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Inverse Kinematics Part 1: Check Reachability
Inverse Kinematics Part 1: Check Reachability
If you don't know whether your robot can reach a target, does any other calculation matter?
Learning Intentions:
Derive the reachability bounds for a two-link arm — |L₁ − L₂| ≤ √(x² + y²) ≤ L₁ + L₂ — and apply the reach rule to classify target points as reachable or unreachable before attempting any IK calculation.
Today's Concept:
Inverse kinematics starts with a question you can't always answer: can the arm even get there?
Before solving for any angle, you need to know whether a solution exists. The robot arm has a dead zone — points too close to the base that the elbow geometry can't reach — and a maximum range, the full extension of both links. Every target has to clear both bounds.
The check is one calculation: find the straight-line distance from the base to the target using the Pythagorean theorem. If that distance falls between |L₁ − L₂| and L₁ + L₂, a solution exists. If it doesn't, no angle combination will get the tip there. Running the IK formula on an unreachable point doesn't give a wrong answer — it gives no valid answer at all. This lesson establishes the gate that every IK problem in Lessons 19 and beyond must pass through first
Station Activity
Station Activity
Explore It – Check Reachability
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