Inverse Kinematics of a 6 DOF Robotic Arm

[RodriRego]

Homework Statement

Hello. My colleague and I have been struggling with this assignment where we have to:
- Given the position and orientation of the end-effector of a robotic arm with 6 degrees of freedom get the joint angle values (inverse kinematics). The robotic arm in question is the SainSmart 6 DOFs robotic arm.

Homework Equations

Axis Position

1 - Geometric Approach (T₀₃)

2 - Algebraic Approach (T₃₆)[/B]
The angles 4, 5 and 6 would be obtained from this:
T₀₆ = T₀₃*T₃₆
T₃₆ = inverse(T₀₃)*T₀₆

T₀₆ is known from the orientation and position of the end-effector (given info);
T₀₃ would be obtained through the geometric approach.

The Attempt at a Solution

We managed to get expressions for the first 3 angles through a geometric approach and the law of cossines. However, to do so we assumed we knew the point at the tip after the 3rd joint. We know how to procede to get the other 3 angles, through an algebraic approach, however, to use that we need the transformation matrix from join 3 to 0 (T₀₃), which would be fine if we actually knew the position of the point at the tip after the 3rd joint.

To sum up, we are struggling at joining the two approaches because of the assumptions made to achieve the geometric approach.

 

[Tom.G]

Way out of my field, but I vaguely recall a discussion that mentioned the unsolvability of at least some of the equations due to an infinite number of solutions (or something like that).

That said, try this article, "Solving Kinematics Problems of a 6 DOF Robotic Arm":
https://pdfs.semanticscholar.org/188d/ca40fa862c5cd574f09ae68e1e4e30852fc5.pdf
There were 283 000 search results found with:
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Cheers,
Tom