Force analysis of an open TBM gripping–thrusting–regripping mechanism

This paper presents an approach for the force analysis of an open TBM gripping–thrusting–regripping mechanism, which is a special parallel mechanism driven by hydraulic actuators and constrained by rocky surroundings. The static equilibrium equations of the cutterhead–mainbeam–saddle subassembly are formulated first by exploring the reaction forces in the cross pin situated between the saddle and the gripper cylinder. This is followed by formulating the static equilibrium equations of the inner closed loops formed by the above subassembly, the torque, and gripper cylinders. Consequently, the linear map between the externally applied wrench imposed on the shield and the equivalent thrust forces of the cylinders is developed. The functionality of the force model developed is twofold, i.e., it can be used either to estimate the thrust forces of the cylinders required to resist against the tunneling loads, or to predict the tunneling loads using the measured thrust forces of these cylinders, thus providing important theoretical basis for the design and control of the mechanism

Stiffness modeling of parallel mechanisms at limb and joint/link levels

Drawing on screw theory and the virtual joint method, this paper presents a general and hierarchical approach for semianalytical stiffness modeling of parallel mechanisms. The stiffness model is built by two essential steps: 1) formulating the map between the stiffness matrices of platform and limbs using the duality of wrench and twist of the platform; and 2) formulating the map between stiffness matrices of a limb and a number of elastic elements in that limb using the duality of the wrench attributed to the limb and the twist of the endlink of that limb. By merging these two threads, the Cartesian stiffness matrix can be explicitly expressed in terms of the compliance matrices of joints and links. The proposed approach bridges the gap between two currently available approaches and is thereby very useful for evaluating stiffness over the entire workspace and investigating the influences of joint/link compliances on those of the platform in a quick and precise manner. A stiffness analysis for a 3-PRS parallel mechanism is presented as an example to illustrate the effectiveness of the proposed approach

A generalized approach for computing the transmission index of parallel mechanisms

This paper presents a novel approach for computing the transmission index of parallel mechanisms. The approach is based on an extended concept to compute the maximal virtual coefficient, which is an important notion involved in the formulation of dimensionally homogeneous transmission indices for singularity analysis and dimensional optimization of parallel mechanisms. By exploiting the dual property of the virtual coefficient, two characteristic points instead of one as in the current state of the art are defined: one characteristic point – termed the transmission characteristic point – is located on the ‘floating’ axis of the transmission wrench, as in existing approaches, while a second one – termed the output characteristic point – is located on the floating axis of the output twist of the platform, which is a novel concept. This allows one to define two characteristic lengths, namely, the transmission and output characteristic lengths, respectively, of which the larger is then used for the measure of the “distance” between the transmission wrench screw and the output twist screw. As shown in this paper, this new measure makes it possible to discern more finely the configuration-dependent properties of kinematic performance of parallel mechanisms, thus making it more suitable for dimensional optimization. Confidence in this statement is demonstrated through the comparative study of two in-parallel mechanisms using the new method and previously existing ones

Compliance analysis of a 3-SPR parallel mechanism with consideration of gravity

By taking gravity and joint/link compliances into account, this paper presents a semi-analytical approach for compliance analysis of a 3-SPR parallel mechanism which forms the main body of a 5-DOF hybrid manipulator especially designed for high-speed machining and forced assembling in the aircraft industry. The approach is implemented in three steps: (1) kinetostatic analysis that considers both the externally applied wrench imposed upon the platform and the gravity of all moving components; (2) deflection analysis that takes both joint and link compliances into account; and (3) formulation of the component compliance matrices using a semi-analytical approach. The advantage of this approach is that the deflections of the platform caused by both the payload and gravity within the given task workspace can be evaluated in an effective manner. The computational results show that the deflection arising from gravity of the moving components may have significant influence on the pose accuracy of the end-effector

Robust millisecond coherence times of erbium electron spins

Erbium-doped solids are prime candidates for optical quantum communication networks due to erbium's telecom C-band emission. A long-lived electron spin of erbium with millisecond coherence time is highly desirable for establishing entanglement between adjacent quantum repeater nodes while long-term storage of the entanglement could rely on transferring to erbium's second-long coherence nuclear spins. Here we report GHz-range electron spin transitions of $^{167}\mathrm{Er}^{3+}$ in yttrium oxide ($\mathrm{Y_2O_3}$) matrix with coherence times that are consistently longer than a millisecond. Instead of addressing field-specific Zero First-Order Zeeman transitions, we probe weakly mixed electron spins with the field orientation along the lower g-factors. Using pulsed electron spin resonance spectroscopy, we find paramagnetic impurities are the dominant source of decoherence, and by polarizing them we achieve a Hahn echo spin $\mathrm{T_2}$ up to 1.46 ms, and a coherence time up to 7.1 ms after dynamical decoupling. These coherence lifetimes are among the longest found in crystalline hosts especially those with nuclear spins. We further enhance the coherence time beyond conventional dynamical decoupling, using customized sequences to simultaneously mitigate spectral diffusion and Er-Er dipolar interactions. Despite nuclear and impurity spins in the host, this work shows that long-lived erbium spins comparable to non-nuclear spin hosts can be achieved. Our study not only establishes $^{167}\mathrm{Er}^{3+}$: $\mathrm{Y_2 O_3}$ as a significantly promising quantum memory platform but also provides a general guideline for engineering long-lived erbium spins in a variety of host materials for quantum technologies.Comment: 10 pages, 4 figure

A simple and visually orientated approach for type synthesis of overconstrained 1T2R parallel mechanisms

This paper presents a simple and highly visual approach for the type synthesis of a family of overconstrained parallel mechanisms that have one translational and two rotational movement capabilities. It considers, especially, mechanisms offering the accuracy and dynamic response needed for machining applications. This family features a spatial limb plus a member of a class of planar symmetrical linkages, the latter connected by a revolute joint either to the machine frame at its base link or to the platform at its output link. Criteria for selecting suitable structures from among numerous candidates are proposed by considering the realistic practical requirements for reconfigurability, movement capability, rational component design and so on. It concludes that a few can simultaneously fulfil the proposed criteria, even though a variety of structures have been presented in the literature. Exploitation of the proposed structures and evaluation criteria then leads to a novel five degrees of freedom hybrid module named TriMule. A significant potential advantage of the TriMule over the Tricept arises because all the joints connecting the base link and the machine frame can be integrated into one single, compact part, leading to a lightweight, cost effective and flexible design particularly suitable for configuring various robotized manufacturing cells