Subject: Kinematics of Machinery

Topic: Kinetics of Rigid Bodies

Difficulty: High

The no. of instantaneous centers in a constrained kinematic chain is equal to the no. of possible combinations two links. The no. of pairs of links or the no. of instantaneous centers is the no. combination of n links taken two at a time. Mathematically, no. of instantaneous centers,

$\quad\quad\quad\quad\quad\quad\quad$ $N=\frac{n(n-1)}{2}$

Where n = number of links.

Types of Instantaneous Centres:

The instantaneous centers for a mechanism are of the following three types:

1. Fixed Instantaneous Centres
2. Permanent Instantaneous Centres and
3. Neither fixed nor permanent Instantaneous Centres

The first two types i.e. fix and permanent instantaneous centers are together known as primary instantaneous centers and the third type is known as secondary instantaneous centers.

Consider four bar mechanism ABCD as shown in fig.2. The number of instantaneous centers (N) in a four bar mechanism is given by

$\quad\quad\quad\quad\quad\quad\quad$ $N=\frac{n(n-1)}{2}=\frac{4(4-1)}{2}=6$

The instantaneous centers $I_{12}$ and $I_{13}$ are called the fixed instantaneous centers as they remain in the same place for all configurations or the mechanism. The instantaneous centers $I_{23}$ and $I_{34}$ are the permanent instantaneous centers as they move when mechanism moves, but the joints are of permanent nature. The instantaneous centers $I_{13}$ and $I_{24}$ are neither fixed nor permanent instantaneous centers as they vary with the configuration of the mechanism.