Consider the motion of a connecting rod and a crank as shown in Fig. 15.7.From the geometry of the figure, we find that

Fig. 15.7. Motion of a crank and connecting rod of a reciprocating steam engine.

Let l = Length of connecting rod between the centres,

r = Radius of crank or crank pin circle,

φ = Inclination of connecting rod to the line of stroke PO, and

n = Ratio of length of connecting rod to the radius of crank = l/r.

**ANGULAR VELOCITY AND ACCELERATION OF THE CONNECTING ROD**

Consider
the motion of a connecting rod and a crank as shown in Fig. 15.7.From the
geometry of the figure, we find that

*CQ *=* l *sin* *φ* *=* r *sin* *θ

The
negative sign shows that the sense of the acceleration of the connecting rod is
such that it tends to reduce the angle φ..

*Q.In a slider crank mechanism, the length of the crank and connecting rod are 150 mm and 600 mm respectively. The crank position is 60° from inner dead centre. The crank shaft speed is 450 r.p.m. *(*clockwise*).* Using analytical method, determine: 1. Velocity and acceleration of the slider, and 2. Angular velocity and angular acceleration of the connecting rod.*

**Solution. **Given :** ***r*** **= 150 mm = 0.15 m ;** ***l*** **= 600 mm = 0.6 m ;** **θ** **= 60°;** ***N*** **= 400 r.p.m or** **ω = π × 450/60 = 47.13 rad/s

**1. Velocity and acceleration of the slider**

We know that ratio of the length of connecting rod and crank,

*n* = *l */* r *= 0.6 / 0.15 = 4

**APPROXIMATE** **ANALYTICAL** **METHOD** **FOR** **VELOCITY AND ****ACCELERATION OF THE PISTON**

Fig. 15.7. Motion of a crank and connecting rod of a reciprocating steam engine.

Let l = Length of connecting rod between the centres,

r = Radius of crank or crank pin circle,

φ = Inclination of connecting rod to the line of stroke PO, and

n = Ratio of length of connecting rod to the radius of crank = l/r.

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