The Degrees of Freedom and Constraints [School]

One of the first concepts we address in the geometry classes is to restrictions and degrees of freedom of a geometric figure. It allows us to quantify the complexity of it and the possible way for determining geometric problems.

My students have internalized this concept and in their blogs is a recurring theme.

Number degree of freedom engineering refers to the minimum number of parameters that need to specify to completely determine the speed of a mechanism or a number of reactions structure.(W)

I leave this analysis HAFF group in their own words that we approach these high interest training concepts

por HAFF

Another important thing to note is the difference between degree of freedom and geometric constraints. The degrees of freedom give us information about FREEDOM with which we can construct a figure based on the number of these; in return, restrictions indicate what are the characteristics of our figure to build non-free. For example, a parallel or as an edge or an angle. Both are related through a simple formula:

P=N-R

where P (Number of parameters needed to construct the figure), N (Number of degrees of freedom that overall figure) and R (Number of constraints that apply to construction).

The way of finding the number of degrees of freedom is a very simple. The total number is the number of vertices by the degrees of freedom of a vertex. In this case, in plane, Each vertex has 2 degree of freedom (coordinate orderly), space 3 (height, depth) and successively for each added dimension of space, one degree of freedom more.

Finally, an example to help illustrate the explanation.

A generic square in the plane (is given by known figure, I hope ...) comprises 4 vertices, belongs to the family of so it would cuadrivértices total 8 degree of freedom. Now, the word "square", per se, is what gives us the various constraints.

• Form: 4 restrictions (or 0 degree of freedom). There are sound: one side and perpendicular to two other parallel to a third and further that any two sides are equal.
• Size: 0 restrictions (1 degree of freedom), the length of the edge is free (unless it is defined in the problem).
• Position: 0 restrictions (2 degree of freedom), the position of a point is to free choice of the person who draws.
• Orientation: 0 restrictions (1 degree of freedom), a side angle relative to an axis orientation mark of the figure and gives freedom.

Summarizing, cuadrivértice possessed the generically 8 degree of freedom. Al definirlo as the square of a total of 4 restrictions (the form) freeing 4 degree of freedom. Otherwise non-generic, These degrees of freedom would be defined in any way increasing the number of restrictions to it.

This work has been performed by the students of the Aeronautical EUIT Polytechnic University of Madrid within the framework of educational innovation projects Educational Blogs e Experimentales INNOVABLOG

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POSITIONING MAP TWO DEGREES OF FREEDOM WITH STATIC AND CONFINED ACTUATORS