The position, velocity, and acceleration of a connecting rod converting rotational to reciprocating motion are described by the following kinematic relationships:

Position of the Rod: $s = r (1 - \cos \phi) + \frac{\lambda}{2} r \sin^2 \phi$

Velocity of the Rod: $v = \omega r \sin \phi (1 + \lambda \cos \phi)$

Acceleration of the Rod: $a = \omega^2 r (\cos \phi + \lambda \cos 2\phi)$

where:

$\phi = \omega t = 2\pi n_s t$ is the crank angle (rad)
$\lambda = \frac{r}{l}$ is the crank ratio (dimensionless)

References

Original Source

Source: engineeringtoolbox.com