FA-88099 / Inverse kinematics solvers / Member archive

Delta rejects a point where one rod is exactly horizontal · case 04

A reachable point on the rod-length boundary returns "unreachable".

Member previewVariant 4 · 3 implementations · 7 checks per implementation

Case contract

Input [R,e,L,x,y,z,hmax]: linear delta printer, towers at 90, 210 and 330 degrees (in that output order) on radius R, effector joints offset e toward the centre so the effective radius is R-e, diagonal rods of length L. Carriage height is z+sqrt(L^2-dx^2-dy^2); a negative radicand returns "unreachable", a carriage above hmax returns "out-of-travel". Return heights 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
rod horizontal at tower one	`"unreachable"`	`[0.0, 6.9282, 6.9282]`	Failed

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