![]() ![]() Euler's rotation theorem states that, in (3D) space, any displacement of a rigid body in such way that a point on the rigid body remains fixed is equivalent to a single rotation about an axis that passes through the fixed point. The representation of orientation in space is a complex issue. "The representation of orientation in space is a complex issue." But how do you then define orientation in space? For example, the position of the robot's end-effector, or more precisely of the TCP ( tool center point), is typically defined as the x, y and z coordinates of the origin of the tool reference frame with respect to the world reference frame. In 3D space, you need a minimum of six parameters to define a pose. You need to know Euler angles in order to define your tool reference frame Besides, in order to define the tool reference frame associated with your end-effector (as in the figure shown below), you would need to calculate the pose of that tool reference frame with respect to the flange reference frame. It is much more efficient to calculate and define your desired pose offline. Of course, you can always jog your robot's end-effector or hand-guide it to approximately the desired pose, but this so-called online programming method is tedious and very imprecise. In other words, you need to be able to program your robot to move its end-effector both to a desired position AND a desired orientation (i.e., to a desired pose). If you use a six-axis robot arm, like Mecademic's Meca500 used in this tutorial as an example, you are most probably interested in positioning its tool ( end-effector) in various orientations. ![]()
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