|Established in 1952
Monday, December 9, 2013
Conventional wisdom says that there are six degrees of freedom. This would be true if the constrained body was rigid, but there is no such thing as a rigid body, so the fact of the matter is, there are actually seven degrees of freedom not six. The inevitable flexibility of all structures is the seventh degree of freedom.
When you have accepted this reality, it will open up entirely
new vistas of design opportunities.
This new reality puts the very concepts of constraint, but especially of over constraint, in a new perspective. With the acceptance of elasticity as the seventh degree of freedom, you can now use self aligning contact to elastically position the complaint body to the most desirable position and then lock it there.
If we even concede the relevance, of elasticity as a major player in kinematic arena, it opens the Pandora’s Box of constraint.
If elasticity is the seventh degree of freedom, how will it manifest itself? Obviously it will be in a direction that is opposite i.e. at 180° to the force that generates the defection!
Elasticity isn’t really the seventh degree, the deflection caused by an applied force accounts for that degree of freedom.
Here is where the real fun begins.
If there are two vector forces instead of one, are there then eight degrees of freedom, or is there a single deflection that is the resultant of the multitude of forces? From a functional standpoint this is obviously the case.
With all of this perversion of the six degrees of freedom and the rigid body concept that we all know now really doesn’t ever exist, where are we on constraint?
When does over constraint occur?
As an example of this constraint dilemma, let’s look at a long cylindrical bar. If we support it at four tangent points that have an included angle of ninety degrees, the cylinder can only roll and translate along around the X axis. When held horizontally, there will be various patterns of sag (elastic deformation) due to the force of gravity.
The pattern of these sags will be determined by the longitudinal position of the four points of contact with the long cylindrical bar.
If we place the four points near the ends of the cylinder, there will be a gradual bow down toward the center of the earth.
Now comes the question of constraint, or rather over constraint. If we support the center of the long cylindrical bar with another cylinder, placed at right angles to the long cylinder, is this over constraint?
If we describe elasticity as a seventh degree of freedom, this would obviously not be over constraint.
The long cylindrical bar will obviously be elastic in all three hundred and sixty degrees, around its longitudinal axis! If we supported the center of the bowed cylinder by two 90° points of contact, would this be over-constraint? I contend that it would not be, due to the nature of the 360° elasticity of the long cylindrical bar.
If we are working with a very long cylinder such as a scale bar, where there would be multiple bows between supports, would a multitude of two point supports be over constraint? I would contend again that it would not be over- constraint.
If we try to go back to the good old six degrees of freedom with “rigid bodies” it wouldn’t be what we now know to be the real bubblegum world.