: Base T Hand Origin = Base A 1 x 1 A 2 x 2 A 3 x 3 A 4 x 4 A 5 x 5 A Hand origin Where: N-1 A n = Homogeneous transformation matrix which relates the coordinate frame of link n to the coordinate frame of link n-1
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X 2 behind Y 2 Z 2 plane X 3 behind Y 3 Z 3 plane Y 4 behind X 4 Z 4 plane
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Homogeneous Transformation -combines rotation and translation DeFnition: ref H loc = homogeneous transformation matrix
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Unformatted text preview: which deFnes a location (position and orientation) with respect to a reference frame Sequential Transformations Translate by x, y, z Rotate about Z, by (270˚ + θ ) Rotate about Y’ by ( α + 90˚) Rotate about Z” by τ Step A: Translation by x, y, z World Coordinate System Step B: Rotation about Z (vertical axis) by 270˚ (shift coordinate frames) Step C: Rotation about Z (vertical axis) by θ ˚ Step D: Rotation about Y’ (orientation vector) by 90˚ (shift coordinate frames) Step E: Rotation about Y’ (Orientation Vector) by α ˚ Step F: Rotation about Z” (approach vector) by τ ˚ Calculation of homogeneous transformation matrix from position and orientation in world coordinates...
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ME5286CourseNotes03-09 - which deFnes a location (position...

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