These images give you a sense of the space the robot moves within:
Here's a screen capture of the simulation of the robot. The robot follows a path curve. The path curve is divided into a certain number of points. For each point the tool remains tangent to the curve at that point. By changing the number of points you can dramatically change the nature of the motion generated.
It's a pretty close match between the simulated path and the actual robot path. But the spline interpolation is different between NURBS and what Kuka is doing with the Spline Movement motion type so they are not an exact match. It's always interesting to see the images produced by the robot.