Dynamic testing to determine and predict trampoline function

Safety standards for domestic trampolines are based on static-load testing using a factor of five times the maximum intended user mass. This paper presents a dynamic test method for trampolines, and provides measures of the users’ performance (e.g., peak acceleration, Accmax) and injury risk (e.g., mean rate of change of acceleration, Jerkmean). Uniform masses (41–116 kg) were dropped from 0.66 m onto the bed centre of nineteen different trampolines. Trampoline bed and spring stretches, mass flight time (FlightT) and accelerations were recorded using motion capture and accelerometers. Thirty-seven percent of trampolines exceeded the static safety standard bed deformation limits (80% of frame height) by 11 ± 6% with dynamic testing (mean ± standard deviation). Across all trampolines and masses dropped, the Accmax ranged from 5.1 to 7.6 g, suggesting the factor of five used in static-loading safety standards needs reviewing. Statistically significant negative correlations (p < 0.05) were found between trampoline bed diameter and Accmax (r = – 0.88), Jerkmean (r = – 0.77) and FlightT (r = – 0.82). Furthermore, significant correlations (p < 0.05) were also found between the mass dropped and Accmax (r = – 0.27), Jerkmean (r = – 0.59) and FlightT (r = 0.25). The combined effects of the spring constants, number of springs, bed diameters and masses dropped were described in predictive multivariate equations for Accmax (explained variance, R2 = 95%) and maximum vertical bed deformation (R2 = 85%). These findings from dynamic testing may assist manufacturers in designing trampolines that meet safety standards while maximising user performance and reducing injury risk.

A simplified cervix model in response to induction balloon in pre-labour

Background: Induction of labour is poorly understood even though it is performed in 20% of births in the United States. One method of induction, the balloon dilator applied with traction to the interior os of the cervix, engages a softening process, permitting dilation and effacement to proceed until the beginning of active labour. The purpose of this work is to develop a simple model capable of reproducing the dilation and effacement effect in the presence of a balloon. Methods: The cervix, anchored by the uterus and the endopelvic fascia was modelled in pre-labour. The spring-loaded, double sliding-joint, double pin-joint mechanism model was developed with a Modelica-compatible system, MapleSoft MapleSim 6.1, with a stiff Rosenbrock solver and 1E-4 absolute and relative tolerances. Total simulation time for pre-labour was seven hours and simulations ended at 4.50 cm dilation diameter and 2.25 cm effacement. Results: Three spring configurations were tested: one pin joint, one sliding joint and combined pin-joint-sliding-joint. Feedback, based on dilation speed modulated the spring values, permitting controlled dilation. Dilation diameter speed was maintained at 0.692 cm · hr−1 over the majority of the simulation time. In the sliding-joint-only mode the maximum spring constant value was 23800 N · m−1. In pin-joint-only the maximum spring constant value was 0.41 N·m· rad−1.With a sliding-joint-pin-joint pair the maximum spring constants are 2000 N · m−1 and 0.41 N · m · rad−1, respectively. Conclusions: The model, a simplified one-quarter version of the cervix, is capable of maintaining near-constant dilation rates, similar to published clinical observations for pre-labour. Lowest spring constant values are achieved when two springs are used, but nearly identical tracking of dilation speed can be achieved with only a pin joint spring. Initial and final values for effacement and dilation also match published clinical observations. These results provide a framework for development of electro-mechanical phantoms for induction training, as well as dilator testing and development.

A simplified cervix model in response to induction balloon in pre-labour

Background: Induction of labour is poorly understood even though it is performed in 20% of births in the United States. One method of induction, the balloon dilator applied with traction to the interior os of the cervix, engages a softening process, permitting dilation and effacement to proceed until the beginning of active labour. The purpose of this work is to develop a simple model capable of reproducing the dilation and effacement effect in the presence of a balloon. Methods: The cervix, anchored by the uterus and the endopelvic fascia was modelled in pre-labour. The spring-loaded, double sliding-joint, double pin-joint mechanism model was developed with a Modelica-compatible system, MapleSoft MapleSim 6.1, with a stiff Rosenbrock solver and 1E-4 absolute and relative tolerances. Total simulation time for pre-labour was seven hours and simulations ended at 4.50 cm dilation diameter and 2.25 cm effacement. Results: Three spring configurations were tested: one pin joint, one sliding joint and combined pin-joint-sliding-joint. Feedback, based on dilation speed modulated the spring values, permitting controlled dilation. Dilation diameter speed was maintained at 0.692 cm · hr−1 over the majority of the simulation time. In the sliding-joint-only mode the maximum spring constant value was 23800 N · m−1. In pin-joint-only the maximum spring constant value was 0.41 N·m· rad−1.With a sliding-joint-pin-joint pair the maximum spring constants are 2000 N · m−1 and 0.41 N · m · rad−1, respectively. Conclusions: The model, a simplified one-quarter version of the cervix, is capable of maintaining near-constant dilation rates, similar to published clinical observations for pre-labour. Lowest spring constant values are achieved when two springs are used, but nearly identical tracking of dilation speed can be achieved with only a pin joint spring. Initial and final values for effacement and dilation also match published clinical observations. These results provide a framework for development of electro-mechanical phantoms for induction training, as well as dilator testing and development.

Cooperative Dynamics in the Fiber Bundle Model

We discuss the cooperative failure dynamics in the fiber bundle model where the individual elements or fibers are Hookean springs that have identical spring constants but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field-type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.

Mechanochemical properties of DNA origami nanosprings revealed by force jumps in optical tweezers

Using a force-jump approach in optical tweezers, the spring constants and dynamic recoiling responses of DNA nanosprings can be recorded.

Estimating the Directional Flexibility of Proteins from Equilibrium Thermal Fluctuations

<b><i>In this manuscript, we demonstrate the abilities of atomistic MD trajectories to estimate the directional spring constants of proteins. The MD-derived spring constants are cross-correlated with single-molecule force spectropcopy (SMFS) experimental data for 5 different globular proteins. We employ the framework to predict the mechanical anisotropy of ubiquitin and associated changes in the anisotropy with functionally relevant protein-protein interactions. Finally, we use the MD-based framework to benchmark and improve computationally inexpensive and scalable elastic network model (ENM) based methods to estimate protein directional flexibility.</i></b>

Estimating the Directional Flexibility of Proteins from Equilibrium Thermal Fluctuations

<b><i>In this manuscript, we demonstrate the abilities of atomistic MD trajectories to estimate the directional spring constants of proteins. The MD-derived spring constants are cross-correlated with single-molecule force spectropcopy (SMFS) experimental data for 5 different globular proteins. We employ the framework to predict the mechanical anisotropy of ubiquitin and associated changes in the anisotropy with functionally relevant protein-protein interactions. Finally, we use the MD-based framework to benchmark and improve computationally inexpensive and scalable elastic network model (ENM) based methods to estimate protein directional flexibility.</i></b>