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Unformatted text preview: UCSB ME 170A / ECE 181 A, Introduction to Robotics Spring 2010 Handout # 1: Inverse Trigonometric and Inverse Kinematics Problems Instructor: Francesco Bullo Date: April 23, 2010 Arctangent function We adopt the following convention. The four-quadrant arctangent function atan 2 computes the inverse tangent map. In other words, for any point ( x, y ) in the plane except for the origin, the value atan 2 ( y, x ) is the angle between the horizontal positive axis and the point ( x, y ) measured counterclockwise. So, for example, atan 2 (0 , 1) = 0 , atan 2 (1 , 0) = π/ 2 , atan 2 (0 , − 1) = π, atan 2 ( − 1 , 0) = − π/ 2 . Two useful property of the four quadrant arctangent function are: atan 2 ( y, x ) = π + atan 2 ( − y, − x ) , atan 2 ( y, x ) = − π 2 + atan 2 ( x, − y ) . Also, it is easy to see that, for all angles θ , θ = atan 2 (sin( θ ) , cos( θ )) . The order of the arguments is very important as there are two possible conventions: ( y, x ) or ( x, y )....
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