- #36

- 41,959

- 10,133

Not sure how you are defining β. I'll assume it's the angle of turn at each joint.ElectricVocaloid said:FINGER PAD CENTER (3 phalanges) = (dx, dy)

= ( ( 2b + lf ) . sen(β) + ( 2b + lf ) . sen(2β) + ( b + lf/2 ) . sen(3β) + a . sen(3β - 90°) ; ( b + ( 2b + lf ) . cos(β) + ( 2b + lf ) . cos(2β) - (b - l/2 ) . cos(3β) + a . cos(3β - 90°) )Here I have obtained the parameterized equation of the point where the fingertip would be...

and I need to conveniently transform the axes so that the positive y is up and the positive x is forward...

View attachment 304423

I was trying vector algebra to calculate at least the position of the point of the fingertip by linking it with the angle β of each joint.

The three phalanges, the base support and the red arrow form a pentagon. To return to the start, two different angles must be navigated. In your diagrams, the base support and the last phalanx are about equal length. If we take that to be near enough then those last two turning angles are equal, α say, then 3β+2α=2π.

Taking the red arrow as the x axis, you can now right down its length as a function of β.