The neutral curve of a flexspline (FS) is usually represented by the function curve of cam-shape curve in the traditional harmonic drive (HD) model. This representation may induce tooth tip interference and excessive deformation. In this study, a novel mathematical model of the FS deformation is established to accurately depict the neutral curve. Then, a tooth profile design method is proposed based on this model, which can obtain an exact conjugate tooth profile when giving an initial tooth profile. In addition, another design method that does not demand the initial tooth profile is proposed for simplicity of design. The HD designed by this method has a larger number of meshing teeth and a larger depth of engagement compared to traditional HDs. Moreover, a meshing model of a tooth pair is employed to verify the feasibility of the two design methods. Next, one of them is used to investigate the effect of the wave generator shape on the engagement of a couple tooth profiles, and the results show that the wave generator shapes with different parallel distances have no effect on the continuous engagement. Furthermore, an instantaneous transmission ratio calculation method of a tooth pair is developed for future calculations of the instantaneous transmission ratio between the input and output shafts of the HD. The calculation results manifest that the instantaneous transmission ratio of the tooth pair belongs to a variable transmission ratio.

在传统的谐波传动（HD）模型中，柔轮（FS）的中性曲线通常用凸轮曲线的函数曲线表示。这种表示可能会导致齿尖干涉和过度变形。在这项研究中，建立了一种新的 FS 变形数学模型，以准确描绘中性曲线。然后，基于该模型提出一种齿廓设计方法，在给出初始齿廓的情况下，可以获得精确的共轭齿廓。此外，为了简化设计，还提出了另一种不需要初始齿形的设计方法。与传统HD相比，采用这种方法设计的HD具有更多的啮合齿和更大的啮合深度。而且，采用齿对的啮合模型来验证两种设计方法的可行性。接下来，利用其中之一来研究波发生器形状对一对齿廓啮合的影响，结果表明不同平行距离的波发生器形状对连续啮合没有影响。此外，还开发了齿对瞬时传动比的计算方法，以供日后计算HD输入轴和输出轴之间的瞬时传动比。计算结果表明，齿对瞬时传动比属于可变传动比。结果表明，不同平行距离的波发生器形状对连续啮合没有影响。此外，还开发了齿对瞬时传动比的计算方法，以供日后计算HD输入轴和输出轴之间的瞬时传动比。计算结果表明，齿对瞬时传动比属于可变传动比。结果表明，不同平行距离的波发生器形状对连续啮合没有影响。此外，还开发了齿对瞬时传动比的计算方法，以供日后计算HD输入轴和输出轴之间的瞬时传动比。计算结果表明，齿对瞬时传动比属于可变传动比。