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Preface

Anatomical Movements

This book presents a mathematical approach to the description of

anatomical movements. The methods described can be applied to anyrotational movement, but they work particularly well with anatomicalmovements because anatomical movements are purposeful, generallymulti-jointed, rotations in three-dimensional space, which arecontrolled by the nervous system to achieve a particular goal. Theirpurpose usually requires that they not only bring a part of the bodyinto a particular location in space, but that it is properly oriented.Orientation is a very important component of anatomical movements.

Anatomical movements are generally rotations that occur in joints,where one bone moves upon another about an ais of rotation. !any

anatomical movements are concatenations of several rotations,occurring in multiple joints, where the orientation of each joint iscontingent upon movements in other joints. This type of organi"ationleads to a comple interplay between several rotations.

#ecause movements generally occur in three dimensions, they arenonlinear in the sense that the order of rotation is critical to theoutcome. $leion followed by lateral rotation leads to a di%erentoutcome than lateral rotation followed by &eion. 'n mathematicalterms rotations are non-commutative.

A consequence of all of these features of anatomical rotations isthat they rapidly become very comple to describe and consequentlydi(cult to plan or control and yet the central nervous system does sowith remarkable elegance. )hat we discover about the nature ofanatomical movements must ultimately tell us something about thenature of neural control.

Description of Anatomical Movements

The description of anatomical movement is often di(cult. The mostcommon method, in terms of cardinal planes, works reasonably well aslong as one is starting from the anatomical position and moving in acardinal plane. Otherwise it becomes both cumbersome andambiguous. The nomenclature of that approach has essentially nopredictive power and it ignores orientation or con&ates it with positionor location. The nomenclature also assumes many, generally unstated,rules. $or instance, which direction is left side-&eion of a vertebra* 'sit the superior or inferior surface that is moving left* 's it theobserver+s left or the skeleton+s left* )ould it still be left side&eion if

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the ais of rotation passes through the superior margin of the vertebralbody* )hat if the ais of rotation is tilted relative to the cardinal aesof the vertebra* There are conventions for all these points, but theyare usually unstated.

The system of description introduced here is precise and concise,intuitive, and adaptable to the level of one+s knowledge about themovement. The logic of rotations in three-dimensional space isembedded in the notation and it allows one to pass directly from theanatomical description to computation of the consequences of theanatomy for its movements. There are no cardinal planes in the usualsense of the term, but the concept is embedded in the description of astructure+s anatomy and its movements in terms of a universalcoordinate system that is automatically dened as part of theanatomical description. The approach deals as easily with oblique andcurvilinear movements as with movement in a cardinal plane.

The approach developed here grows out of the concepts developedby !aconaill !aconaill /0123 !aconaill /0114 and populari"ed by!aconaill and #asmajian !aconaill and #asmajian /0554. 't alsodraws upon the approach of 6apandji 6apandji /0524. A modernsummary of these concepts may be found in 7ray+s Anatomy8tandring 9::;4. uaternions are a form of hypercomple number, with fourcomponents, that were discovered by 8ir )illiam ?owan

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The rst step is dening orientation in a way that allows one tocompute with it. That is accomplished here by creating a set ofmutually orthogonal unit vectors that point in anatomically signicantdirections. 8uch a set of vectors is called a frame of reference, oroften, just a frame. A frame of reference is a component of a framed

vector.

8ince a frame of reference is a set of vectors, it may be transformedby quaternion multiplication in a manner that precisely models thetransformation of a structure+s orientation by a rotation. onsequently,we not only model orientation, but also its behavior duringmovements.

Summary

The approach described here is simple in the sense that there are afew basic concepts that are applied in a consistent fashion.

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!aconaill, !. A. /0124. IBoint movements.IChysiotherapyFovember4= ;0-15.

!aconaill, !. A. /0114. IThe geometry and algebra of articularkinematics.I #io-!ed Eng 1= 9:;-9/9.

!aconaill, !. A. and B. J. #asmajian /0554. !uscles and !ovements.A basis for human kinesiology. Few Gork, 6rieger.

8tandring, 8. 9::;4. 7rayKs Anatomy. The Anatomical #asis of linicalCractice. Edinburgh, Elsevier hurchill Hivingstone.

8tewart, '. 9::54. )hy #eauty is Truth. A