The links are joined as shown in the figure. Which type of chain

SOLUTION

Concept:

Kinematic chain:

When the kinematic pairs are coupled in such a way that the last link is joined to the first link to transmit definite motion (i.e. completely or successfully constrained motion), it is called a kinematic chain.

A relationship between the number of links (l) and the number of joints (j) which constitute a kinematic chain:

\(j = \frac{3}{2}l - 2\)

• L.H.S. > R.H.S: Locked chain (no relative motion is possible)
• L.H.S. = R.H.S: Constrained kinematic chain/ kinematic chain (the relative motion is completely constrained)
• L.H.S. < R.H.S: Unconstrained chain (the relative motion is not completely constrained)

Calculation:

Given:

l = 3, j = 3

RHS = \(\frac{3}{2}l - 2 \Rightarrow \left(\frac{3}{2}\times3\right)\;-\;2=2.5\)

LHS = 3

∴ LHS > RHS i.e. the chain is locked.

 

When one of the links of a kinematic chain is fixed, the chain is known as a mechanism.