Toward Understanding the Terminology of Exercise Mechanics
The purpose of this paper is to reduce the confusion and misunderstanding of exercise mechanics terminology by giving simplified definitions of the most important physical quantities and terms. Isometric, isotonic, and isokinetic exercises are discussed and related to the appropriate physical quantities. The correct use of the most confusing and frequently misused terms is discussed.
Key Words: Biomechanics, Exercise therapy, Physical therapy, Vocabulary.
Many physical therapists who are familiar with isometric and isotonic exercises are now being ex posed to another type of exercise, isokinetic exercises. While reading the literature on exercise, unfamiliar or confusing terminology is often encountered. A better understanding of exercise terminology and ex ercise mechanics should make this literature more useful to: 1) therapists developing exercise programs for patients, 2) educators disseminating new infor mation to students, and 3) researchers assimilating the work of their colleagues or writing articles for publication. A review and discussion of terms and definitions, with examples, should reduce confusion and clarify some of the apparent contradictions found in the literature. DEFINITIONS
In scientific writing, physical characteristics are described as either "defined terms" or "definable terms." Defined terms are those that describe funda mental physical quantities, such as force or velocity, and that have precise and universally accepted math ematical definitions that should not vary from author to author, nor from article to article. Definable terms, on the other hand, describe more subjective physical properties, such as endurance or strength, that may be defined to suit the author's needs as long as each definition is made clear to the reader in each article. Definitions of most of the fundamental physical characteristics of mechanics that are used in physical therapy literature on exercise are discussed below.1 2 Dr. Laird is a Research Engineer in Geophysics for Mobil Re search and Development Corp. PO Box 900, Dallas, TX 75221. Dr. Rozier is Director, School of Physical Therapy. Texas Woman's University, Box 22487, TWU Station, Denton. TX 76204.
Volume 59 / Number 3, March 1979
Understanding these terms and definitions is impor tant for analysis of exercises, especially isokinetic exercises. Definitions that require calculus for precise explanation are simplified to avoid using calculus notation and nomenclature. Scalar. A quantity that has only a magnitude and does not require a direction to be completely speci fied. Scalar quantities, such as temperature or length, can be specified by a single number, such as 26°C or 53 inches. Vector. A quantity that has both magnitude and direction. Force is a vector because it has magnitude and because the direction in which it is acting must be known in order to define it completely. Distance. The amount of space between two entities such as points, lines, or objects. The standard metric unit for distance is the meter. Displacement. The change in position of a point, particle, or object. Displacement is a vector because both the distance and the direction that an object is moved must be specified to describe the change in position. The metric unit for displacement, like dis tance, is the meter. Velocity. A vector equal to the rate of change of the position, or of the displacement, of an object with respect to time. The unit for velocity is meters per second. Average velocity is the distance divided by time, or, more properly, displacement divided by time. When the velocity is not constant, the concept of instantaneous velocity is important. Instantaneous velocity at a particular location or point in time is determined by dividing an appropriately small inter val of displacement by the corresponding small inter val of time. Speed. The magnitude of velocity. Speed is a scalar quantity because it does not imply a direction. 287
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CHARLES E. LAIRD, Jr, PhD, and CAROLYN K. ROZIER, PhD
288
the displacement changes while work is being done, the concept of work over small distance intervals becomes important. Work is measured in units of force times distance, or newton-meters. Power. The rate that work is done with respect to time. A verage power is simply the total work done by a force divided by the total time it takes the force to do the work. As with velocity and acceleration, if the force or the direction of displacement is not constant, the idea of instantaneous power is important. Two equivalent definitions for power are 1) force times velocity and 2) torque times angular velocity. The metric unit for power is the watt; one watt equals one newton-meter per second, or 0.7376 foot-pounds per second. An additional unit for power is horsepower; one horsepower equals 745.7 watts, or 550 foot pounds per second. Energy. The capacity to do work. Definitions of energy can be very complex because energy occurs in many different forms, such as heat, light, sound, electrical, nuclear, and mechanical. The main form of energy in exercise mechanics is mechanical energy. Mechanical energy is either potential energy, which is stored, or kinetic energy, which is the energy of motion. Energy, like work, is measured in newtonmeters or foot-pounds. Mechanical potential energy is usually the weight of an object times the distance it has been placed above some reference level, such as the ground, the floor, or a table top. The mechan ical kinetic energy of an object is equal to one-half its mass times the square of its speed.
