How do you use the ICR method for a crank and connecting rod (two-link) mechanism?

In one line

Use the crank's known rotation to get the velocity of the crank pin, then locate the connecting rod's ICR from the crank-pin and slider velocity directions.

Explained simply

In a car engine or a hand pump, a rotating crank pushes a rod, which pushes a piston back and forth. Knowing how fast the crank turns, we want the piston speed at a given position. The ICR turns this into simple geometry.

Technically, the crank pin A has velocity \( v_A = \omega_{OA} \cdot OA \), perpendicular to OA. The slider B moves along its guide. The rod AB's ICR is where the line OA (extended) meets the perpendicular to the guide at B.

How it works

1. Draw the mechanism at the given crank angle; find all lengths and angles (sine rule).
2. \( v_A = \omega_{OA} \times OA \), perpendicular to OA.
3. Perpendicular to \( v_A \) is the line OA itself; extend it.
4. Perpendicular to \( v_B \) (along the guide) is a line at B normal to the guide.
5. Intersection = I. Measure IA and IB.
6. \( \omega_{AB} = v_A / IA \); \( v_B = \omega_{AB} \cdot IB \).
7. If the crank is perpendicular to the guide, the two perpendiculars are parallel, I is at infinity, \( \omega_{AB} = 0 \) and \( v_B = v_A \).

Key formula

\( v_A = \omega_{OA} \cdot OA \); \( \omega_{AB} = v_A/IA \); \( v_B = \omega_{AB} \cdot IB \). Lengths in m, \( \omega \) in rad/s.

Quick example

Crank OA = 0.2 m at 10 rad/s, rod AB = 0.6 m, crank at 45°. A is at (0.1414, 0.1414) m; B is at x = 0.1414 + \( \sqrt{0.36 - 0.02} \) = 0.7245 m. I lies on line OA at x = 0.7245, so I = (0.7245, 0.7245). IA = 0.8246 m, IB = 0.7245 m. \( v_A = 2 \) m/s, \( \omega_{AB} = 2/0.8246 = 2.43 \) rad/s, \( v_B = 2.43 \times 0.7245 = 1.76 \) m/s.

Common mistakes

• Drawing the perpendicular to \( v_A \) at A but not through O; for a crank it is the line OA itself.
• Using \( \omega \) of the crank for the rod; each link has its own \( \omega \).
• Forgetting the special 'ICR at infinity' case.

How MU asks it

6 to 8-mark numerical: 'In the mechanism shown, crank OA rotates at N rpm; find the angular velocity of AB and the velocity of slider B'. Convert rpm, draw the figure, locate I, show the sine-rule geometry and give results with directions. Mechanisms with more than 2 links are outside the syllabus.