# Conn-Rod Mechanism

## The connecting rod mechanism

A connecting rod - conn-rod - mechanism converts rotating motion to reciprocating motion - or vice versa.

The position of the rod can be expressed as

*s = r (1 - cos φ) + (λ / 2) r sin ^{2}φ (1)*

*where *

*s = position of the rod (m)*

*r = radius of crank (m)*

*φ = ω t *

* = 2 π n _{s} t *

* = angular position of crank (rad)*

*ω* = crank *angular velocity (rad/s)*

*t = time (s)*

*n _{s} = revolution per second (1/s)*

*λ = r / l *

* = crank ratio*

*l = length of rod (m)*

The velocity of the rod can be expressed as

* v = ω r sin φ (1 + λ cos φ) (2)*

*where *

*v = velocity of rod (m/s)*

The acceleration of the rod can be expressed as

* a = ω ^{2} r (cos φ + λ cos 2φ) (3)*

*where *

*a = acceleration of rod (m/s ^{2}^{})*