What is Inverse Kinematics?

Inverse Kinematics (IK) is a mathematical process used in robotics, computer animation, and engineering to determine the joint parameters required to place an end-effector (like a robotic hand or a character's foot) at a specific position in space. Unlike forward kinematics, which calculates the position based on known angles, inverse kinematics works backward from the destination to find the necessary movements.

How to Use This Calculator

This tool simulates a standard 2-link robotic arm. Simply enter the length of the first arm segment (L1), the second segment (L2), and the target coordinates (X, Y). The calculator will solve the trigonometric equations using the Law of Cosines to find the angles θ1 and θ2. You can also click or tap directly on the canvas to move the target point in real-time.

Understanding Reachability

Not every point in space is reachable by a robotic arm. There are two primary constraints: the Maximum Reach, which is the sum of L1 and L2, and the Minimum Reach, which is the absolute difference between L1 and L2. If you enter a target outside these bounds, the system will flag the target as "Unreachable," as the geometry of the triangles cannot be solved (mathematically, the cosine value would exceed 1 or -1).

Frequently Asked Questions

Q: What are the units used?
A: This calculator is unit-agnostic. You can use millimeters, inches, or pixels, as long as you remain consistent across all inputs.

Q: Why are there often two solutions?
A: For most reachable points, there are "elbow-up" and "elbow-down" configurations. This calculator specifically solves for the standard configuration commonly used in basic robotics simulations.

Q: How is the math calculated?
A: We use the Law of Cosines: cos(θ2) = (x² + y² - L1² - L2²) / (2 * L1 * L2) and atan2 for stable angle calculation across all quadrants.