I'm designing a 3D printable prosthetic hand.

Each finger has 3 joints. The first 2 joints let the finger only move in the vertical (y) direction. The final joint is like a ball and socket joint (connects finger to palm) and lets the finger rotate Up/down & left/right about 30 degrees in each direction.

Summary of 3 joints: 1 joint = finger moving in vertical (y) direction + 1 joint moving in vertical (y) direction + 1 joint rotating in vertical (y) and horizontal (x) directions

From a mechanical engineering perspective, can someone help me here by telling me how many degrees of freedom are on each finger here? How would you calculate it based on the motion I have stated above? Thanks!

I'm guessing 1 degree of freedom for the 2 vertical joints each because they only move in one dimension =2 DOF so far + 2 DOF for the rotatable joint ? = 4

  • $\begingroup$ 4 sounds right to me. $\endgroup$ – Jiminion Jan 18 '16 at 19:53
  • $\begingroup$ The number of degrees of freedom for a given problem in physics is a matter of choice. The better an approximation that you chose, the more degrees of freedom you will have to deal with. If you are choosing to assume that all segments of your mechanical finger are perfectly stiff, then your approximation by four angles is correct. If you let go of the assumption that you are dealing with perfectly stiff materials, then you will have to add more degrees of freedom to model the deformations. $\endgroup$ – CuriousOne Jan 19 '16 at 11:27

If you care about the orientation of the finger tip, you have a 4 degree of freedom system. If you only care about the position of the fingertip, you have a 3 degree of freedom system (since there are multiple ways to combine the y flexion of the three joints to get to the same y height, and in the end you would only have 3 DOF in your answer: x,y,z). If you care about the angle as well, you have 4 motions you can program independently - so 4 degrees of freedom.

  • $\begingroup$ Kinematically, it's 4 DOF regardless, no? $\endgroup$ – Jiminion Jan 18 '16 at 20:15
  • $\begingroup$ @Jiminion - yes. $\endgroup$ – Floris Jan 18 '16 at 20:27
  • $\begingroup$ @Floris can you please break down how its 4 or 3 DOF? I understand the 2 vertical joints are 2 DOF each. But shouldn't the sphere be 3 DOF because it roates in x y and z? so 2+3 = 5 $\endgroup$ – user2788405 Jan 19 '16 at 4:59
  • $\begingroup$ You said the 3rd joint rotates only in x and y. 1+1+2 = 4. $\endgroup$ – Jiminion Jan 19 '16 at 15:27
  • $\begingroup$ You cannot reach any point on a sphere at any orientation. As Jiminion says, there are only four axes so at most four degrees of freedom. And if you only consider the position of the tip of the finger, that is fully specified with just 3 coordinates, so 3 degrees of freedom (although there may be infinitely many settings for the 4 joints to get to certain positions). $\endgroup$ – Floris Jan 19 '16 at 15:29

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