Curve Decomposition for Large Deflection Analysis of Fixed-Guided Beams With Application to Statically Balanced Compliant Mechanisms

Statically balanced compliant mechanisms require no holding force throughout their range of motion while maintaining the advantages of compliant mechanisms. In this paper, a postbuckled fixed-guided beam is proposed to provide the negative stiffness to balance the positive stiffness of a compliant mechanism. To that end, a curve decomposition modeling method is presented to simplify the large deflection analysis. The modeling method facilitates parametric design insight and elucidates key points on the force-deflection curve. Experimental results validate the analysis. Furthermore, static balancing with fixed-guided beams is demonstrated for a rectilinear proof-of-concept prototype.

Planetary Gear Modal Vibration Experiments and Correlation against Lumped-Parameter and Finite Element Models

Experimental modal analysis techniques are applied to characterize the planar dynamic behavior of two spur planetary gears. Rotational and translational vibrations of the sun gear, carrier, and planet gears are measured. Experimentally obtained natural frequencies, mode shapes, and dynamic response are compared to the results from lumped-parameter and finite element models. Two qualitatively different classes of mode shapes in distinct frequency ranges are observed in the experiments and confirmed by the lumped-parameter model, which considers the accessory shafts and fixtures in the system to capture all of the natural frequencies and modes. The finite element model estimates the high-frequency modes that have significant tooth mesh deflection without considering the shafts and fixtures. The lumped-parameter and finite element models accurately predict the natural frequencies and modal properties established by experimentation. Rotational, translational, and planet mode types presented in published mathematical studies are confirmed experimentally. The number and types of modes in the low-frequency and high-frequency bands depend on the degrees of freedom in the central members and planet gears, respectively. The accuracy of natural frequency prediction is improved when the planet bearings have differing stiffnesses in the tangential and radial directions, consistent with the bearing load direction. (C) 2012 Elsevier Ltd. All rights reserved.

Second-Generation Orthopaedic Measurement Device for in-vivo Assessment of Bone Quality

There are two main types of bone in the human body, trabecular and cortical bone. Cortical bone is primarily found on the outer surface of most bones in the body while trabecular bone is found in vertebrae and at the end of long bones (Ross 2007). Osteoporosis is a condition that compromises the structural integrity of trabecular bone, greatly reducing the ability of the bone to absorb energy from falls. The current method for diagnosing osteoporosis and predicting fracture risk is measurement of bone mineral density. Limitations of this method include dependence on the bone density measurement device and dependence on type of test and measurement location (Rubin 2005). Each year there are approximately 250,000 hip fractures in the United States due to osteoporosis (Kleerekoper 2006). Currently, the most common method for repairing a hip fracture is a hip fixation surgery. During surgery, a temporary guide wire is inserted to guide the permanent screw into place and then removed. It is believed that directly measuring this screw pullout force may result in a better assessment of bone quality than current indirect measurement techniques (T. Bowen 2008-2010, pers. comm.). The objective of this project is to design a device that can measure the force required to extract this guide wire. It is believed that this would give the surgeon a direct, quantitative measurement of bone quality at the site of the fixation. A first generation device was designed by a Bucknell Biomedical Engineering Senior Design team during the 2008- 2009 Academic Year. The first step of this project was to examine the device, conduct a thorough design analysis, and brainstorm new concepts. The concept selected uses a translational screw to extract the guide wire. The device was fabricated and underwent validation testing to ensure that the device was functional and met the required engineering specifications. Two tests were conducted, one to test the functionality of the device by testing if the device gave repeatable results, and the other to test the sensitivity of the device to misalignment. Guide wires were extracted from 3 materials, low density polyethylene, ultra high molecular weight polyethylene, and polypropylene and the force of extraction was measured. During testing, it was discovered that the spring in the device did not have a high enough spring constant to reach the high forces necessary for extracting the wires without excessive deflection of the spring. The test procedure was modified slightly so the wires were not fully threaded into the material. The testing results indicate that there is significant variation in the screw pullout force, up to 30% of the average value. This significant variation was attributed to problems in the testing and data collection, and a revised set of tests was proposed to better evaluate the performance of the device. The fabricated device is a fully-functioning prototype and further refinements and testing of the device may lead to a 3rd generation version capable of measuring the screw pullout force during hip fixation surgery.

Evaluation of the Design of Komendant's Cycloidal, Thin Shell Roofs At the Kimbell Art Museum Using Finite Element Analysis

The analysis of Komendant's design of the Kimbell Art Museum was carried out in order to determine the effectiveness of the ring beams, edge beams and prestressing in the shells of the roof system. Finite element analysis was not available to Komendant or other engineers of the time to aid them in the design and analysis. Thus, the use of this tool helped to form a new perspective on the Kimbell Art Museum and analyze the engineer's work. In order to carry out the finite element analysis of Kimbell Art Museum, ADINA finite element analysis software was utilized. Eight finite element models (FEM-1 through FEM-8) of increasing complexity were created. The results of the most realistic model, FEM-8, which included ring beams, edge beams and prestressing, were compared to Komendant's calculations. The maximum deflection at the crown of the mid-span surface of -0.1739 in. in FEM-8 was found to be larger than Komendant's deflection in the design documents before the loss in prestressing force (-0.152 in.) but smaller than his prediction after the loss in prestressing force (-0.3814 in.). Komendant predicted a larger longitudinal stress of -903 psi at the crown (vs. -797 psi in FEM-8) and 37 psi at the edge (vs. -347 psi in FEM-8). Considering the strength of concrete of 5000 psi, the difference in results is not significant. From the analysis it was determined that both FEM-5, which included prestressing and fixed rings, and FEM-8 can be successfully and effectively implemented in practice. Prestressing was used in both models and thus served as the main contribution to efficiency. FEM-5 showed that ring and edge beams can be avoided, however an architect might find them more aesthetically appropriate than rigid walls.