The reliability mathematical model of load-sharing parallel systems based on fatigue cumulative damage

Conventional reliability models for parallel systems are not applicable for the analysis of parallel systems with load transfer and sharing. In this short communication, firstly, the dependent failures of parallel systems are analyzed, and the reliability model of load-sharing parallel system is presented based on Miner cumulative damage theory and the full probability formula. Secondly, the parallel system reliability is calculated by Monte Carlo simulation when the component life follows the Weibull distribution. The research result shows that the proposed reliability mathematical model could analyze and evaluate the reliability of parallel systems in the presence of load transfer.

Towards the design of monolithic decoupled XYZ compliant parallel mechanisms for multi-function applications

This paper deals with the monolithic decoupled XYZ compliant parallel mechanisms (CPMs) for multi-function applications, which can be fabricated monolithically without assembly and has the capability of kinetostatic decoupling. At first, the conceptual design of monolithic decoupled XYZ CPMs is presented using identical spatial compliant multi-beam modules based on a decoupled 3-PPPR parallel kinematic mechanism. Three types of applications: motion/positioning stages, force/acceleration sensors and energy harvesting devices are described in principle. The kinetostatic and dynamic modelling is then conducted to capture the displacements of any stage under loads acting at any stage and the natural frequency with the comparisons with FEA results. Finally, performance characteristics analysis for motion stage applications is detailed investigated to show how the change of the geometrical parameter can affect the performance characteristics, which provides initial optimal estimations. Results show that the smaller thickness of beams and larger dimension of cubic stages can improve the performance characteristics excluding natural frequency under allowable conditions. In order to improve the natural frequency characteristic, a stiffness-enhanced monolithic decoupled configuration that is achieved through employing more beams in the spatial modules or reducing the mass of each cubic stage mass can be adopted. In addition, an isotropic variation with different motion range along each axis and same payload in each leg is proposed. The redundant design for monolithic fabrication is introduced in this paper, which can overcome the drawback of monolithic fabrication that the failed compliant beam is difficult to replace, and extend the CPM’s life.

Conceptual designs of multi-degree of freedom compliant parallel manipulators composed of wire-beam based compliant mechanisms

This paper proposes conceptual designs of multi-degree(s) of freedom (DOF) compliant parallel manipulators (CPMs) including 3-DOF translational CPMs and 6-DOF CPMs using a building block based pseudo-rigid-body-model (PRBM) approach. The proposed multi-DOF CPMs are composed of wire-beam based compliant mechanisms (WBBCMs) as distributed-compliance compliant building blocks (CBBs). Firstly, a comprehensive literature review for the design approaches of compliant mechanisms is conducted, and a building block based PRBM is then presented, which replaces the traditional kinematic sub-chain with an appropriate multi-DOF CBB. In order to obtain the decoupled 3-DOF translational CPMs (XYZ CPMs), two classes of kinematically decoupled 3-PPPR (P: prismatic joint, R: revolute joint) translational parallel mechanisms (TPMs) and 3-PPPRR TPMs are identified based on the type synthesis of rigid-body parallel mechanisms, and WBBCMs as the associated CBBs are further designed. Via replacing the traditional actuated P joint and the traditional passive PPR/PPRR sub-chain in each leg of the 3-DOF TPM with the counterpart CBBs (i.e. WBBCMs), a number of decoupled XYZ CPMs are obtained by appropriate arrangements. In order to obtain the decoupled 6-DOF CPMs, an orthogonally-arranged decoupled 6-PSS (S: spherical joint) parallel mechanism is first identified, and then two example 6-DOF CPMs are proposed by the building block based PRBM method. It is shown that, among these designs, two types of monolithic XYZ CPM designs with extended life have been presented.

A completely kinematostatically decoupled XY compliant parallel manipulator through new topology structure

This paper deals with a completely kinematostaticaly decoupled XY compliant parallel manipulator (CPM) composed of exactly-constrained compliant modules. A new 4-PP XY translational parallel mechanism (TPM) with a new topology structure is firstly proposed where each two P (P: prismatic) joints on the base in two non-adjacent legs are rigidly connected. A novel 4-PP XY CPM is then obtained by replacing each traditional P join on the base in the 4-PP XY TPM with a compound basic parallelogram module (CBPM) and replacing each traditional P joint on the motion stage with a basic parallelogram module (BPM). Approximate analytical model is derived with comparison to the FEA (finite element analysis) model and experiment for a case study. The proposed novel XY CPM has a compact configuration with good dynamics, and is able to well constrain the parasitic rotation and the cross-axis coupling of the motion stage. The cross-axis motion of the input stage can be completely eliminated, and the lost motion between the input stage and the motion stage is significantly reduced.

