Jim Mcmahon

07-09-1996, 01:35 PM

Dear Colleagues,

I hope one, or several, of you can help me with a problem I've

encountered. I'm trying to estimate max. bite force using measurements on

a series of dry skulls; so I need to construct a biomechanical model of

mastication in order to determined what measurements are appropriate.

I've "dabbled" in biomechanics but have no formal training, and thus must

rely on the experts. I'm making the assumption that the jaw acts as a

Class III lever (an assumption made by many of the people who do this

kind of work). The general formula should apply:

Resultant Muscle Force=F

Angle betweeen resultant force and line of bite resistance=A

Lever Arm length=LEVER

Load Arm length=LOAD

(F cosine A) x LEVER

Bite Force = ---------------------

LOAD

This much seems to be clear. But my review of the literature has turned

up numerous different measurements for these values.

Most models place the fulcrum at the TMJ and the "weight" at the bite

point, so that the Load arm length should be the distance between the TMJ

and the bite point (some specified tooth).

But Dechow and Carlson (Amer J. Phys. Anthr. vol 83,2) calculate Bite

force using the occlusal plane (OP) as the lever. They simply extend a

vertical line down from TMJ until it intersects OC. Likewise, the load

arm of the temporalis mm. is the intersect of a vertical line drawn down

from the "tip" of the coronoid process to OP. How can this be?

Demes and Creel (J Hum Evo. vol 17) and Anapol and Lee (Amer J. Phys. Anthr.

vol 94,2) use the Frankfort Horizontal: "lever arm of temporalis--estimated

to be one-half the distance along the FH from the most caudal extent of the glenoid fossa to

the most rostral limit of the temporal fossa on the dorsal aspect of the

zygomatic arch" (Anapol and Lee, p. 241).

I think, in a biomechanical model it should be the actual line connecting

the TMJ and bite point NOT the occlusal plane nor the Frankfort

Horizontal, that represents the lever arm, and that the load arm is also

measured along this line. Greaves (J. Zool. Lond. vol 184) uses this

type of model. I also think that in the (F cosine A) part of the equation

A should be taken between the Muscle Resultant vector and a line

perpendicular to the occlusal plane, since this is the direction of bite

force reaction. Am I right? OK, my big problem is how to locate the load

arm along this line. Well one point is clearly fulcrum (TMJ), and the

other point should be the intersection of the resultant muscle

vector algon the TMJ-bite point line. Right?

If I'm right about all this so far, then

a resultant vector acting perpendicular to the occlusal plane will have a

cosine of 1 and the full magnitude of the force will be transmitted to

the bite point. But that means that the intersection of this vector and

TMJ-bite point line will be posteriorly place making for a short load arm

and decreased mechanical advantage; compared to a muscle vector that

intersects the bite point, which would have an optimum mechanical

advantage (lever arm=load arm), but whose angle relative to the bite

reaction force (perpendicular to occlusal plane) would be oblique

resulting in an angle cosine of much less than 1. In other words, there

is a trade off between the two vector situations.

Any comments on any of this, references, etc, would be greatly

appreciated. I'd really like to know if I'm on the right track. None of

the biomechanics or mechanics books I've come across address this precise

problem. Thanks in advance,

James McMahon

Doctoral Student

Biological Anthropology Program

City University of New York

I hope one, or several, of you can help me with a problem I've

encountered. I'm trying to estimate max. bite force using measurements on

a series of dry skulls; so I need to construct a biomechanical model of

mastication in order to determined what measurements are appropriate.

I've "dabbled" in biomechanics but have no formal training, and thus must

rely on the experts. I'm making the assumption that the jaw acts as a

Class III lever (an assumption made by many of the people who do this

kind of work). The general formula should apply:

Resultant Muscle Force=F

Angle betweeen resultant force and line of bite resistance=A

Lever Arm length=LEVER

Load Arm length=LOAD

(F cosine A) x LEVER

Bite Force = ---------------------

LOAD

This much seems to be clear. But my review of the literature has turned

up numerous different measurements for these values.

Most models place the fulcrum at the TMJ and the "weight" at the bite

point, so that the Load arm length should be the distance between the TMJ

and the bite point (some specified tooth).

But Dechow and Carlson (Amer J. Phys. Anthr. vol 83,2) calculate Bite

force using the occlusal plane (OP) as the lever. They simply extend a

vertical line down from TMJ until it intersects OC. Likewise, the load

arm of the temporalis mm. is the intersect of a vertical line drawn down

from the "tip" of the coronoid process to OP. How can this be?

Demes and Creel (J Hum Evo. vol 17) and Anapol and Lee (Amer J. Phys. Anthr.

vol 94,2) use the Frankfort Horizontal: "lever arm of temporalis--estimated

to be one-half the distance along the FH from the most caudal extent of the glenoid fossa to

the most rostral limit of the temporal fossa on the dorsal aspect of the

zygomatic arch" (Anapol and Lee, p. 241).

I think, in a biomechanical model it should be the actual line connecting

the TMJ and bite point NOT the occlusal plane nor the Frankfort

Horizontal, that represents the lever arm, and that the load arm is also

measured along this line. Greaves (J. Zool. Lond. vol 184) uses this

type of model. I also think that in the (F cosine A) part of the equation

A should be taken between the Muscle Resultant vector and a line

perpendicular to the occlusal plane, since this is the direction of bite

force reaction. Am I right? OK, my big problem is how to locate the load

arm along this line. Well one point is clearly fulcrum (TMJ), and the

other point should be the intersection of the resultant muscle

vector algon the TMJ-bite point line. Right?

If I'm right about all this so far, then

a resultant vector acting perpendicular to the occlusal plane will have a

cosine of 1 and the full magnitude of the force will be transmitted to

the bite point. But that means that the intersection of this vector and

TMJ-bite point line will be posteriorly place making for a short load arm

and decreased mechanical advantage; compared to a muscle vector that

intersects the bite point, which would have an optimum mechanical

advantage (lever arm=load arm), but whose angle relative to the bite

reaction force (perpendicular to occlusal plane) would be oblique

resulting in an angle cosine of much less than 1. In other words, there

is a trade off between the two vector situations.

Any comments on any of this, references, etc, would be greatly

appreciated. I'd really like to know if I'm on the right track. None of

the biomechanics or mechanics books I've come across address this precise

problem. Thanks in advance,

James McMahon

Doctoral Student

Biological Anthropology Program

City University of New York