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• # DoF (Degrees of Freedom)

Discussion in 'The main mechanical design forum' started by desai95, Mar 7, 2014.

1. ### desai95Member

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Can anyone help me out with clear concept of degree of freedom? What happens if my degree of freedom is more of some mechanism? Is it that for better working degree of freedom should be kept as low as possibe?please amigos help me out clear my concepts

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3. ### PierArgWell-Known Member

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Hi desai95.

The "degrees of freedom" for a rigid body means how it can move in the space or in a fixed plane.

A rigid body in a space has 6 DOF because you can identify its position by 6 independent movements:
1) translation along X axis
2) translation along Y axis
3) translation along Z axis
4) rotation along X axis
5) rotation along Y axis
6) rotation along Z axis

If we consider a datum plane XY, the rigid body has only 3 DOF: you can identify its position only by 3 independent movements
1) translation along X axis
2) translation along Y axis
3) rotation along Z axis

This is just the DOF concept and everithing's ok so far.
But, how to calculate the DOF in a mechanism?
There is a simple equation called Gruber's formula.
Assuming the mechanism in the plane, therefore 3 DOF , the formula is:

Ndof = 3(n-1) - 2L - H

Ndof = total DOFs in the mechanism
3 = we are assuming the plane, so every free and NOT constrained rigid body/link has 3 DOF
n = number of links including the frame
L = number of lower pairs (joints that allow only 1 DOF to the mechanism)
H = number of higher pairs (joints that allow 2 DOF to the mechanism)

Next question is: "How many DOF must have a rigid body, a mechanism or a structure?"
It depends on the mechanism or structure's role because each application must have the exact number of DOF
Generally a static structure which role is to sustain (for example the supporting structure of a building) must be isostatic that means 0 DOF.
Contrariwise, a mechanism wich role is to transfer the mechanical energy through the movement, must have the right DOF nmumber.
Exceeding or restricting the DOF number is not good.
For example a high speed rotating shaft; what if it had more than 1 DOF?
Exceeding the DOF number leads to vibrations and shocks

Otherwise restricting the DOF number leads to overstressing.
Imagine if the Tour Eiffel was iperstatic (negative DOF): just the temperature variation should be enough to bring to a disastrous failure due to thermal stresses.
When the iron is heated or cooled it tends to strain itself.
But the Tour Eiffel is isostatic and can "breathe".

I hope I was clear.

Last edited: Mar 7, 2014
4. ### desai95Member

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Feb 2014
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Dof

Hey pierarg u wer not just clear but perfect keep it up and thanks and yeah u ve cleared all my doubts thanks a lot bro

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