Shock oscillations on a series of V-shaped blunt leading edges with R/r (i.e., the crotch rounding radius R to the leading edge radius r) ranging from 0 to 9 are experimentally investigated at Mach 6. A combination of high-speed schlieren and image processing technologies is used to capture the flow features during the shock oscillations. The observed primary shock structures are categorized as regular reflection (type A), Mach reflection (type B), and regular reflection from the same family (type C). It is revealed that the competition of the two opposite jets near the stagnation point and the breathing-like motion of the flow at the crotch region cause severe oscillations for types B and C. These oscillations are classified into four patterns with the increase of R/r: global swing, mixing of swing and arch-recover, global arch-recover, and local arch-recover. Correspondingly, the coherent structure of the oscillations gradually changes from an antisymmetric one to a symmetrical one. The transitions of the four patterns are quantitatively identified by the analyses of the root mean square of the fluctuations of the triple point TP and the shock point SP on the symmetrical line, which almost linearly decrease with the increase of R/r. Moreover, both TP and SP in the shock oscillations present energetic dominant frequencies that vary significantly with R/r. However, a nearly universal Strouhal number is obtained when the distances from TP (for type B) and the self-induced kink (for type C) to the stagnation point are employed as the relevant lengths, which suggests a possible physical mechanism for the oscillations. This study indicates that the shock oscillations can be suppressed by a properly large R/r, which is recommended for the design of V-shaped cowl lips.