Question 1

What is inverse kinematics and why does a two-link arm have two solutions?

Accepted Answer

Inverse kinematics computes the joint angles needed to place the end effector at a desired position. A two-link arm has two solutions because the elbow can bend either way to reach the same point. These are called elbow-up and elbow-down configurations. The two solutions come from the plus or minus sign when computing theta 2 from the cosine inverse.

Question 2

What is a singularity in robot kinematics and when does it occur?

Accepted Answer

A singularity occurs when the Jacobian matrix becomes singular meaning its determinant is zero. For a two-link arm the determinant equals L1 times L2 times sine of theta 2 which is zero when the arm is fully extended theta 2 equals 0 or fully folded theta 2 equals pi. At a singularity the arm cannot move in certain directions and the inverse Jacobian blows up causing infinite joint velocities.

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Two-Link Robot Arm (Forward & Inverse Kinematics)