ME5286CourseNotes02-09

# ME5286CourseNotes02-09 - Post-Multiplication  Coordinate...

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Mathematics of Coordinate Transformation

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Origin of frame 2 is translated and the axes rotated relative to frame 1.
Mathematical Representations: Robot arm links rotate and/or translate with respect to a reference coordinate system. By considering a body- attached coordinate frame at the joint for each link, one can develop a description representing the location of robot arm links W.R.T. a Fxed reference frame. That description is based on Fnding a transformation matrix that relates the two. Wish to know where pt. P, deFned W.R.T. object, is located W.R.T. reference coordinate frame. Rotation in XY plane about Z axis.

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Consider two dimensional example: Rotation about z by θ To defne P in terms oF base coordinate Frame YOX, given P defned in moving coordinate Frame VOU

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Unformatted text preview: Post-Multiplication:  Coordinate frame shifted (i.e. translated and/or rotated) with respect to previous frame Since matrix multiplication is N Non-commutative A B ≠ B A Must specify sequence carefully The orientation of an object is very much a function of the sequence in which rotations about the various axes are taken Rotations: About X About Y About Z Orientation Defnitions OP in Front oF ZOX plane Method A : φ : Rotation about Y θ : Rotation about X’ ψ : Rotation about Z’ OP behind ZOX plane Method B : α : Rotation about Z β : Rotation about Y’ ψ : Rotation about Z’ To get OP in Front oF the ZOX plane, α would have to be negative Position and Orientation of End Effector...
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ME5286CourseNotes02-09 - Post-Multiplication  Coordinate...

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