Question

In a mechanism as shown in Fig. 8.40, the crank

OA is 100 mm long and rotates in a clockwise

direction at a speed of 100 r.p.m. The straight

rod BCD rocks on a fixed point at C. The links

BC and CD are each 200 mm long and the link

AB is 300 mm long. The slider E, which is

driven by the rod DE is 250 mm long. Find the

velocity and acceleration of E.

[ Ans. 1.26 m/s; 10.5 m/s2]

Answer 1

Find the velocity and acceleration of E.

Configuration Diagram :

OA = 0.1 m

AB = 0.3 m

BC = 0.2 m

CD= 0.2 m

DE = 0.25 m

\(V_{O A}=r w=\frac{0.1 \times 2 \pi \times 100}{60}\)

\(V_{O A}=1.05 \mathrm{~m} / \mathrm{s}\)

Velocity diagram :

\(V_{A}=1.05 \mathrm{~m} / \mathrm{s}\)

\(V_{B C}=1.26 \mathrm{~m} / \mathrm{s}\)

\(V_{A B}=1.41 \mathrm{~m} / \mathrm{s}\)

\(V_{C D}=1.26 \mathrm{~m} / \mathrm{s}\)

\(V_{D E}=0.34 \mathrm{~m} / \mathrm{s}\)

\(V_{D E}=1.29 \mathrm{~m} / \mathrm{s}\) Velocity of slider \(\mathrm{E}\)

Acceleration diagram :

Link	Length	$a_c$
OA	0.1	11.25	0
AB	0.3	6.67	?
BC	0.2	79	?
DE	0.25	0.46	?

\(a_{a o}=11.25 \mathrm{~m} / \mathrm{s}^{2}\)

\(a_{a b}=6.75 \mathrm{~m} / \mathrm{s}^{2}\)

\(a_{b c}=a_{c d}=10.26 \mathrm{~m} / \mathrm{s}^{2}\)

\(a_{d c}=9 \mathrm{~m} / \mathrm{s}^{2}\)

\(a_{e o}=5.63 \mathrm{~m} / \mathrm{s}^{2}\) Acceleration of slider \(\mathrm{E}\)