In the Whitworth quick-return (crank-and-slotted lever) mechanism obtained as an inversion of the slider–crank chain, which link must be kept fixed to produce unequal cutting and return strokes characteristic of quick return?

Introduction / Context

Quick-return mechanisms allow the tool (or ram) to spend more time on the cutting stroke and less on the return stroke, improving productivity. The Whitworth mechanism is a classic inversion of the slider–crank chain using a crank and a slotted lever.

Given Data / Assumptions

• A slider–crank chain is the parent mechanism.
• We need the inversion that yields a crank driving a slotted lever about a fixed pivot.
• Goal: unequal forward and return stroke times.

Concept / Approach

In the Whitworth arrangement, the slotted lever oscillates about a fixed pivot on the frame, while a rotating crank drives a slider (block) that runs within the slot. This configuration is obtained by fixing the link opposite the slider, i.e., the frame that houses the lever pivot. The geometry causes non-uniform angular motion of the lever for uniform crank rotation, delivering the quick-return effect.

Step-by-Step Solution

Verification / Alternative check

Textbook kinematic inversions list the Whitworth mechanism as the inversion where the frame opposite the slider is the fixed link, creating a slotted lever pivot.

Why Other Options Are Wrong

• Coupler fixed: yields other inversions (e.g., oscillating cylinder) but not the Whitworth quick return.
• Slider fixed: produces different layouts (e.g., crank and guide) without the characteristic slotted lever geometry.
• Smallest link fixed or longest link fixed: size is not the defining criterion; the correct inversion is specific to which link is the frame opposite the slider.

Common Pitfalls

• Confusing the Whitworth inversion with the crank-and-rod quick return (drag link or slotted disc types).
• Thinking link length alone determines inversion; it is the fixed link choice that matters.

Final Answer

Frame opposite the slider is fixed