CUBEs: decoupled, compact, and monolithic spatial translational compliant parallel manipulators

This paper deals with the conceptual design of decoupled, compact, and monolithic XYZ compliant parallel manipulators (CPMs): CUBEs. Position spaces of compliant P (P: prismatic) joints are first discussed, which are represented by circles about the translational directions. A design method of monolithic XYZ CPMs is then proposed in terms of both the kinematic substitution method and the position spaces. Three types of monolithic XYZ CPMs are finally designed using the proposed method with the help of three classes of kinematical decoupled 3-DOF (degree of freedom) translational parallel mechanisms (TPMs). These monolithic XYZ CPMs include a 3-PPP XYZ CPM composed of identical parallelogram modules (a previously reported design), a novel 3-PPPR (R: revolute) XYZ CPM composed of identical compliant four-beam modules, and a novel 3-PPPRR XYZ CPM. The latter two monolithic designs also have extended lives. It is shown that the proposed design method can be used to design other decoupled and compact XYZ CPMs by using the concept of position spaces, and the resulting XYZ CPM is the most compact one when the fixed ends of the three actuated compliant P joints thereof overlap.

Numerical Simulations for the Design of Novel Integrated Parallel Reception, Excitation, and Shimming (iPRES) Coil Arrays

Magnetic field inhomogeneity results in image artifacts including signal loss, image blurring and distortions, leading to decreased diagnostic accuracy. Conventional multi-coil (MC) shimming method employs both RF coils and shimming coils, whose mutual interference induces a tradeoff between RF signal-to-noise (SNR) ratio and shimming performance. To address this issue, RF coils were integrated with direct-current (DC) shim coils to shim field inhomogeneity while concurrently emitting and receiving RF signal without being blocked by the shim coils. The currents applied to the new coils, termed iPRES (integrated parallel reception, excitation and shimming), were optimized in the numerical simulation to improve the shimming performance. The objectives of this work is to offer a guideline for designing the optimal iPRES coil arrays to shim the abdomen.

In this thesis work, the main field () inhomogeneity was evaluated by root mean square error (RMSE). To investigate the shimming abilities of iPRES coil arrays, a set of the human abdomen MRI data was collected for the numerical simulations. Thereafter, different simplified iPRES(N) coil arrays were numerically modeled, including a 1-channel iPRES coil and 8-channel iPRES coil arrays. For 8-channel iPRES coil arrays, each RF coil was split into smaller DC loops in the x, y and z direction to provide extra shimming freedom. Additionally, the number of DC loops in a RF coil was increased from 1 to 5 to find the optimal divisions in z direction. Furthermore, switches were numerically implemented into iPRES coils to reduce the number of power supplies while still providing similar shimming performance with equivalent iPRES coil arrays.

The optimizations demonstrate that the shimming ability of an iPRES coil array increases with number of DC loops per RF coil. Furthermore, the z direction divisions tend to be more effective in reducing field inhomogeneity than the x and y divisions. Moreover, the shimming performance of an iPRES coil array gradually reach to a saturation level when the number of DC loops per RF coil is large enough. Finally, when switches were numerically implemented in the iPRES(4) coil array, the number of power supplies can be reduced from 32 to 8 while keeping the shimming performance similar to iPRES(3) and better than iPRES(1). This thesis work offers a guidance for the designs of iPRES coil arrays.

Design and analysis of a compliant parallel pan-tilt platform

In combination of the advantages of both parallel mechanisms and compliant mechanisms, a compliant parallel mechanism with two rotational DOFs (degrees of freedom) is designed to meet the requirement of a lightweight and compact pan-tilt platform. Firstly, two commonly-used design methods i.e. direct substitution and FACT (Freedom and Constraint Topology) are applied to design the configuration of the pan-tilt system, and similarities and differences of the two design alternatives are compared. Then inverse kinematic analysis of the candidate mechanism is implemented by using the pseudo-rigid-body model (PRBM), and the Jacobian related to its differential kinematics is further derived to help designer realize dynamic analysis of the 8R compliant mechanism. In addition, the mechanism’s maximum stress existing within its workspace is tested by finite element analysis. Finally, a method to determine joint damping of the flexure hinge is presented, which aims at exploring the effect of joint damping on actuator selection and real-time control. To the authors’ knowledge, almost no existing literature concerns with this issue.

A constraint and position identification (CPI) approach for the synthesis of decoupled spatial translational compliant parallel manipulators

This paper introduces a screw theory based method termed constraint and position identification (CPI) approach to synthesize decoupled spatial translational compliant parallel manipulators (XYZ CPMs) with consideration of actuation isolation. The proposed approach is based on a systematic arrangement of rigid stages and compliant modules in a three-legged XYZ CPM system using the constraint spaces and the position spaces of the compliant modules. The constraint spaces and the position spaces are firstly derived based on the screw theory instead of using the rigid-body mechanism design experience. Additionally, the constraint spaces are classified into different constraint combinations, with typical position spaces depicted via geometric entities. Furthermore, the systematic synthesis process based on the constraint combinations and the geometric entities is demonstrated via several examples. Finally, several novel decoupled XYZ CPMs with monolithic configurations are created and verified by finite elements analysis. The present CPI approach enables experts and beginners to synthesize a variety of decoupled XYZ CPMs with consideration of actuation isolation by selecting an appropriate constraint and an optimal position for each of the compliant modules according to a specific application.

Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor

I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequence of the existence of a nontrivial parallel spinor field).

(Table 1) TOC content, BIT, TEX86 and UK'37 indices, and sea surface temperature reconstruction for the middle Miocene to Pliocene of ODP Hole 175-1085A

The initiation of the Benguela upwelling has been dated to the late Miocene, but estimates of its sea surface temperature evolution are not available. This study presents data from Ocean Drilling Program (ODP) Site 1085 recovered from the southern Cape Basin. Samples of the middle Miocene to Pliocene were analyzed for alkenone-based (UK'37, SSTUK) and glycerol dialkyl glycerol tetraether (GDGT) based (TEX86, TempTEX) water temperature proxies. In concordance with global cooling during the Miocene, SSTUK and TempTEX exhibit a decline of about 8°C and 16°C, respectively. The temperature trends suggest an inflow of cold Antarctic waters triggered by Antarctic ice sheet expansion and intensification of Southern Hemisphere southeasterly winds. A temperature offset between both proxies developed with the onset of upwelling, which can be explained by differences in habitat: alkenone-producing phytoplankton live in the euphotic zone and record sea surface temperatures, while GDGT-producing Thaumarchaeota are displaced to colder subsurface waters in upwelling-influenced areas and record subsurface water temperatures. We suggest that variations in subsurface water temperatures were driven by advection of cold Antarctic waters and thermocline adjustments that were due to changes in North Atlantic deep water formation. A decline in surface temperatures, an increased offset between temperature proxies, and an increase in primary productivity suggest the establishment of the Benguela upwelling at 10 Ma. During the Messinian Salinity Crisis, between 7 and 5 Ma, surface and subsurface temperature estimates became similar, likely because of a strong reduction in Atlantic overturning circulation, while high total organic carbon contents suggest a "biogenic bloom." In the Pliocene the offset between the temperature estimates and the cooling trend was reestablished.

(Table S1) TEX86 and BIT record from sediment core PBBC-1

A molecular organic geochemical proxy (TEX86) for sea surface temperature (SST) is compared with a foraminifera-based SST proxy (Mg/Ca) in a decadal-resolution marine sedimentary record spanning the last 1000 years from the Gulf of Mexico. We assess the relative strengths of the organic and inorganic paleoceanographic techniques for reconstructing high-resolution SST variability during recent climate events, including the Little Ice Age (LIA) and the Medieval Warm Period (MWP). SST estimates based on the molecular organic proxy TEX86 show a similar magnitude and pattern of SST variability to foraminiferal Mg/Ca-SST estimates but with some important differences. For instance, both proxies show a cooling (1°C-2°C) of Gulf of Mexico SSTs during the LIA. During the MWP, however, Mg/Ca-SSTs are similar to near-modern SSTs, while TEX86 indicates SSTs that were cooler than modern. Using the respective SST calibrations for each proxy results in TEX86-SST estimates that are 2°C-4°C warmer than Mg/Ca-SST throughout the 1000 year record. We interpret the TEX86-SST as a summer-weighted SST signal from the upper mixed layer, whereas the Mg/Ca-SST better reflects the mean annual SST. Downcore differences in the SST estimates between the two proxies (DeltaT = TEX86 - Mg/Ca) are interpreted in the context of varying seasonality and/or changing water column temperature gradients.

Sea surface temperature (TEX86), marine GDGTs and BIT index from ODP Hole 161-977A

The TEX86H temperature proxy is a relatively new proxy based on crenarchaeotal lipids and has rarely been applied together with other temperature proxies. In this study, we applied the TEX86H on a sediment core from the Alboran Sea (western Mediterranean, core ODP-977A) covering the penultimate climate cycle, that is, from 244 to 130 ka, and compared this with previously published sea surface temperatures derived from the Uk'37 of alkenones of haptophyta and Mg/Ca records of planktonic foraminifera. The TEX86H temperature record shows remarkably similar stadial-interstadial patterns and abrupt temperature changes to those observed with the Uk'37 palaeothermometer. Absolute TEX86H temperature estimates are generally higher than those of Uk'37, though this difference (<3°C in 81% of the data points) is mainly within the temperature calibration error for both proxies, suggesting that crenarchaeota and haptophyta experienced similar temperature variations. During occasional events (<5% of the analyzed time span), however, the TEX86H exhibits considerably higher absolute temperature estimates than the Uk'37. Comparison with Mg/Ca records of planktonic foraminifera as well as other Mediterranean TEX86 and Uk'37 records suggests that part of this divergence may be attributed to seasonal differences, that is, with TEX86H reflecting mainly the warm summer season while Uk'37 would show annual mean. Biases in the global calibration of both proxies or specific biases in the Mediterranean are an alternative, though less likely, explanation. Despite differences between absolute TEX86H and Uk'37 temperatures, the correlation between the two proxies (r**2 = 0.59, 95% significance) provides support for the occurrence of abrupt temperature variations in the western Mediterranean during the penultimate interglacial-to-glacial cycle.