Jawaharlal Nehru Technological University Hyderabad B.Tech II KINEMATICS OF MACHINERY Previous Question Paper (October 2020 - R16)

When the crank of a single slider crank chain is fixed, the relative motion between the links changes, resulting in two primary inversions: the Whitworth quick return mechanism and the Rotary internal combustion engine (Gnome engine).

1. Whitworth Quick Return Mechanism: In this inversion, the crank is fixed. The connecting rod acts as a rotating link, which drives a slotted lever. This lever oscillates about a fixed pivot. Because the crank rotates at a constant speed, the time taken for the forward stroke is greater than the time taken for the return stroke, providing the quick return motion essential for shaping and slotting machines.

2. Rotary Internal Combustion Engine: In this inversion, the crank is fixed, and the cylinder block rotates about the crank center. The pistons reciprocate within the cylinders while the entire assembly revolves. This design was historically used in aircraft engines to achieve air cooling and a compact, balanced configuration.

Sketch Description: For the Whitworth mechanism, draw a fixed crank connected to a rotating link that drives a slotted lever pivoted at one end, with a slider moving within the slot to provide output motion. For the Rotary engine, draw a central fixed crank with multiple cylinders arranged radially around it, where the cylinders rotate as a unit around the fixed crank center.

In a Whitworth quick return motion mechanism, the ratio of the time of cutting stroke to the time of return stroke is determined by the angle of rotation of the crank. Let α be the angle of the crank during the cutting stroke and β be the angle during the return stroke.

Given: Crank length AC = 90 mm, distance between fixed centres CD = 60 mm. The angle α is given by cos(α/2) = CD / AC = 60 / 90 = 2/3. Thus, α/2 = 48.19°, which gives α = 96.38°.

The return stroke angle is β = 360° - 96.38° = 263.62°. The ratio of the time of cutting stroke to the time of return stroke is:

To find the length of the effective stroke, we determine the extreme positions of the slider R. The slotted lever AP = 180 mm. The extreme positions of the slider occur when the crank is perpendicular to the line of centres. The distance of the slider from the centre D at the extreme positions is determined by the geometry of the slotted lever and connecting rod. The stroke length is 2 × (distance of P from D) × (PR / AP). With the given dimensions, the stroke length is calculated as 2 × (AP × (AC / CD)) is not applicable here as the slider is driven by the slotted lever. The stroke length is 2 × (AP × (AC / CD)) is incorrect; the correct stroke is 2 × (AP × (AC / CD)) is not the formula. The stroke length is 2 × (AP × sin(θ)), where the effective radius of the path of P is R = AP × (AC / CD) = 180 × (90 / 60) = 270 mm. The stroke length is 2 × 270 = 540 mm.