TYPES OF EXERCISE
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Acceleration. The rate of change of velocity with respect to time. Acceleration can be expressed as the rate of change with respect to time of the rate of change with respect to time of displacement. The unit for acceleration is meters per second per second. The definitions for average acceleration and instantaneous acceleration are analogous to those given for velocity. Angular displacement. The amount of rotation needed to bring one line into coincidence with an other. The unit for angular displacement is the radian or degree; 2 TT radians equal 360 degrees and one radian equals 57.3 degrees. Angular displacement is a vector because the direction must be specified (clockwise or counterclockwise) as well as the amount of rotation. In describing angular displacement and other rotational quantities, universal convention de fines counterclockwise quantities as positive and clockwise quantities as negative. Angular velocity. The rate of change with respect to time of angular displacement, given in units of radians per second or degrees per second. Angular acceleration. The rate of change of angular velocity with respect to time and given in units of radians per second per second or degrees per second per second. Force. An external influence, a push or a pull, exerted on an object. The metric unit for force is the newton; one newton equals 0.225 pounds. Mass. A fundamental scalar property of an object that describes the amount of acceleration an object will have when a given force is applied to it. The metric unit of mass is the kilogram; one kilogram equals 2.205 pounds avoirdupois. Weight. The gravitational force exerted on an ob ject, usually by the earth. The unit of weight, like that of force, is the newton. The difference between weight and mass is that the weight of an object will vary with the force of gravity, but the mass remains the same. For example, an object will weigh less on the moon than it does on earth, because the moon's gravity is less, but the mass is the same in both places. Torque. A measure of the effort of some force to rotate an object about some axis of rotation. Torque is equal to the length of the lever arm, measured from the axis of rotation to the point of application of the force, multiplied by the component of force that is perpendicular to the lever arm. Torque is measured in units of force times distance, or newton-meters. Work. A force moving a resistance through a dis tance. The amount of work done by a force is the product of the amount of force in the direction of the displacement times the distance the resistance is moved. Regardless of the force applied to an object, no work is done without movement. If the magnitude or direction of the force changes, or the direction of
Three basic types of exercise are used in exercise research: isometric, isotonic, and isokinetic. Basic def initions are found in many places in exercise litera ture, as are certain physical quantities pertaining to each type of exercise. 15 Having defined these quan tities, specific exercises can now be discussed pre cisely. Each of these exercise types is examined in terms of the physical quantities that can be applied, that can be measured and compared, and that are not appropriate but are sometimes misused in the exercise literature.
Isometric
An isometric exercise is a static exercise. The mus cle contracts with little or no shortening. This type of exercise has been referred to as simply "an equal length exercise." :i Because nothing moves during an isometric exercise, no work is being done; because no work is done, the concepts of power and mechanical energy do not apply. Force, torque, and possibly time PHYSICAL THERAPY
Isotonic
An isotonic exercise is a dynamic exercise with a constant load or resistance. '' 4 ' b ' 7 The muscle shortens and the load is displaced. Work is done, because a force is moving a resistance through a distance. Be cause time is now involved, the quantities of velocity, acceleration, power, and mechanical energy have meaning. None of these quantities, however, is easily measured or calculated for an isotonic exercise, be cause most of the so-called isotonic exercises do not have a constant resistance and are, therefore, not truly isotonic. What is usually measured, or known, is the weight that provides the resistance and the number of repetitions done. An example of an exercise not being truly isotonic is use of a standard DeLorme boot to exercise the quadriceps muscles, as shown in the force diagram in Figure 1. Force (F), or the resistance that the quad riceps muscles must overcome, is the weight (W) that is perpendicular to the lever arm. The lever arm is a line drawn from the axis of rotation (the knee) to the point of application of the force (the foot). The length of the lever arm is r. The static resistance force as a function of the angle of flexion (0) is given by the simple equation F = (W)(cos 9). The weight of the leg is disregarded in this equation, and the speed of the exercise is assumed to be such that the dynamic forces are approximately equal to the static forces. For a numerical example, a weight of 100 newtons Volume 59 / Number 3, March 1979
Fig. I. Schematic for DeLorme boot exercise.
