# Degrees of freedom and rotation

1. Oct 10, 2008

Can anyone explain to me why does a figure which can't move from a plain has three degrees of freedom?

2. Oct 10, 2008

### Helios

If you think it has two degrees of freedom, you may be forgetting rotation.

3. Oct 10, 2008

thank you

4. Oct 10, 2008

### HallsofIvy

A rigid figure in the plane has three degrees of freedom. Choose any two points on the figure. If you know the position of one point, and the angle the line between the two points makes with some "reference" (say, the x-axis) then you can calculate the postion of any point on the figure. The position of one point on a two dimensional surface is given by two numbers (that's basically what "two dimensional" means) and the angle is the third number: 3 numbers to determine the position of every point= 3 "degrees of freedom".

5. Oct 11, 2008

### schroder

A great deal depends upon the type of figure. If it is a sphere which is constrained by having to maintain one contact point with a plane, it will have five degres of freedom. Two of these are translational in the x and y directions, and three of these are rotational along x, y and z axis. If there are two spheres connected by a rod and it is maintaining two points of contact with a plane, then two degrees of freedom are lost, (one translational and one rotational) but four still remain. Now consider three spheres connected by three rods and maintaining three points of contact with a plane. This body will still have translational motion in two directions and rotational motion about one axis, so it still has three degrees of freedom and has lost three. In general, one degree of freedom is lost for each point of contact with the plane, excluding redundant contact points. The lesson here is to avoid redundant constraints when designing machinery as the required precision increases with the number of constraints. A three-legged chair is much easier to make even with a plane floor than a four-legged chair!

6. Oct 13, 2008

And why do the scissors on a plane have four degrees of freedom?

7. Oct 13, 2008

I guess because we can fix one part of the scissors - then the other would have 2 degrees of freedom, and if we fix the other - the first one would have 2 degrees of freedom as well. 2+2=4 degrees of freedom ;)

8. Oct 13, 2008