By Robert J. Nikolai

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**Additional info for Bioengineering Analysis of Orthodontic Mechanics**

**Example text**

Moving the line of action of a force 0 through introduction of a couple C. The reverse of the process illustrated in Figure 2-16. 46 Bioengineering Analysis of Orthodontic Mechanics into which permanent bends or twists have been placed. The dimension of the couple magnitude is the product of force and length. The couple tends to cause only rotation of the body on which it acts. In addition to its importance as a displacement-producing system, the couple is useful in analysis because it alone enables the transfer of a concentrated force, exerted on a rigid body, from its given location to a parallel, alternative line of action associated with the same rigid body.

An accurate set of calculations cannot make up for inaccuracies in initial data. Hand-held, electronic calculators and digital computers will yield numerical solutions to six or more figures, but no more digits should appear in the answer than can be justified. The evaluation of the accuracy of mathematical procedures is a complex matter and will not be investigated here. It is perhaps sufficient to indicate that most input data in orthodontic bioengineering problems are accurate to no more than three significant figures and, therefore, no more than three significant figures should be recorded in the solutions obtained.

A concentrated torce and moment vectors with respect to lines (axes) through point 0. 38 Bioengineering Analysis of Orthodontic Mechanics potential of the force to produce rotation about a particular line through the point may be obtained. The rotational potential with respect to a line, a moment axis, has the greater application in orthodontic mechanics. In Figure 2-9, the moment of F about point 0 is also the moment of the given force with respect to the line Z-Z. To obtain the moment about another line through point 0, line L-L in Figure 2-9 for example, the magnitude of the moment about line Z-Z is multiplied by the cosine of the angle between L-L and Z-Z.