(about 10.2 kg or 22.5 lb) is used. The resistance is not constant and ranges from 0 newtons at 90 degrees of flexion to a maximum of 100 newtons at 0 degrees of flexion (Fig. 2). The equation for the work done between two angles of flexion 0\ and d 2 is Interval Work = (w)(r)(sin #i-sin d 2 ). In the two equations in this section, the resistance force is independent of the subject, but the amount of work done depends upon the length of the leg (r). Also shown in Figure 2 is the amount of work done
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are the only physical quantities that can be measured during an isometric contraction. The laws of physics specify that because nothing moves (no acceleration), the resistance force equals the applied force. In reality, however, because some kind of strain gauge must be deformed slightly to measure the applied force, a small but usually negligible amount of work is done at the onset of the contraction. Other terms encountered with isometric exercises include BME (brief maximal exercise) and BRIME (brief repetitive isometric maximal exercise). "Maxi mal" is a fairly well defined and universal term, usually implying that the subject exerts the maximum force throughout the exercise. Any discussion of max imal efforts should, however, include comments on subject motivation. Additional terms encountered, such as strength, endurance, and fatigue, are subjective or "definable terms" and may have many different definitions. Therefore, comparisons or discussions of the defina ble terms should include precise definitions. Other wise, the reader may become confused by the results, misunderstand them, or be justified in questioning their validity.
function of an angle of flexion (6), is much more complicated but is given by the equation F = W cos 90° — 6
Fig. 3. Schematic for weight and pulley exercise.
for each 10-degree interval from 90 degrees to 0 degrees when the leg length is 45 cm, or 0.45 meters. The work per 10-degree interval is also not constant, but increases with decreasing flexion. If each repeti tion were timed as a function of angle, the average power could be computed. This calculation is not shown here. A second example of an exercise not being truly isotonic is when using the weight and pulley system in Figure 3. The static resistance force (F), as a
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— arc tan
Again, r is the length of the leg, this time from the axis of rotation (the knee) to the point of application of the resistance (a heel strap). The parameter (h) is the difference in height above the floor of the heel strap at 90 degrees of flexion and the pulley (A), as shown in Figure 3. The horizontal distance between these two points is d. For a numerical example, W is 100 newtons and r is 45 cm; h is 18 cm, and d is 15 cm. The resistance force as a function of the angle and the work done during each 10-degree interval are displayed in Figure 4. Again, the resistance force is not constant and the exercise is, therefore, not iso tonic. In this example, the maximum resistance force occurs at a flexion angle of 57.6 degrees. The location of this maximal force is not constant, however, and depends upon the leg length (r) and the parameters (h) and (d). A third example of an exercise that is not isotonic is the simple bench press with a barbell. Here, the resistance force is clearly a constant at the point of application and is equal to the weight of the barbell. The problem with studying this and similar examples is that, although the load is constant, the distribution of the load among the different muscles and muscle groups that act against the resistance varies through out the displacement of the load. No single muscle or muscle group acts on a constant resistance throughout the range of motion of the exercise. The purpose of the three examples provided is to show that, for most of the classical isotonic exercises, the resistance (load) for a specific muscle group varies with the displacement of the load. This point is important and should not be overlooked when mak ing comparisons based on isotonic exercises. The way that the resistance varies with position can differ from one exercise apparatus to another and even from one subject to another on the same exercise apparatus. Knowing that the distribution of the load was differ ent in two experiments may help to explain apparent discrepancies between the results of the two experi ments. Isokinetic
Flexion Angle
Fig. 4. Resistance force and incremental work for weight and pulley example.
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An isokinetic exercise is a dynamic, resistive exer cise that incorporates a full range of movement, with PHYSICAL THERAPY
* Cybex. Cybex Division of Lumex, Inc, Bayshore, NY 11706.
