Kinematic Modeling and Inverse Kinematics of Serial 6R Fragment of Molecule

Abstract Depending on their mobilities around bond axes, molecules (e.g., proteins, DNA, and RNA) can be modeled as robotic manipulators. We focus on the serial 6R fragments, or the fragments containing six revolute joints connected in series, extracted from these molecules. We solved the inverse kinematics problems of the fragments. We obtained multiple conformations that maintained the relative position and orientation between both ends. Raghavan and Roth’s solution effectively conveys all real solutions. However, the solution is not directly applicable when some link lengths are zeros. To cope with the problem, in addition to the known method based on the modified elimination, we introduced the small-length link strategy. Here, by setting sufficiently small values for the zero-length links, we solved the inverse kinematics problems based on Raghavan and Roth’s solution combined with the symbolic formulation. Moreover, we formulated a method to systematically build manipulator models from structural data of molecules. We systematically identified the Danavit-Hartenberg parameters (link length, offset, and twist angle) and joint angles at the conformation in the structural data from the seven pairs of positions of atoms. Finally, using the structural data of a protein stored in the protein data bank, we demonstrated an application example of kinematic modeling and inverse kinematics calculation.