In the last years, more and more studies have highlighted the advantages of complementing traditional master classes with additional activities that improve students’ learning experience. This combination of teaching techniques is specially advised in the field of structural engineering, where intuition of the structural response it is of vital importance to understand the studied concepts. This paper deals with the introduction of a new (and more encouraging) educational tool to introduce students intuitively to the dynamic response of structures excited with an educational shaking table. Most of the educational structural health monitoring systems use sensors to determine the dynamic response of the structure. The proposed tool is based on a radically different approach, as it is based on low-cost image-recognition techniques. In fact, it only requires the use of an amateur camera, a black background, and a computer. In this study, the effects of both the camera location and the image quality are also evaluated. Finally, to validate the applicability of the proposed methodology, the dynamic response of small-scale buildings with different typologies is analyzed. In addition, a series of surveys were conducted in order to evaluate the activity based on student´s satisfaction and the actual acquisition and strengthening of knowledge.

This article introduces new types of rational approximations of the inverse involute function, widely used in gear engineering, allowing the processing of this function with a very low error. This approximated function is appropriate for engineering applications, with a much reduced number of operations than previous formulae in the existing literature, and a very efficient computation. The proposed expressions avoid the use of iterative methods. The theoretical foundations of the approximation theory of rational functions, the Chebyshev and Jacobi polynomials that allow these approximations to be obtained, are presented in this work, and an adaptation of the Remez algorithm is also provided, which gets a null error at the origin. This way, approximations in ranges or degrees different from those presented here can be obtained. A rational approximation of the direct involute function is computed, which avoids the computation of the tangent function. Finally, the direct polar equation of the circle involute curve is approximated with some application examples.

In the last years, more and more studies highlight the advantages of complementing traditional master classes with additional activities that improve students´ learning experience. This combination of teaching techniques is specially advised in the field of structural engineering, where intuition of the structural response it is of vital importance to understand the studied concepts. This paper deals with the introduction of a new (and more encouraging) educational tool to introduce intuitively students in the dynamic response of structures excited with an educational shaking table. Most of the educational structural health monitoring systems use sensors to determine the dynamic response of the structure. The proposed tool is based on a radically different approach, as it is based on low-cost image-recognition techniques. In fact, it only requires the use an amateur camera, a black background and a computer. In this study, the effects of both the camera location and the image quality are also evaluated. Finally, to validate the applicability of the proposed methodology, the dynamic response of small-scale buildings with different typologies is analyzed. In addition, a series of surveys were conducted in order to evaluate the activity based on student´s satisfaction and the actual acquisition and strengthening of knowledge.

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Background. Advances in 3D shape capture technology have made powerful shape analyses, such as geometric morphometrics, more feasible. While the highly accurate micro-computed tomography (μCT) scanners have been the "gold standard," recent improvements in 3D surface scanners may make this technology a faster, portable, and cost-effective alternative. Several studies have already compared the two devices but all use relatively large specimens such as human crania. Here we perform shape analyses on Australia's smallest rodent to test whether a 3D scanner produces similar results to a μCT scanner. Methods. We captured 19 delicate mouse (Pseudomys delicatulus) crania with a μCT scanner and a 3D scanner for geometric morphometrics. We ran multiple Procrustes ANOVAs to test how variation due to scan device compared to other sources such as biologically relevant variation and operator error. We quantified operator error as levels of variation and repeatability. Further, we tested if the two devices performed differently at classifying individuals based on sexual dimorphism. Finally, we inspected scatterplots of principal component analysis (PCA) scores for non-random patterns. Results. In all Procrustes ANOVAs, regardless of factors included, differences between individuals contributed the most to total variation. The PCA plots reflect this in how the individuals are dispersed. Including only the symmetric component of shape increased the biological signal relative to variation due to device and due to error. 3D scans showed a higher level of operator error as evidenced by a greater spread of their replicates on the PCA, a higher level of multivariate variation, and a lower repeatability score. However, the 3D scan and μCT scan datasets performed identically in classifying individuals based on intra-specific patterns of sexual dimorphism. Discussion. Compared to μCT scans, we find that even low resolution 3D scans of very small specimens are sufficiently accurate to classify intra-specific differences. We also make 3 recommendations for best use of low resolution data. First, we recommend that extreme caution should be taken when analyzing the asymmetric component of shape variation. Second, using 3D scans generates more random error due to increased landmarking difficulty, therefore users should be conservative in landmark choice and avoid multiple operators. Third, using 3D scans introduces a source of systematic error relative to μCT scans, therefore we recommend not combining them when possible, especially in studies expecting little biological variation. Our findings support increased use of low resolution 3D scans for most morphological