Muscle moment arms

Both agonist and antagonist muscles contribute (unequally) to the net torque developed about a joint In fact, for any given joint in the body, there are many more muscles crossing the joint than there are dof prescribing joint movement llie knee, for example, has at most 6 dof, yet there are at least 14 muscles that actuate this joint One consequence of this arrangement is that the force developed by each muscle carmot be determined uniquely. Specifically, there are more unknown musculotendinous actuator forces than net actuator torques exerted about the knee that is, m > n in Eq. (6.9), which means that the matrix of muscle moment arms is not square and therefore not invertible. This is the so-called indeterminate problem in biomechanics, and virtually all attempts to solve it are based on the aj Ucation of optimization theory (see also the Qiap. 5 by Manal and Buchanan). 

Deciding whether to measure force (a translational quantity) or torque (a rotational quantity) is an important issue in testing strength. Even when the functional units of interest produce rotational motion, force measurement at some point along the moment arm is common. This is due to the evolution from manual muscle tests to the use of objective measurements where a force sensor replaces the human examiner sense of force resisted or generated. If d is the distance from the point of rotation to the point of force measurement and the force vector is tangent to the arc of motion, then... 

Muscles with larger moment arms, longer muscle fibers, and less pennation tend to be capable of generating greater speed. Many of the same factors influencing strength, discussed earher, such as muscle... 

Muscles develop forces and cause rotation of the bones about a joint. The tendency of a musculotendinous actuator to rotate a bone about a joint is described by the actuator s moment arm. Two methods are commonly used to measure the moment arm of an actuator—the geometric method and the tendon excursion method. 

In the geometric method, a finite center of rotation is found by x-rays, computed tomography, or magnetic resonance imaging, and the moment arm is found by measuring the perpendicular distance from the joint center to the line of action of the muscle (Jensen and Davy, 1975). In the tendon excursion method, the change in... 

Equations (6.2) and (6.3) have the same geometric interpretation thg moment arm of a muscle force r", given either by X F" from Eq. (6.2) or by dF/d0 from Eq. (6.3), is equal to the perpendicular (shortest) distance between the ISA of B relative to A and the line of action of the muscle force, multiplied by the sine of the angle between these two lines (Pandy, 1999). 

F ff is the peak isometric force developed by the ith musculotendinous actuator, a quantity that is directly proportional to the physiological cross-sectional area of the ith muscle. Equation (6.12) expresses the n relationships between the net actuator torques T " , the matrix of actuator moment arms R(q), and the unknown actuator forces F". Equation (6.13) is a set of m equations that constrains the value of each actuator force to remain greater than zero and less than the peak isometric force of the actuator defined by the cross-sectional area of the muscle. Standard nonlinear programming algorithms can be used to solve this problem [e.g., sequential quadratic programming (Powell, 1978)],... 

Pandy, M. G. (1999). Moment arm of a muscle force, Exercise and Sport Sciences Reviews, 27 79-118. 

Van Spronsen P.H., Weijs W.A., Van Ginkel F.C., Prahl-Andersen B. (1996) Jaw muscle orientation and moment arms of long-faee and normal adults. J Dent Res 75 1372-1380. 

When the spine is placed under load as you attempt to lift a weight from the ground, you must develop an extensor moment in the muscles of the spine to permit you to straighten up. Structures which lie close to the center of rotation have a short lever arm and therefore have to generate higher tensile forces to produce the same extensor moment. The tensile forces act to compress the intervertebral disc, and this compressive penalty is highest for the posterior annulus and is lowest for the lumbodorsal fascia. 

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