Kutzbach Criterion 493z2c

1.1 Degrees of Freedom of a Rigid Body in a Plane. 

The degrees of freedom (DOF) of a rigid body is defined as the number of independent movements it has. Figure shows a rigid body in a plane.

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In a two dimensional plane has 3 DOF.

1.2. Degrees of Freedom of a Rigid Body in Space 

An unrestrained rigid body in space has six degrees of freedom:

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Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system.

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The kinematic pairs are divided into lower pairs and higher pairs, depending on how the two bodies are in .

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There are two kinds of lower pairs mechanisms: revolute pairs and prismatic pairs.

Fig of Revolute pair

in

planar

Fig of prismatic pair 

In this two pair two degree of freedom is arrested.

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If a pair in motion has a line or point between 2 elements. Eg. Belt, rope, chain drives etc

Fig of higher pair

The equation used in kutzbach criterion is n = 3(l-1) – 2j – h Where n = number of dof l = number of links j = number of ts h = number of higher pair 

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The equation used in this is n = 6 ( l - 1 ) – 5p 1 - 4p 2 - 3p 3 – 2p4 - p5 Where n = number of dof p1 = number of pairs having one dof p2 = number of pairs having two dof p3 = number of pairs having three dof p4 = number of pairs having four dof p5 = number of pairs having five dof