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