P.S. Here is the BB-8 translation of the setup, as a source/collection of ideas.

The Yellow sphere, can be positioned, while the Target_for_Tool defines the direction of the tool. Both have Layer colors applied to spot them quickly.

File …_61 is static, with the two animated parts having a Position Freeze, so they can be reset with the PSR-Reset.
CV4_2025_drs_25_CAsd_61.c4d

File …_63 is filled with shapes, and yes, there is one short cut in it. Priorities are updated
CV4_2025_drs_25_CAsd_63.c4d

File …_64, just for fun, 240 frames and a longer animation
CV4_2025_drs_25_CAsd_64.c4d

Preview:
https://projectfiles.maxon.net/Cineversity_Forum_Support/2025_CLIPS_DRS/20250621_CV4_2025_drs_25_CAsd_63.mp4
As loop and longer
https://projectfiles.maxon.net/Cineversity_Forum_Support/2025_CLIPS_DRS/20250621_CV4_2025_drs_25_CAsd_64.mp4
Screenshot 2025-06-21 at 12.13.22 PM.jpg

Screenshot 2025-06-21 at 8.33.37 PM.jpg

The tool head will show an Euler angle problem if placed exactly vertically to the target.

Here, the idea was to define a target and then just position the Yellow sphere (Keyframes only for Position).

This allows for a tool axis movement, as seen between frames 100-120 in file 62.

I found that here is the best compromise between IK and manual setup.

You talked about that axis are not all on one plane. I would check with the Company of the arm if that is the target and why this was done.

Colors are as much as possible used from your example image

My best wishes