Hey /sci/,
What started as a little brain exercise, has turned into a massive pain in the ass for me. Some hints or help would be greatly appreciated. Also if you think this problem is not solvable, it would be nice to know not to waste more time on it (especially since the application of this I have already solved using numerical optimization).
The problem is a gripper (2 fingers and a palm) in 5 point contact with a cylindrical object. Further I assume that the distal fingers (L2) are touching (at the vertical axis).
Pic related shows all the finger lengths of half a circle (as its symmetrical I think it can be solved with just half the circle).
I have also included two angle definitions, but I dont think these would be necessary for solving the problem.
Now for what I am looking for, I think this geometry can be fully defined by the three gripper dimensions (L0, L1 and L2). I.e. I think it is possible to express radius R in terms of the three finger lengths, which is what I want to figure out.
Firstly I have tried to solve it with trigonometry and algebra, but that got me nowhere.
What started as a little brain exercise, has turned into a massive pain in the ass for me. Some hints or help would be greatly appreciated. Also if you think this problem is not solvable, it would be nice to know not to waste more time on it (especially since the application of this I have already solved using numerical optimization).
The problem is a gripper (2 fingers and a palm) in 5 point contact with a cylindrical object. Further I assume that the distal fingers (L2) are touching (at the vertical axis).
Pic related shows all the finger lengths of half a circle (as its symmetrical I think it can be solved with just half the circle).
I have also included two angle definitions, but I dont think these would be necessary for solving the problem.
Now for what I am looking for, I think this geometry can be fully defined by the three gripper dimensions (L0, L1 and L2). I.e. I think it is possible to express radius R in terms of the three finger lengths, which is what I want to figure out.
Firstly I have tried to solve it with trigonometry and algebra, but that got me nowhere.