Volume 59 / Number 3, March 1979
or kinetic mechanical energy, but the dimensions, or units (newton-meters), are correct for energy. This energy is more properly a measure of the heat energy used by the body, or "muscular energy" expended, rather than a measure of mechanical energy. A common misuse of the term power in discussions of isokinetic exercises is in the expressions low power (low speed, high load) exercises and high power (high speed, low load) exercises. Work is the force on a load times the displacement of the load. High load is equivalent to high work, and low load is equivalent to low work, because the displacements are equal for a given exercise. Power is the rate at which work is done in one repetition divided by the time of one repetition. High work divided by long time (low speed, high load) and low work divided by snort time (high speed, low load) might very well be equal. A much simpler way of viewing this is to use one of the equivalent definitions for power: power equals torque times angular velocity. A high average torque times a low angular velocity could conceivably equal a low average torque times a high angular velocity. In one pilot study, the total work of the quadriceps muscle done in two minutes was the same for two groups of subjects, even though one group was exer cising at three times the velocity of the other group." The average power of the group doing the low-speed exercise was the same as the average power of the group doing the high speed exercise, because the average power would be the total work done in two minutes divided by 120 seconds. This equality will not be true in all, or even most, cases, but this example should illustrate that high power and low power are inappropriate terms for classifying isokinetic exer cises. Low and high speed or velocity are correct and sufficient terms for describing these exercises, and they necessarily imply high load and low load, re spectively, when dealing with maximal exercises. One further caution concerns the use of the quan tity peak torque. The peak torque achieved during one repetition of an exercise is a valid measurement, but its relationship to the average torque may not be consistent. Conclusions based on peak torque may not be the same as those based upon average torque. It is possible for peak torque to increase and average torque to decrease and vice versa. More probably, peak torque and average torque would both increase or both decrease, but not necessarily at the same rate. Percent increases or decreases in peak torque will not usually be the same as those in the average torque. When comparing results from different experiments, it is important to know and understand the quantities
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the muscle exerting the maximal force at all points in the range of motion:' With the isokinetic exercise, the speed of motion is a controlled variable not present in isometric or isotonic exercise. With an isokinetic exercise machine,* the angular velocity of the motion is specified and the resistance automatically accom modates to the exerted force so that the specified velocity is maintained. Isokinetic exercise is also called "accommodating resistance exercise." 5 The torque at the rotating joint, as a function of both time and angle of displacement, can be measured by using a pen recorder. When the length of the lever arm, the torque, and the angular velocity are known, the force at the point of application, the linear velocity, the work done during any increment of time or angle, and the instantaneous or average power can be cal culated. Because many physical quantities of isokinetic ex ercises can be specified, measured, calculated, and compared, terms describing these quantities should be used properly to prevent any confusion or misun derstanding. Definitions for all the pertinent physical quantities have been presented in an earlier section and will not be repeated except when necessary to clarify a particular point. A commonly misused term is acceleration, which is the rate of change of the velocity of some object with respect to time, whereas velocity is the rate of change of the displacement of that object with respect to time. A velocity can increase or decrease at some rate, but a velocity cannot be accelerated. An object can be accelerated but a velocity cannot. Other confusing terms describing isokinetic exer cise are work, power, and energy, with their relation ships to time. Work is force times distance, and power is the rate at which work is done. It is important not to confuse "the total amount of work done in a given time period" with average power, which is "the total amount of work done during a given time period divided by the time period." For example, suppose 50 newton-meters of work is done in 25 seconds. The total work done is 50 newton-meters, but the average power is 50 newton-meters divided by 25 seconds, or two newton-meters per second (two watts of average power for 25 seconds). Energy can be related to power in that average power for some time period multiplied by that length of time is an expression of energy. Using the same example as above two watts of power for 25 seconds is 50 newton-meters of energy. This use of the term energy does not fit the earlier definitions for potential
