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UoM E S1

Mobility of Mechanisms

Lower 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 one degree of freedom, and the two degrees of freedom are lost.

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 two degrees of freedom: translating along the curved surface and turning about the instantaneous contact point.

Grubler’s Equation

Suppose kinematic elements are brought together. of them is fixed. The remaining elements have degrees of freedom. But each lower pairs loses degrees of freedom. Each higher pairs loses degree of freedom.

Here:

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