Question

Number of links (I) and the number of joints (J) for a single degree of freedom kinematic chain, with only lower pair joints, is related by the expression:
1. J = 2.5l  - 2
2. J = 2.5l - 1
3. J = 1.5l  - 2
4. J = 1.5l - 1

Answer 1

Correct Answer - Option 3 : J = 1.5l  - 2

Explanation:

Kinematic chain

•  A kinematic chain is a combination of kinematic pairs joined in such a way that each kinematic link forms two kinematic pairs having completely or successfully constrained motion between them.
• A kinematic chain has no fixed link.

The relation between the number of link and number of kinematic pair is given by,

 l = 2p - 4

where, l = number of links, p = number of kinematic pair.

For a simple mechanism, the degree of freedom (F) is given by the Grubler’s criterion:

F = 3 (l - 1) - 2J - h

Where J = number of revolute joints, l = number of links, h = number of higher pairs

here, F = 1, h = 0

1 = 3(l - 1) - 2J

∴ J = 1.5l  - 2