that are being compared and whether the comparison is appropriate. Concluding Remarks
1. Resnick R. Halliday D: Physics for Students of Science and Engineering: Part I. New York. John Wiley & Sons, Inc, 1960 2. Lissner HR. Williams M, LeVeau B: Biomechanics of Human Motion, ed. 2. Philadelphia. W B Saunders Co, 1977 3. Berger RA: Comparison of static and dynamic strength increases. Res Q Am Assoc Health Phys Ed 33(3):330-333, 1962 4. Miiller EA: Influence of training and of inactivity on muscle strength. Arch Phys Med Rehabil 51:449-462, 1970 5. Thistle HG, Hislop HJ, Moffroid M, et al: Isokinetic contraction: A new concept of resistive exercise. Arch Phys Med Rehabil 48: 279-282, 1966 6. Berger R: Effect of varied weight training programs on strength. Res Q Am Assoc Health Phys Ed 33(2): 168-181, 1962 7. Berger R A: Optimum repetitions for the development ofstrength. Res Q Am Assoc Health Phys Ed 33(3):334-338, 1962 8. Moffroid MA. Whipple RH: Specificity of speed of exercise. Phys Ther 50:1692-1700, 1970
WHY PHYSICAL THERAPY? and TAKE THREE STEPS STOOP DOWN PICK UP A PENCIL
Take Three Steps
k
Stoop Down
Pick Up a Pencil
Two brochures available from Associ ation Headquarters are just what you need to spread the word! Helpful to new patients, students interested in the physical therapy profession, com munity service organizations . . . at service prices, too. To order, return the coupon enclosing check made payable to the American Physical Therapy Association.
NAME ADDRESS CITY STATE ZIP Take Three Steps # cppies 30e/ea; $15/100 Why Physical Therapy # copies 50 e/ea; $25/100 Am't enclosed Return to APTA, 1156 15th St NW, Washington, DC 20005.
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We have not discussed all the confusing or misused terms and expressions that exist in exercise literature. We have, however, defined most of the physical quantities encountered in exercise literature and pre sented several examples to illustrate and explain some of the most confusing or misused terms. These defi nitions and examples should help in understanding the articles and texts on exercise and exercise me chanics and make them more meaningful for all persons involved with physical exercises.
REFERENCES
PHYSICAL THERAPY
The purpose of this paper is to reduce the confusion and misunderstanding of exercise mechanics terminology by giving simplified definitions of the most important physical quantities and terms. Isometric, isotonic, and isokinetic exercises are discussed and related to the appropriate physical quantities. The correct use of the most confusing and frequently misused terms is discussed.
Key Words: Biomechanics, Exercise therapy, Physical therapy, Vocabulary.
Many physical therapists who are familiar with isometric and isotonic exercises are now being ex posed to another type of exercise, isokinetic exercises. While reading the literature on exercise, unfamiliar or confusing terminology is often encountered. A better understanding of exercise terminology and ex ercise mechanics should make this literature more useful to: 1) therapists developing exercise programs for patients, 2) educators disseminating new infor mation to students, and 3) researchers assimilating the work of their colleagues or writing articles for publication. A review and discussion of terms and definitions, with examples, should reduce confusion and clarify some of the apparent contradictions found in the literature. DEFINITIONS
In scientific writing, physical characteristics are described as either "defined terms" or "definable terms." Defined terms are those that describe funda mental physical quantities, such as force or velocity, and that have precise and universally accepted math ematical definitions that should not vary from author to author, nor from article to article. Definable terms, on the other hand, describe more subjective physical properties, such as endurance or strength, that may be defined to suit the author's needs as long as each definition is made clear to the reader in each article. Definitions of most of the fundamental physical characteristics of mechanics that are used in physical therapy literature on exercise are discussed below.1 2 Dr. Laird is a Research Engineer in Geophysics for Mobil Re search and Development Corp. PO Box 900, Dallas, TX 75221. Dr. Rozier is Director, School of Physical Therapy. Texas Woman's University, Box 22487, TWU Station, Denton. TX 76204.
