Mechanics of one- and two-joint muscles. American Museum novitates ; no. 2319

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New York, N.Y. : American Museum of Natural History
"The mechanics of one- and two-joint muscles are described by means of free-body diagrams. Both static and dynamic (rotational and linear) conditions are analyzed. Free-body diagrams treat all the forces acting on bodies and allow analysis of the consequences of these forces; the associated equations are simple summations. D'Alembert's principle is employed (inclusion of a fictitious force or torque) in examples of linear or angular acceleration so that the forces and torques are reduced to an equilibrium and can be treated by the method of statics. Centripetal and tangential forces are included whenever a bone is rotating. Equations are written for examples of one-joint and two-joint muscles. A general three-dimensional model is presented. The use of the notion of first-, second-, and third-class levers is discouraged, because such a classification of lever systems is more misleading than useful. The mechanics of 'spurt' and 'shunt' muscles are analyzed, with special emphasis on the amount of torque produced and the contribution to the needed centripetal and tangential forces. 'Shunt' muscles could produce as mush torque as could 'spurt' muscles muscles; the needed centripetal force may be less than that supplied by the muscles or could be provided by ligaments at the articulation. It is argued that this division of muscles is misleading and even erroneous, and that these terms should be avoided. The contraction of a muscle does not produce a force couple on each bone onto which the muscle attaches, as has been advocated in the earlier literature. The force at the articulation depends on all other forces, real and fictitious, acting on the bone and, except by rare chance, is not equal in magnitude, parallel, and opposite in direction to the muscle force. Two-joint muscle-bone systems are non-static (and non-stable if static) and are indeterminate (the consequences of the muscle force cannot be ascertained merely from a knowledge of the morphology). No simple correlation exists between the relationship of the force vector of the muscle to the longitudinal axis of the central bone and the direction of rotation of the central bone. Some of the advantages and disadvantages of two-joint muscles as compared with one-joint muscles are discussed. A completely satisfactory analysis of these advantages and disadvantages must wait until empirical studies of many two-joint muscle-bone systems have been made. The advantages and disadvantages of free-body diagrams in biomechanical studies are outlined, with the recommendation that all analyses of bone-muscle systems should use free-body diagrams or methods that are clearly derived from free-body diagrams. The strength of such a method is that all the forces acting on each free-body (bone) are included and the consequences of their combined actions can be readily ascertained"--P. 41-42.
45 p. : ill. ; 24 cm.
Includes bibliographical references (p. 42-45).