This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint configuration space (configuration space singularities), (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end-effector loses one or more degrees of freedom of available motion (end-effector singularities). The proposed geometric classification provides a high-level taxonomy for mechanism singularities that is independent of the choice of local coordinates used to describe the kinematics, and includes mechanisms that have more actuators than kinematic degrees of freedom.
This paper presents a coordinate-invariant differential geometric analysis of manipulability for closed kinematic chains containing active and passive joints. The formulation treats both redundant and nonredundant mechanisms, as well as over-actuated and exactly actuated ones, in a uniform manner. Dynamic characteristics of the mechanism and manipulated object can also be naturally included by an appropriate choice of Riemannian metric. We illustrate the methodology with several closed chain examples, and provide a practical algorithm for manipulability analysis of general chains.
We determine high magnetic field (B//a) vs temperature phase diagram of TbMn 2 O 5 by measurements of dielectric constant (ε//b) and magnetization under static and pulsed B up to 45 T, and pyroelectric/magnetoelectric currents up to 9 T. Our results reveal that a ferroelectric (FE) transition temperature at TC = 38 K at B = 0 T changes little under B up to 33 T, while incommensurate antiferromagnetic phase, characterized as increased ε and negative polarization below 25 K at B = 0 T, becomes unstable above B = ∼20 T at low temperatures. Furthermore, a positive FE polarization component, coined with a Tb f-spin ordering below ∼15 K at B = 0 T, abruptly disappears with Tb f-spin reorientation under B ≤ ∼2 T. Determined phase diagram shows that both magnitude of FE polarization and ε value are sensitively dependent on the evolution of magnetic order parameters of both Mn-d and Tb-f spins tuned by high magnetic fields.
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