Propulsive capability of manta rays' flapping pectoral fins has inspired many to incorporate these fins as propulsive mechanisms for autonomous underwater vehicles. In particular, geometrical factors such as sweep angle have been postulated as being influential to these fins' propulsive capability, specifically their thrust generation. Although effects of sweep angle on static/flapping wings of aircrafts/drones have been widely studied, little has been done for underwater conditions. Furthermore, the findings from air studies may not be relatable to the underwater studies on pectoral fins because of the different Reynolds number (compared to the flapping wings) and force generation mechanism (compared to the static wings). This paper aims to establish a relationship between the sweep angle and thrust generation. An experiment was conducted to measure the thrust generated by 40 fins in a water channel under freestream and still water conditions for chord Reynolds number between 2.2 × 104 and 8.2 × 104. The fins were of five different sweep angles (0 deg, 10 deg, 20 deg, 30 deg, and 40 deg) that were incorporated into eight base designs of different flexibility characteristics. The results showed that the sweep angle (within the range considered) may have no significant influence on these fins' thrust generation, implying no significant effects on thrust under uniform flow condition and on the maximum possible thrust under still water. Overall, it can be concluded that sweep angle may not be a determinant of thrust generation for flapping pectoral fins. This knowledge can ease the decision-making process of design of robots propeled by these fins.
Load-displacement relationships of spinal motion segments are crucial factors in characterizing the stiffness of scoliotic spine models to mimic the spine responses to loads. Although nonlinear approach to approximation of the relationships can be superior to linear ones, little mention has been made to deriving personalized nonlinear load-displacement relationships in previous studies. A method is developed for nonlinear approximation of load-displacement relationships of spinal motion segments to assist characterizing in vivo the stiffness of spine models. We propose approximation by tangent functions and focus on rotational displacements in lateral direction. The tangent functions are characterized using lateral bending test. A multi-body model was characterized to 18 patients and utilized to simulate four spine positions; right bending, left bending, neutral, and traction. The same was done using linear functions to assess the performance of the proposed tangent function in comparison with the linear function. Root-mean-square error (RMSE) of the displacements estimated by the tangent functions was 44 % smaller than the linear functions. This shows the ability of our tangent function in approximation of the relationships for a range of infinitesimal to large displacements involved in the spine movement to the four positions. In addition, the models based on the tangent functions yielded 67, 55, and 39 % smaller RMSEs of Ferguson angles, locations of vertebrae, and orientations of vertebrae, respectively, implying better estimates of spine responses to loads. Overall, it can be concluded that our method for approximating load-displacement relationships of spinal motion segments can offer good estimates of scoliotic spine stiffness.
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