Analytical method [Appropriate] for velocity and acceleration of the piston.

Let,

$L =$ Length of connecting rod between the centre’s.

$R =$ Rides of crank.

$\phi$ = Inclination of connecting rod to the line of stroke PO

$N =$ Ratio of length of connecting rod to the radius of crank = $\frac{L}{r}$

[1] Velocity of the piston,

$Vp_o = VP = w.r. [sin \ \theta \ + \frac{sin \ 2 \theta}{2n}]$

$w=$ Angular speed of crank.

$r=$ Radius of crank

[2] Acceleration of the piston,

$a_p = w^2. r[cos \ \theta \ +\frac{cos \ 2\theta}{n}]$

[3] Angular velocity of the connecting rod,

$\omega_{pc} = \frac{\omega. cos \ \theta}{n}$

[4] Angular acceleration of the connecting rod,

$\alpha_{pc} = \frac{\omega^2. Sin \ \theta}{n}$