Lathe speeds: A lathe with four steps on the cone pulley and with back-gears engaged provides how many distinct spindle speeds?

Introduction / Context:
Older engine lathes use stepped cone pulleys for speed selection. Back-gears provide a secondary, slower set of speeds by introducing a gear reduction between the cone pulley and spindle. Understanding this arrangement helps operators choose suitable cutting speeds when variable-frequency drives are not present.

Given Data / Assumptions:

• Four steps on the cone pulley (4 belt positions).
• Back-gear mechanism available for speed reduction.
• No additional gearbox is considered.

Concept / Approach:
Each belt step gives one direct (back-gear disengaged) speed. Engaging back-gears multiplies each step by a fixed reduction, creating a corresponding indirect (reduced) speed. Therefore, a 4-step cone with back-gears yields 4 direct plus 4 indirect speeds, i.e., 8 distinct spindle speeds.

Step-by-Step Solution:

Verification / Alternative check:
Lathe manuals and nameplates show two speed columns for each belt position: direct and back-gear, confirming the 4 + 4 arrangement.

Why Other Options Are Wrong:
Only direct or only indirect speeds ignore the dual-mode nature; eight indirect speeds is incorrect because half are direct, half are indirect.

Common Pitfalls:
Trying to change belt position with back-gears engaged; forgetting to properly disengage the bull gear pin when using back-gears, which can lock the spindle.

Final Answer:
four direct and four indirect speeds