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Cartesian Coordinates, Mathematics

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In the view below of the robot type of Cartesian Coordinates, is not the "Z" and "Y" coordinates reversed? https://www.expertsmind.com/topic/robot-types/cartesian-coordinates-910383.aspx The "Y" should be in and out and the "Z" should be up and down? If you look at this picture https://ceeps.colostate-pueblo.edu/Engineering/RoboticsLaboratory/MoveMaster/PublishingImages/cartesianA.gif it shows the correct motion of a robotic arm.

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