Flexure hinges have been used to produce frictionless and backlashless transmission in a variety of precision instruments. Many kinds of flexure profile were proposed during the past decade. The present work brings elliptical arc, parabolic, and hyperbolic profiles together by proposing a generalized conic flexure hinge model. By utilizing the generalized equation for conic curves in polar coordinates, all the elements in the compliance and precision matrices for conic flexure hinges are deduced. These equations were verified by finite element analysis and experimentation. The analytical results are within 11% error compared to the finite element results and within 6% error compared to the experimental results.

Based on the geometrical nonlinear theory of large deflection elastic beams, the governing differential equations of post-buckling behavior of clamped-clamped inclined beams subjected to combined forces are established. By using the implicit compatibility conditions to solve the nonlinear statically indeterminate problems of elastic beams, the strongly nonlinear equations formulated in terms of elliptic integrals are directly solved in the numerical sense. When the applied force exceeds the critical value, the numerical simulation shows that the inclined beam snaps to the other equilibrium position automatically. It is in the snap-through process that the accurate configurations of the post-buckling inclined beam with different angles are presented, and it is found that the nonlinear stiffness decreases as the midpoint displacement is increased according to our systematical analysis of the inward relations of different buckling modes. The numerical results are in good agreement with those obtained in the experiments.

A new objective fabric pilling evaluation method based on wavelet transform and the local binary pattern (LBP) is developed. The surface pills are identified from the high-frequency noise, fabric texture, and illuminative variation of a pilled fabric image by the two-dimensional discrete wavelet transform. The energies of each detailed sub-image at scales 4–6 in three orientations (horizontal, vertical, and diagonal) and the LBP features of the reconstructed detail image from scales 3 to 6 are calculated as elements of the pilling feature vector to characterize the pilling intensity. These feature values are normalized and the vector dimensions are reduced by principal component analysis. Then the support vector machine, a kind of data mining tool, is used as a classifier to classify the pilling grades. The result suggests that the proposed method can successfully evaluate the pilling intensity of knitted fabrics and could be applicable to practical objective pilling evaluation.

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