Molecular Manipulator Dynamic Design Criteria
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The ability to intentionally manipulate three-dimensional (3-D) irregular-shaped matter with atomic precision, abiding to physical laws, is considered as one of the ultimate goals of nanoscience and engineering. Nature has given us a vast assortment of biological molecular machines that demonstrate the viability of this goal, including, among others, the ribosome (which can translate mRNA instructions into proteins) and kinesin, an enzyme that acts as a molecular motor which pulls things toward the outer reaches of the cell. In nerve cells, it is kinesin that pulls vesicles or other cellular materials from the cell body to the nerve endings. These biological systems are primarily “application-specific molecular machines.” They are not universal assemblers that could, in principle, be used in a programmable fashion to perform alternate functions at the molecular level. Self-replicating programmable manufacturing systems able to arrange atoms for multiple “applications” would require a universal assembler with an appropriate end-effector and a corresponding controller. The scope of this entry explores design criteria for such a universal assembler.
This article reviews the literature on the creation of nanometer-scale spatial positioners, from a kinematic and dynamic standpoint, as one of the basic building blocks for an atomic-scale manipulator (to arrange differently functionalized molecular building blocks into a lattice or any other nanometer-scale object in a specified and complex pattern, it is necessary to introduce positional control). The development of theoretical criteria for the design of reduced constrained dynamic complexity of a nanoscale positioning device (nanomanipulator), based on the equations of motion (EOM) for spatial serially articulated rigid multibodies, is presented in this article. By using a rigid-body semiclassical mechanics approach, it is shown how dynamic complexities, such as coupling and nonlinearities introduced by high-speed operation, complicate the control task and deteriorate performance. The first section of the article introduces the reader to appropriate state space forms of the EOM for a serially coupled set of rigid bodies using internal coordinates. This allows a compact mathematical description of the problem at hand and exposes the intended solution by permitting concise physical insight. The second section develops the complete set of EOM for both the Newton–Euler and Lagrange–Euler formulations. From the state space equivalence of both methods, the EOM are then expressed as a function of the articulated body inertia operator for the multibody, leading to a highly dependent form of the EOM on this operator. The internal matrix structure of the articulated body inertia is then revealed. The third section presents the analysis that leads to a reduced set of EOM from the structural simplification of the articulated body inertia matrix and develops the general kinematics and mass distribution criteria for doing so. From the resulting analysis, a set of compliant manipulator configurations that could, in principle, be built from carbon nanotubes, linked by direct-driven rotational molecular joints, is shown. Finally, the last section concludes on the obtained results and describes current and future work.