FA-88027 / Inverse kinematics solvers / Member archive

SCARA quill extension is computed upward · case 02

Reachable heights are rejected and heights above the home plane are accepted.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input [l1,l2,d0,stroke,px,py,pz,yaw,arm]. The quill extends downward: d3=d0-pz must lie in [0,stroke] else "out-of-stroke" (checked first). Planar reach uses cos t2=(px^2+py^2-l1^2-l2^2)/(2 l1 l2); |cos|>1 returns "unreachable". arm "right" takes t2<=0. Tool yaw (degrees) equals t1+t2+t4. Return [t1,t2,d3,t4] with angles in degrees wrapped to (-180,180], all rounded to 4 places.

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
right arm nominal	`"out-of-stroke"`	`[55.12, -80.4059, 4, 55.2859]`	Failed

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