A generic answer as to what is degree of freedom is the minimum number of independent variables required to completely describe a body.

When it comes to mechanism, generally, we are always referring to a rigid body, unless you mean a compliant mechanism.

For a rigid body, it would mean the number of independent co ordinates needed to define the position of the body.

In a planar mechanism, a body (typically a link) can translate along x axis, or y axis or it can rotate about the z axis, in xy plane. Hence to completely define the position of the link, we need to specify the x co ordinate, the y co ordinate and the magnitude by which the link is inclined to either x or y axis. Hence we have three independent variables, hence 3 dof.

In a spatial mechanism, we would have 6 dof, translation along the three axes and the rotation about them.

So much about the degrees of freedom of an independent body.

Now, when it comes to a mechanism, there are more than one bodies, and they are no longer independent, since they are joined to each other in a particular fashion. This is called a constrained body, since it will no longer have as many degrees of freedom as an independent body, and is hence constrained.

The constrained are physically applied by connecting two bodies to each other through what is called a joint. Thus a joint allows certain degrees of freedom between the links, and constraints some of them. This results in formation of what is called as a kinematic pair.

The kinematic pair may allow only one degree of freedom, called a lower pair, or may allow more degrees of freedom, called a higher pair.

example of lower pairs are pin joint, which allow only planar rotation, or slider joint which allows only translation in one direction.

The degree of freedom of a mechanism is the total number of independent variables required to define completely the particular mechanism. This can be found very easily using the Grublers equation...

A generic answer as to what is degree of freedom is the minimum number of independent variables required to completely describe a body.

When it comes to mechanism, generally, we are always referring to a rigid body, unless you mean a compliant mechanism.

For a rigid body, it would mean the number of independent co ordinates needed to define the position of the body.

In a planar mechanism, a body (typically a link) can translate along x axis, or y axis or it can rotate about the z axis, in xy plane. Hence to completely define the position of the link, we need to specify the x co ordinate, the y co ordinate and the magnitude by which the link is inclined to either x or y axis. Hence we have three independent variables, hence 3 dof.

In a spatial mechanism, we would have 6 dof, translation along the three axes and the rotation about them.

So much about the degrees of freedom of an independent body.

Now, when it comes to a mechanism, there are more than one bodies, and they are no longer independent, since they are joined to each other in a particular fashion. This is called a constrained body, since it will no longer have as many degrees of freedom as an independent body, and is hence constrained.

The constrained are physically applied by connecting two bodies to each other through what is called a joint. Thus a joint allows certain degrees of freedom between the links, and constraints some of them. This results in formation of what is called as a kinematic pair.

The kinematic pair may allow only one degree of freedom, called a lower pair, or may allow more degrees of freedom, called a higher pair.

example of lower pairs are pin joint, which allow only planar rotation, or slider joint which allows only translation in one direction.

The degree of freedom of a mechanism is the total number of independent variables required to define completely the particular mechanism. This can be found very easily using the Grublers equation...

Hi, a question often asked by my students. Get a copy of Dynamics by Meriam and make sure you look a standard Euclidian Geometry and Euler's angles so you get the orientation right, it is the +ve directions that confuse people the most.

Hello Vishal,

you already have a very good answer at the top. Maybe a quick short one. The degree of freedom describes in what way a body/ system can move in space. So, we have a threedimensional space, i.e. there are maximum 6 degrees of freedom for an ordinary body - 2 per axis (x,y,z). You can move along each axis and you can rotate around them. If you have a system that is only able to move along one axis (e.g. along a rail) it has only one degree of freedom and so on.

thanks to everyone.PETER, can you provide me concerned link you said above?

the book is a series of two one called statics, the other called dynamics. both are authored, originally, by Meriam. if you do a search using dynamics meriam in amazon, google etc it will cone up as it is a core text for most universities.

Thanks mr. Peter

For example, a rotating crankshaft provides a pivot connection: thus a degree of freedom which is rotation about an axis

It should be said that a particle has 3 DoFs in space and a RIGID body has 6 DoFs in space. It should also be understood that an elastic body (which consists of an infinite number of particles) has an infinite numebr of DoFs. Because the above difference, the type of equations governing the motion of particles/rigid bodies is different from that of elastic bodies.

Dear Vishal

The degree of mobility M is the number of independent motions of a mechanism. The most simple example is the four bar linkage (four bar mechanism).

This mechanism has (taking into account the ground as a fixed base of the mechanism) has four bars (links) which are connected using four revolute joints. Such a mechanism has only one degree of freedom. You can see the following video published by "lonboy99":

http://www.youtube.com/watch?v=c_PnjGARuNU

We have also the example of crankshaft mechanism which has also one degree of freedom.

For the Pendulum having two bars (links) for example, such a mechanism has two degrees of freedom, which are the independent angular variables (independent angular motions); we have one for each link.

Another example: the aircraft flying, which has six degrees of freedom.

Best regards,

Khaled-Assad ARROUK

no. of variables required to define the mechanism.

to estimate the position of a mechanism, you need these many variables. The no. of variables that are required are called degree of freedom

The number of variables required define the motion of a body is called degree of freedom. For example consider a body in space, it has rotary and translation in x-direction, similarly y-direction, similarly in z-direction. so any body in space has maximum of 6 degree of freedom. when comes to pairs it varies with relative motions. finally one can say that degrees of freedom of a body varies from 0 to 6.

For planar motion it is the number variables required to define the position of link.

in that time we are solving problems expolation core barber  hyper particles by planar motation

The number of variables required define the motion of a body is called degree of freedom. For example consider a body in space, it has rotary and translation in x-direction, similarly y-direction, similarly in z-direction. so any body in space has maximum of 6 degree of freedom. when comes to pairs it varies with relative motions. finally one can say that degrees of freedom of a body varies from 0 to 6.

Can someone explain to me the degree of freedom very clearly with examples in relation to the theory of machines?. Available from: https://www.researchgate.net/post/Can_someone_explain_to_me_the_degree_of_freedom_very_clearly_with_examples_in_relation_to_the_theory_of_machines [accessed May 1, 2017].