Why can a 6-DOF manipulator have multiple inverse kinematics solutions for the same end-effector pose?

• A. Because IK always yields a unique solution; no need constraints.
• B. Because there are multiple joint configurations that achieve the same pose; additional constraints choose the solution.
• C. The arm cannot have multiple solutions.
• D. The extra solutions come from numerical rounding only.

Answer: (B)

A fixed end-effector pose does not uniquely determine all joint angles in a 6-DOF arm because the geometry allows more than one way to reach the same position and orientation. The arm can configuration different joints—such as the elbow being up or down, or the shoulder and wrist angles adjusting in tandem—while the hand ends up pointing exactly the same way and occupying the same spot. This redundancy means the inverse kinematics problem has multiple valid solutions, not a single one. In practice, additional constraints like joint limits, collision avoidance, preferred posture, or a chosen path are used to select one specific solution. Numerical IK routines may also converge to different valid configurations depending on the starting guess, reflecting this multiplicity.