We define framed curves (or frontals) on Euclidean 2-sphere, give a moving frame of the framed curve and define a pair of smooth functions as the geodesic curvature of a regular curve. It is quite useful for analysing curves with singular points. In general, we can not define evolutes at singular points of curves on Euclidean 2-sphere, but we can define evolutes of fronts under some conditions. Moreover, some properties of such evolutes at singular points are given.
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Yu et al. (2015) studied this question.