# Problem understanding number of degrees of freedom

Hi,

I do a classical mechanics course, and part of it relates to degrees of freedom.

For a system M of point masses with j constraints, there is N=3M-j DoF

For a rigid body, I know there is 6 DoF (3 translational, 3 rotational).

However, I've tried using drawing the constraints on a 4 point mass system to make it a rigid system. I've done this with 5 constraints (3 rigid rods in blue and 2 fixed angles in green). With 5 constraints the formula gives N=(3x4)-5=7 DoF.

Could someone explain this please?

[PLAIN]http://img152.imageshack.us/img152/7426/degreesoffreedom.png [Broken]

It'd be greatly appreciated. Thanks

EDIT: I think I understand this now, because it's a rigid body, you can work out all other positions in the system itself from the 5 given constraints. All that you can't work out, is the rotational and translational DoF of the system as a whole.

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## Answers and Replies

The figure you have drawn does have 7 degrees of freedom. The "constraints" (rods) that you've placed between the points do not fully constrain the object in 3 dimensions---you can twist the vertical and horizontal bars around the diagonal bar (if that makes sense).

In other words, there are 3x translation, 3x rotation, and also an undefined angle between one of the green angles and the plane of the other. To fully constrain the arrangement of your figure, you would have to add another fixed angle, or fixed distance.