A Hyper-Flexible Manipulator (HFM, for short) is a kind of continuum robots with a simple mechanical structure like a cable, rope and string, which are useful tools utilized everywhere in various forms. In this paper, in order to achieve dexterous and useful manipulation by this type of robot, we discuss kinematics and dynamics of an HFM. We rigorously derive a spatial, nonlinear and continuum dynamics model with an underactuated mechanism using special kinematics based on curve geometry and theory of robot manipulation.

A free-flying space robot with a 6-DOF manipulator cannot follow an arbitrary trajectory in the 9D generalized coordinates (3 of the satellite orientation and 6 of the manipulator) with only manipulator joint control, though it was shown to be commonly controllable in the literature. In this paper, we propose a method to approximate the desired 9D path by introducing a perturbation around it. We call the approximated trajectory the "spiral motion". A computational scheme for planning the spiral motion is presented, and is followed by computer simulation that illustrates the effectiveness of the scheme.

Quantum effects expressed by the energy shift ΔE from the Néel energy ${\mathit{E}}^{\mathrm{N}\mathrm{é}\mathrm{el}}$ and the spin reduction ΔS for zero-point fluctuations of magnons are investigated theoretically for the triangular antiferromagnets (TLAF) on the xy plane with the one-ion-type axial anisotropy -‖D‖(${\mathit{S}}^{\mathit{z}}$ ${)}^2$. We use a method of constructing the canonical transformation without knowledge of the analytical expression called the Bogoliubov transformation. As a result, boson-type excitations are obtained numerically. Here, characteristic properties are discussed in comparison with those for TLAF with the plane-type anisotropy +‖D‖(${\mathit{S}}^{\mathit{z}}$ ${)}^2$, for which the canonical transformation can be given in analytical form. Furthermore, the calculation is performed to reveal quantum effects in a six-sublattice structure, which is formed in layered TLAF with the interlayer antiferromagnetic exchange interaction. The behavior of calculated ΔE and ΔS is discussed in the context of magnetic properties of ${\mathrm{VBr}}_2$, ${\mathrm{VCl}}_2$, ${\mathrm{CsNiBr}}_3$, and ${\mathrm{CsMnI}}_3$.