Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Walking in hospital is associated with a shorter length of stay in older medical inpatients

Evidence suggests that inactivity during a hospital stay is associated with poor health outcomes in older medical inpatients. We aimed to estimate the associations of average daily step-count (walking) in hospital with physical performance and length of stay in this population. Medical in-patients aged ⩾65 years, premorbidly mobile, with an anticipated length of stay ⩾3 d, were recruited. Measurements included average daily step-count, continuously recorded until discharge, or for a maximum of 7 d (Stepwatch Activity Monitor); co-morbidity (CIRS-G); frailty (SHARE F-I); and baseline and end-of-study physical performance (short physical performance battery). Linear regression models were used to estimate associations between step-count and end-of-study physical performance or length of stay. Length of stay was log transformed in the first model, and step-count was log transformed in both models. Similar models were used to adjust for potential confounders. Data from 154 patients (mean 77 years, SD 7.4) were analysed. The unadjusted models estimated for each unit increase in the natural log of stepcount, the natural log of length of stay decreased by 0.18 (95% CI −0.27 to −0.09). After adjustment of potential confounders, while the strength of the inverse association was attenuated, it remained significant (βlog(steps) = −0.15, 95%CI −0.26 to −0.03). The back-transformed result suggested that a 50% increase in step-count was associated with a 6% shorter length of stay. There was no apparent association between step-count and end-of-study physical performance once baseline physical performance was adjusted for. The results indicate that step-count is independently associated with hospital length of stay, and merits further investigation.