A fast inverse kinematics solver using intersection of circles

Abstract

Kinematics is the study of motion without regard to the forces that causes it. In computer animation and robotics, Inverse Kinematics (IK) calculates the joint angles of an articulated object so that its end effector can be positioned as desired. This paper presents an efficient IK method using a geometric solver based on the intersection of circles. For an articulated object with n joints, our method will position the end-effector accurately and requires only a reverse iteration of (n-2). An intuitive user interface is provided, which automatically keeps the end effector between the maximum and minimum extent of the articulated object. Common problems that can occur with other IK methods are avoided. The algorithm has been implemented using WebGL and Javascript and tested by simulating a human hand, a three joint robot arm and human cycling motion, achieving interactive rates of up to 60 FPS.