Clinical Biomechanics: Mechanical Concepts and Terms
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This is Chapter 2 from RC’s best-selling book:
Second Edition ~ Wiliams & Wilkins
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Chapter 2: Mechanical Concepts and Terms
All motor activities such as walking, running, jumping, squatting, pushing, pulling, lifting, and throwing are examples of dynamic musculoskeletal mechanics. To better appreciate the sometimes simple and often complex factors involved, this chapter reviews the basic concepts and terms involved in maintaining static equilibrium. Static equilibrium is the starting point for all dynamic activities.
Energy and Mass
Biomechanics is constantly concerned with a quantity of matter (whatever occupies space, a mass) to which a force has been applied. Such a mass is often the body as a whole, a part of the body such as a limb or segment, or an object such as a load to be lifted or an exercise weight. By the same token, the word “body” refers to any mass; ie, the human body, a body part, or any object.
Energy is the power to work or to act. Body energy is that force which enables it to overcome resistance to motion, to produce a physical effect, and to accomplish work. The body’s kinetic energy, the energy level of the body due to its motion, is reflected solely in its velocity, and its potential energy is reflected solely in its position. Mathematically, kinetic energy is half the mass times the square of the velocity: m/2 X V524. In a closed system where there are no external forces being applied, the law of conservation of mechanical energy states that the sum of kinetic energy and potential energy is equal to a constant for that system.
Potential energy (PE), measured in newton meters or joules, is also stored in the body as a result of tissue displacement or deformation, like a wound spring or a stretched bowstring or tendon. It is expressed mathematically in the equation PE = mass X gravitational acceleration X height of the mass relative to a chosen reference level (eg, the earth’s surface). Thus, a 100-lb upper body balanced on L5 of a 6-ft person has a potential energy of about 300 ft-lb relative the ground.
The Center of Mass
The exact center of an object’s mass is sometimes referred to as the object’s center of gravity. When an object’s mass is evenly distributed throughout, the center of mass is located at the object’s geometric center. In the human body, however, this is infrequently true, and the center of mass is located towards the heavier, often larger, aspect. When considering the body as a whole, the center of mass in the anatomic position, for instance, is constantly shifted during activity when weight is shifted from one area to another during locomotion or when weight is added to or subtracted from the body.
The term weight is not synonymous with the word mass. Body weight refers to the pull of gravity on body mass. Mass is the quotient obtained by dividing the weight of a body by the acceleration due to gravity (32 ft/sec524). Each of these terms has a different unit of measurement. Weight is measured in pounds or kilograms, while mass is measured by a body’s weight divided by the gravitational constant. The potential energy of gravity can be simply visualized as an invisible spring attached between the body’s center of mass and the center of the earth. The pull is always straight downward so that more work is required to move the body upward than horizontally (Fig. 2.1).
Newton’s Laws of Mechanics
Sir Isaac Newton’s three laws of mechanics apply in any movement or injury and serve as the basis for the science of mechanical engineering. They are applied throughout the study of biomechanics and deserve definition and explanation.
The Law of Inertia
NEWTON’S FIRST LAW
A body remains at rest or in a state of uniform motion in a straight line until acted upon by an unbalanced or outside force. When a body is at rest, the forces acting upon it are completely balanced. When the body or a part is in motion, it will continue to move until some force causes it to stop. All objects express inertia in that they resist change whether at rest or in motion. The force necessary to overcome the inertia of a body depends upon the weight of the body and the rate at which it is moving. It is for this reason that more effort is required to put a shot than throw a baseball the same distance.
An object does not move unless a force has been applied that is greater than the object’s inertia. A body at rest may have many forces acting upon it; and if their magnitudes and directions completely cancel one another, there is zero net force and a state of static equilibrium. If these forces are unbalanced and result in a net force other than zero, movement (dynamics) occurs.
The Law of Acceleration
NEWTON’S SECOND LAW
The acceleration of an object is proportional to the unbalanced forces acting upon it and inversely proportional to the object’s mass. In other words, the net force acting on a body gives it an acceleration that is proportional to the force in both direction and magnitude and inversely proportional to the mass of the body.
A forceful push moves a small object rapidly; a light push on a large object moves it slowly. Acceleration is a quantity, where changes in direction or magnitude may occur, which refers to the rate of change of linear velocity. It is measured by its magnitude in feet or meters per second per second. Mathematically, acceleration = force/mass, or final velocity minus original velocity divided by time.
The Law of Reaction
NEWTON’S THIRD LAW (INTERACTION)
For every action there is an equal and opposite reciprocal reaction. Inertia is manifest as a reaction equal and opposite to the action that created the acceleration. Thus, forces are always in pairs that are equal in magnitude but opposite in direction. It is arbitrary which force is called the action and which the reaction, but usually in biomechanics we refer to internal body forces as actions and external forces applied to the body as reactions (eg, weights, floor reactions).
EXAMPLES OF REACTION
Regardless what degree of force is induced upon a part, there is always a counteracting stress because for every action there must be a reaction. For instance, a downward pressure equals an opposing upward thrust (eg, as that of a rocket). When an individual pushes against or lifts up any object, the object pushes against the person or pulls down with equal force in a line directly opposite to that of the individual’s force. A force pulling right is equal to a pull toward the left, expressed in terms of centripetal and centrifugal force. A spiraling force in one direction must be accompanied by an equal twisting force in the opposite direction. A force permitting a part to slide downward must be resisted by an adequate upward force. And a force tending to bend a structure along its axis must be resisted by a force equal to prevent such bending.
Force, simply, is any push or pull produced by one object acting upon another. It is anything that tends to cause or change the yield movement acceleration of an object. For example, when an object at rest is pushed (or pulled), it moves in the direction of the push at a speed relative to the strength and time of the pushing force. Linear movement without turning is called translation, and it is the result of the force passing through the center of mass. Some degree of rotation will accompany translation if the line of push or pull does not pass through the center of mass. The further the line of force is from the center of mass, the greater is the rotational component.
Force is measured in gravitational units: pounds or kilograms. It has two components: strength (magnitude of force) and direction.
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