Hi Kronecker Delta,
Not exactly the same, you can make the sample below as multiple 3D trajectory plots in Origin.
Here is the summery of what I did to make and customize the graph:
1) Organize the worksheet XYZ column triplets like in the sample.
2) Make a 3D trajectory plot from the first XYZ.
3) Add other XYZ triplets using Layer Contents dialog.
4) Customize the plots such as: a) Set the 3D projection to "Orthogonal" (from Miscellaneous" tab
in the layer-level Plot Details dialog).
b) Set the axis length to show the 3D frame in the desired proportion
(from Axis" tab in the layer-level Plot Details dialog).
c) Show XY projection of each plot with a connected hidden(i.e. size=0) symbols.
Hope this works for you.
--Hideo Fujii
OriginLab