The velocity ratio of the differential wheel and axle is A. $$\frac{{\text{R}}}{{{{\text{r}}_1} – {{\text{r}}_2}}}$$ B. $$\frac{{2{\text{R}}}}{{{{\text{r}}_1}}}$$ C. $$\frac{{3{\text{R}}}}{{{{\text{r}}_1} – {{\text{r}}_2}}}$$ D. $$\frac{{2{\text{R}}}}{{{{\text{r}}_1} + {{\text{r}}_2}}}$$

The correct answer is $\frac{{2{\text{R}}}}{{{{\text{r}}_1} + {{\text{r}}_2}}}$.

The velocity ratio of a differential wheel and axle is the ratio of the speed of the output shaft to the speed of the input shaft. It is calculated by dividing the radius of the output shaft by the sum of the radii of the input shafts.

In the given question, the output shaft is the axle of the differential, and the input shafts are the axles of the wheels. The radius of the output shaft is ${\text{R}}$, and the radii of the input shafts are ${\text{r}}_1$ and ${\text{r}}_2$. Therefore, the velocity ratio is:

$$\frac{{2{\text{R}}}}{{{{\text{r}}_1} + {{\text{r}}_2}}}$$

Option A is incorrect because it divides the radius of the output shaft by the difference of the radii of the input shafts. Option B is incorrect because it divides the radius of the output shaft by the radius of the input shaft. Option C is incorrect because it divides the radius of the output shaft by the sum of the radii of the input shafts, but it is multiplied by 3.