Compound Indexing

Q. A non standard thread of pitch $3.175mm$ is to be cut on a lathe having lead screw of pitch $6mm$. A change gear set provdied with the lathe has one gear each with the following number of teeth: $20,30,40,50,60,70,80,90,100,110,120,127.$ The correct pairs of change gears $(a/b\times c/d)$ for machining the given thread are (assuming that transmission ratio of the rest of the kinematic train between the late spindle and lead screw is equal to 1)

1. $\frac{127}{30}\times \frac{20}{80}$
2. $\frac{127}{40}\times \frac{20}{120}$
3. $\frac{127}{30}\times \frac{30}{120}$
4. $\frac{127}{50}\times \frac{30}{80}$