<p style="text-align: justify">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. These fragments are the basic units to define the specific three-dimensional shapes of 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, based on dialytic elimination, 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. The manipulator analysis, including three zero-length links, confirmed the solution of the inverse kinematics problem by both methods. Moreover, we formulated a method to systematically build manipulator models from structural data of molecules. We systematically identified the Danavit and 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. The first six pairs expressed bond axes with the mobilities, and the last pair corresponded to the hand link. Finally, using the structural data of Lactoferrin stored in the protein data bank, we demonstrated an application example of kinematic modeling and inverse kinematics calculation. We solved the inverse kinematics problems with the small-link length strategy for all the serial 6R fragments. The numbers of the real solutions were from two to eight. Eighty-nine percent of the fragments had four or fewer solutions, and most of the fragments extracted from alpha-helices had two solutions. Those extracted from beta-sheets had four or more solutions, and fragments with eight solutions were found mainly at the parts between the secondary structures.<br>
&nbsp;</p>

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

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

Supporting the need among researchers worldwide for additional online and multimedia content, ASME now offers the ASME Conference Video Collection. This platform will collect and provide long-term access to conference presentation videos, encompassing all technology areas within ASME's technical conference and events program. About 30,000-40,000 engineers across all mechanical engineering and related disciplines participate in ASME conferences each year. This includes authors of approximately 6,000 to 8,000 technical papers published by ASME, the majority of whom also submit video presentations for our virtual conferences. The video collection will be available as an add-on to existing product packages or as a separate subscription.