# Kinematic Chain

A kinematic chain is an assembly of links connected by joints, which allow relative motion between them. In other words, if few links are connected, and there is a relative motion, it’s considered a Kinematic Chain.

The kinematic chain mechanism is used to transform motion. And it consists assembly of links connected by movable joints, to form a closed kinematic chain by considering one link as the reference.

## Types of Loops

By considering how the links are connected, there are two kinds of loops in kinematic chains.

Closed-loop

When every element in a chain is connected with two other elements, it’s known as a closed-loop.

Open-loop

When every element in a chain is not connected to two other elements, it’s known as an open-loop.

## Simplest Kinematic Chain

The simplest kinematic chain we have is the four-bar mechanism. Because in the three-bar mechanism, there is no relative motion between the links. So, the three-bar mechanism is known as a locked chain.

## Kinematic Chain and Crankshaft

A Crankshaft

When the crankshaft is connected with the bearing, it’s a kinematic pair. And there are some other kinematic pairs. So, the connecting rod and the crankshaft forms the second kinematic pair. Then the piston with the connecting rod forms the third kinematic pair. Then, the third kinematic pair and the piston form the fourth kinematic pair. And, all the four pairs in the mechanism are the kinematic chain.

## Types of Chain Mechanisms

### Locked chain mechanism

A chain mechanism that cannot have a relative motion between links is known as a locked mechanism. In other words, a locked chain mechanism is a type of chain mechanism which doesn’t have a relative motion between links.

When one link is fixed, a kinematic mechanism can have a relative motion. But, link mechanisms like the 3 bar mechanism are fixed, and there is no relative motion between links.

### Kinematic chain of one degree of freedom

A kinematic chain of one degree of freedom is a chain in which a single link is sufficient to specify the position of all other links.

### Constrained kinematic chain

If all links move only in prescribed paths, such a chain mechanism is known as a constrained kinematic chain mechanism.

### Unconstrained chain

An unconstrained chain is a chain in which the relative motion is not completely constrained.

### Compound kinematic chain

A compound kinematic chain refers to a chain with more than four links.

## Types of Kinematic Closed Chains

By considering the type of loops, the kinematic chain is divided into few groups. When a chain contains only binary links, it’s known as a simple closed chain. However, if the chain has more than just binary links, it’s known as a compound closes chain.

## Relationship for Kinematic Chain Having Lower Pairs Only

L = 2P – 4

J = 3L/2 – 2

L is the number of binary links, and P is the number of lower pairs. J is the number of binary joints.

## Relationship for Kinematic Chain Having Higher Pairs

J + H/2 = (3/2)L – 2

H is the number of higher pairs.

We say that one link is fixed in a kinematic chain mechanism. What does that mean? Even we call it a fixed link, it doesn’t have to be fixed. Because it’s the reference link in the mechanism. And all motion of other links is measured related to the fixed link.

However, in a practical machine, this fixed link is usually a stationary platform or base of the machine.

## Multiple-loop Kinematic Chain

A mechanism can, of course, be composed of a multiple-loop kinematic chain. In such a case, more than one loop-closure equation is required to completely model the mechanism. The procedures for obtaining the loop-closure equations, however, are identical to those shown in the previous two examples.

If a kinematic chain consists of more than one loop, it’s called a multiple loop kinematic chain. So, we need a different approach, since one loop-closure equation is not enough. Therefore, we need more than one loop-closure equations.