Mobility of Mechanisms

Independent object

Has degrees of freedom.

Lower Pair

Aka. primary pair. A pair of kinematic elements which share a surface of contact.

When a rigid body is constrained by a lower pair, which allows only rotational or sliding movement. It has degree of freedom, and the degrees of freedom are lost.

Some examples:

• Turning pair
• Sliding pair
• Helical thread

Higher Pair

A pair of kinematic elements which share only a line or a point of contact.

When a rigid body is constrained by a higher pair, it has degrees of freedom: translating along the curved surface and turning about the instantaneous contact point.

Gear is an example.

When 2 independent objects are brought together to create a link, some degree of freedom will be lost.

“You lose some freedom when you become a couple.” — Our Dynamics Lecturer

Grubler’s Equation

Suppose kinematic elements are brought together. of them is fixed. The remaining elements have degrees of freedom. Each lower pairs loses degrees of freedom. Each higher pairs loses degree of freedom. For a workable mechanism, resultant degrees of freedom must be .

Here:

• - degree of freedoms
• - number of kinematic elements
• - number of lower pairs
• - number of higher pairs