On the inverse kinematics of a fragment of protein backbone

Abstract

This paper studies the structure of the inverse kinematics (IK) map of a fragment of protein backbone with 6 torsional degrees of freedom. The images (critical sets) of the singularities of the orientation and position maps are computed for a slightly idealized kinematic model. They yield a decomposition of SO(3) and R 3 into open regions where the number of IK solutions is constant. A proof of the existence of at least one 16-solution cell in R 3 × SO(3) is given and one such case is shown.