The geometrical tooth surface properties of skew gears have a significant influence on gear performance. We consider the contact line angle, slip rate, and relative curvature as tooth surface properties. An overall image of the tooth surface properties is an effective means of optimization. However, this whole image is unknown, because the tooth surface properties are represented by four elements of the tooth surface, and it is difficult to express them in one coordinate space. This problem is overcome by expressing the tooth surface properties using three elements. First, three-element expressions for the tooth surface properties are derived and the tooth surface property space, which expresses the overall image of the tooth surface properties, is constructed using the three elements as coordinate axes. Next, the characteristic surface of the tooth surface property space is clarified and an image of the space is simulated. From this, it is possible to visually and intuitively capture the features of the tooth surface property space, i.e., the whole image. Finally, the wide range of applications of the tooth surface property space is discussed. This demonstrates that the tooth surface property space provides important indicators and standards for the future development and designs.

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