FA-87899 / Inverse kinematics solvers / Member archive

Shoulder bearing aims at the tool tip rather than the wrist centre · case 04

The two-link sub-chain is rotated toward the tip, so the wrist lands off the required centre.

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [l1,l2,l3,px,py,phi,elbow]: planar three-link arm, phi is the required tool heading in degrees. Subtract l3 along phi to get the wrist centre, solve the two-link sub-chain (elbow "up" gives q2>=0), set q3=phi-q1-q2 and wrap each joint to [-180,180) in degrees rounded to 4 places. A wrist centre outside |l1-l2|..l1+l2 returns "unreachable".

Why this case matters

Inverse kinematics code turns task-space goals into joint commands; a wrong branch, sign, limit or update order sends a real arm to the wrong pose.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
tool pointing down	`[-63.2748, 128.6822, -155.4074]`	`[-48.0197, 128.6822, -170.6625]`	Failed

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