Active design of tooth profiles using parabolic curve as the line of action

This paper proposes a method for the design of gear tooth profiles using parabolic curve as its line of action. A mathematical model, including the equation of the line of action, the equation of the tooth profile, and the equation of the conjugate tooth profile, is developed based on the meshing theory. The equation of undercutting condition is derived from the model. The influences of the two design parameters, that present the size (or shape) of the parabolic curve relative to the gear size, on the shape of tooth profiles and on the contact ratio are also studied through the design of an example drive. The strength, including the contact and the bending stresses, of the gear drive designed by using the proposed method is analyzed by an FEA simulation. A comparison of the above characteristics of the gear drive designed with the involute gear drive is also carried out in this work. The results confirm that the proposed design method is more flexible to control the shape of the tooth profile by changing the parameters of the parabola.

Assessing residual reasoning ability in overtly non-communicative patients using fMRI

It is now well established that some patients who are diagnosed as being in a vegetative state or a minimally conscious state show reliable signs of volition that may only be detected by measuring neural responses. A pertinent question is whether these patients are also capable of logical thought. Here, we validate an fMRI paradigm that can detect the neural fingerprint of reasoning processes and moreover, can confirm whether a participant derives logical answers. We demonstrate the efficacy of this approach in a physically non-communicative patient who had been shown to engage in mental imagery in response to simple audi- tory instructions. Our results demonstrate that this individual retains a remarkable capacity for higher cogni- tion, engaging in the reasoning task and deducing logical answers. We suggest that this approach is suitable for detecting residual reasoning ability using neural responses and could readily be adapted to assess other aspects of cognition.