In the Whitworth quick-return motion mechanism (an inversion of the slider–crank), the kinematic composition consists of three turning (revolute) pairs and one sliding pair—state whether this statement is correct for the standard crank-and-slotted-lever form.

Introduction / Context

The Whitworth quick-return mechanism achieves unequal cutting and return times by converting uniform crank rotation into non-uniform lever oscillation. Recognizing its joint types helps in DOF (degree of freedom) accounting, wear analysis, and synthesis.

Given Data / Assumptions

• Standard crank-and-slotted-lever Whitworth mechanism.
• Ideal pin joints (revolute) and a block sliding in a slot.
• Planar kinematics.

Concept / Approach

The Whitworth mechanism is an inversion of the slider–crank chain in which a slotted lever oscillates about a fixed pivot. A crank drives a block (slider) that moves inside the slot. The joints are: (i) crank to frame (turning pair), (ii) crank pin to block (turning pair), (iii) block in slot (sliding pair), and (iv) lever to frame (turning pair). Hence 3 revolute + 1 prismatic (sliding).

Step-by-Step Solution

Verification / Alternative check

Gruebler’s criterion with one DOF confirms consistent mobility for a four-link, four-joint (three R, one P) planar mechanism.

Why Other Options Are Wrong

• Wrong: contradicts the standard geometry and joint inventory.
• Only true for special geometries: joint types do not change with geometry; only proportions change the quick-return ratio.
• True only at one extreme position: joint classification is not configuration-dependent.
• Indeterminate: the classic form is well-defined.

Common Pitfalls

• Confusing the Whitworth with the slotted-disk or drag-link quick-return variants; the joint count here is specific to the crank-and-slotted-lever mechanism.

Final Answer

Right