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Planar spiral spring is important for the dimensional miniaturisation of motor-based elastic actuators. However, when the stiffness calculation of the spring arm is based on simple beam bending theory, the results possess substantial errors compared with the stiffness obtained from finite-element analysis (FEA). It deems that the errors arise from the spiral length term in the calculation formula. Two Gaussian process regression models are trained to amend this term in the stiffness calculation of spring arm and complete spring. For the former, 216 spring arms' data sets, including different spiral radiuses, pitches, wrap angles and the stiffness from FEA, are employed for training. The latter engages 180 double-arm springs' data sets, including widths instead of wrap angles. The simulation of five spring arms and five planar spiral springs with arbitrary dimensional parameters verifies that the absolute values of errors between the predicted stiffness and the stiffness from FEA are reduced to be less than 0.5% and 2.8%, respectively. A planar spiral spring for a powered ankle–foot prosthesis is designed and manufactured to verify further, of which the predicted value possesses a 3.25% error compared with the measured stiffness. Therefore, the amendment based on the prediction of trained models is available. [ABSTRACT FROM AUTHOR]

Elastic actuators are broadly applied in the design of the powered ankle-foot prosthesis, so it is a significant task to select and optimize a suitable elastic actuator. Dynamic models of seven kinds of elastic actuators are constructed from a two-degrees-of-freedom vibration system in rotation. With input parameters from sound ankle data during walking, motor data, and the three-dimensional model of the proposed prosthesis, two objectives, which are to minimize the peak mechanical power and mean energy consumption power of the motor, respectively, are optimized by changing the parameters of elastic elements. Unidirectional parallel elastic actuator (UPEA) and UPEA with series spring (SE+UPEA) optimize nearly 75% compared to the direct-driver actuator (DDA) in minimizing the characteristic of peak mechanical power. When it comes to reducing mean energy consumption power, UPEA is also the best, and its performance is at least 15% better than those of the other four kinds of elastic actuators with effective optimization. Besides, features of torque and velocity on the driver end are also compared from elastic actuators to sound ankle. The comparison contributes to understanding the optimization mechanism of different elastic elements, and the optimized and compared performances of elastic actuators can be utilized as the selection basis in the design of the powered ankle-foot prosthesis. [ABSTRACT FROM AUTHOR]