FA-88152 / Inverse kinematics solvers / Member archive

Hexapod femur pitch selects the knee-down triangle · case 02

The knee bends below the femur-foot line, dragging the tibia through the ground.

Member previewVariant 2 · 3 implementations · 7 checks per implementation

Case contract

Input [coxa,femur,tibia,x,y,z,fmin,fmax]: foot target in the leg root frame (z up). Coxa yaw is atan2(y,x); the femur/tibia pair works in the vertical plane at horizontal distance hypot(x,y)-coxa. With D the distance from the femur pivot to the foot, D>femur+tibia or D<|femur-tibia| or D==0 is "unreachable". Femur pitch is atan2(z,h) plus the triangle angle at the femur pivot (knee up); tibia angle is the interior knee angle minus 180 (0 = straight). Femur pitch outside [fmin,fmax] returns "limit". Degrees rounded to 4.

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
foot straight out	`[0.0, -75.4366, -95.9792]`	`[0.0, 38.5667, -95.9792]`	Failed

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