Lathe capacity — relation between swing over bed and swing over carriage In a centre lathe, the swing diameter over the carriage (or cross-slide) compared with the swing diameter over the bed is always:

Introduction / Context:
“Swing” indicates the largest diameter of work that can rotate without interference. Swing over bed is measured from the lathe bed, while swing over carriage (or cross-slide/compound) reflects the reduced clearance when the tool-holding structures are in place. Understanding this distinction is vital for checking workpiece fit.

Given Data / Assumptions:

• Swing over bed ≥ swing over carriage (cross-slide and compound sit above bed level).
• Standard centre lathe geometry.
• No special gap bed or removed top-slide arrangements considered.

Concept / Approach:
The cross-slide and compound rest occupy vertical space above the bed, reducing available clearance to the rotating job. Therefore, the permissible diameter over the carriage is always less than that over the bed.

Step-by-Step Solution:
Define swing over bed = 2 * (distance from spindle centre to bed).Define swing over carriage = 2 * (distance from spindle centre to highest obstruction on carriage).Because the carriage sits above the bed, the second distance is smaller; thus swing over carriage is less.

Verification / Alternative check:
Lathe specification sheets list both values; swing over carriage is consistently smaller. Gap bed lathes may temporarily increase swing near the faceplate, but the general statement remains true.

Why Other Options Are Wrong:
“No” contradicts geometry. Spindle nose does not set carriage clearance. Equality is not typical, and “greater over carriage” is impossible in standard layout.

Common Pitfalls:
Confusing special gap or faceplate areas with general swing; mixing “between centres” capacity with swing.

Final Answer:
Yes