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ME5286CourseNotes11-09

# ME5286CourseNotes11-09 - Determining Path Trajectories...

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Determining Path Trajectories: Interpolation and Spline Functions

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The Manipulator Path: Motion between positions Consider series of positions: Posn. 1: (T 6 ) 1 x Tool 1 = Coord 1 x Pos 1 Posn. 2: (T 6 ) 2 x Tool 2 = Coord 2 x Pos 2 Posn. 3: (T 6 ) 3 x Tool 3 = Coord 3 x Pos 3 Two approaches: A. Joint Coordinates B. World or Cartesian coordinates A. Joint Coordinates: Solve above equations for T 6 ! Calc. Δ (Joint coordinates) Control joint trajectories B. Cartesian Coordinates: Calculate distance and direction between consecutive positions Calculate orientation change between two positions Control trajectory in world coordinates
Given: Desired velocity Can obtain: Time T 2 to move from position (i) to position (i + 1) Then deFne: Time t to run from 0 to T i between each pair of positions Must redeFne present position in terms of subsequent coordinate systems and tool deFnitions ±or each position, deFne a second transformation in terms of the next coordinate system

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ME5286CourseNotes11-09 - Determining Path Trajectories...

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