Hello my fellow roboticists!

I am working on the forward kinematics of the Denso 6DOF vs087 line of serial robots. In their Users' Manual, they categorize the set of joint configurations by three different metrics:

  1. Lefty\Righty
  2. Above\Below
  3. Flip\NonFlip

While the first two are quite straightforward, the Flip/NonFlip is unclear. It has to do with the setup of the 4th, 5th, and 6th joints, in that the gripper pose is the same if they are all flipped by 180 degrees.

But how are the "Flip" vs "NonFlip" configurations mathematically defined? Is there any way they can be categorized using DH parameters and transformation matrices? I tried all sorts of trigonometric inequalities, but none of them gave the correct answer in all cases. Ideas, anyone?

Thanks in advance.

  • $\begingroup$ Welcome to Robotics, Max Eisenhardt. I haven't heard these terms before and they don't have any immediate meaning to me. Are the terms defined in the manual? Do you have a link to the manual you could provide? My guess would be the terms are basically like flip horizontal, flip vertical, and rotate 180 degrees (i.e., flip horizontal AND flip vertical), but I can't say for sure. Any supplemental documentation you could provide would be a great help to answering this question with confidence :) $\endgroup$
    – Chuck
    Commented Aug 3, 2022 at 17:41
  • $\begingroup$ Chuck - The manual for the robot can be found at: cs.cmu.edu/~./RoboticManipulation/handouts/denso/Program1.pdf The explanation is given on page 22-4. I understand the intuition of flip/ nonflip, I just do not know how to correctly define it mathematically, i.e. under what range of J4&J5 is it "flip" and under which range is it "nonflip"? $\endgroup$ Commented Aug 3, 2022 at 21:27

1 Answer 1


To flip the wrist on a 6 axis robot, rotate joint 4 by 180 degrees. Rotate joint 6 by 180 degrees in the opposite direction. Move joint 5 to mirror of it previous position, that is if joint 5 was at +15 degrees, move it to -15 degrees. The robot's tool will now be at the same coordinates as it was previously.

Which you call flip and which you call no flip is somewhat arbitrary and each robot manufacturer will pick which they want to use.

Other robot suppliers, such as Staubli (the company I work for), uses wrist positive or wrist negative instead of flip and no flip. We also use elbow positive and elbow negative instead above and below.


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