Volume 59 / Number 3, March 1979
Understanding these terms and definitions is impor tant for analysis of exercises, especially isokinetic exercises. Definitions that require calculus for precise explanation are simplified to avoid using calculus notation and nomenclature. Scalar. A quantity that has only a magnitude and does not require a direction to be completely speci fied. Scalar quantities, such as temperature or length, can be specified by a single number, such as 26°C or 53 inches. Vector. A quantity that has both magnitude and direction. Force is a vector because it has magnitude and because the direction in which it is acting must be known in order to define it completely. Distance. The amount of space between two entities such as points, lines, or objects. The standard metric unit for distance is the meter. Displacement. The change in position of a point, particle, or object. Displacement is a vector because both the distance and the direction that an object is moved must be specified to describe the change in position. The metric unit for displacement, like dis tance, is the meter. Velocity. A vector equal to the rate of change of the position, or of the displacement, of an object with respect to time. The unit for velocity is meters per second. Average velocity is the distance divided by time, or, more properly, displacement divided by time. When the velocity is not constant, the concept of instantaneous velocity is important. Instantaneous velocity at a particular location or point in time is determined by dividing an appropriately small inter val of displacement by the corresponding small inter val of time. Speed. The magnitude of velocity. Speed is a scalar quantity because it does not imply a direction. 287
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CHARLES E. LAIRD, Jr, PhD, and CAROLYN K. ROZIER, PhD
288
the displacement changes while work is being done, the concept of work over small distance intervals becomes important. Work is measured in units of force times distance, or newton-meters. Power. The rate that work is done with respect to time. A verage power is simply the total work done by a force divided by the total time it takes the force to do the work. As with velocity and acceleration, if the force or the direction of displacement is not constant, the idea of instantaneous power is important. Two equivalent definitions for power are 1) force times velocity and 2) torque times angular velocity. The metric unit for power is the watt; one watt equals one newton-meter per second, or 0.7376 foot-pounds per second. An additional unit for power is horsepower; one horsepower equals 745.7 watts, or 550 foot pounds per second. Energy. The capacity to do work. Definitions of energy can be very complex because energy occurs in many different forms, such as heat, light, sound, electrical, nuclear, and mechanical. The main form of energy in exercise mechanics is mechanical energy. Mechanical energy is either potential energy, which is stored, or kinetic energy, which is the energy of motion. Energy, like work, is measured in newtonmeters or foot-pounds. Mechanical potential energy is usually the weight of an object times the distance it has been placed above some reference level, such as the ground, the floor, or a table top. The mechan ical kinetic energy of an object is equal to one-half its mass times the square of its speed.
TYPES OF EXERCISE
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Acceleration. The rate of change of velocity with respect to time. Acceleration can be expressed as the rate of change with respect to time of the rate of change with respect to time of displacement. The unit for acceleration is meters per second per second. The definitions for average acceleration and instantaneous acceleration are analogous to those given for velocity. Angular displacement. The amount of rotation needed to bring one line into coincidence with an other. The unit for angular displacement is the radian or degree; 2 TT radians equal 360 degrees and one radian equals 57.3 degrees. Angular displacement is a vector because the direction must be specified (clockwise or counterclockwise) as well as the amount of rotation. In describing angular displacement and other rotational quantities, universal convention de fines counterclockwise quantities as positive and clockwise quantities as negative. Angular velocity. The rate of change with respect to time of angular displacement, given in units of radians per second or degrees per second. Angular acceleration. The rate of change of angular velocity with respect to time and given in units of radians per second per second or degrees per second per second. Force. An external influence, a push or a pull, exerted on an object. The metric unit for force is the newton; one newton equals 0.225 pounds. Mass. A fundamental scalar property of an object that describes the amount of acceleration an object will have when a given force is applied to it. The metric unit of mass is the kilogram; one kilogram equals 2.205 pounds avoirdupois. Weight. The gravitational force exerted on an ob ject, usually by the earth. The unit of weight, like that of force, is the newton. The difference between weight and mass is that the weight of an object will vary with the force of gravity, but the mass remains the same. For example, an object will weigh less on the moon than it does on earth, because the moon's gravity is less, but the mass is the same in both places. Torque. A measure of the effort of some force to rotate an object about some axis of rotation. Torque is equal to the length of the lever arm, measured from the axis of rotation to the point of application of the force, multiplied by the component of force that is perpendicular to the lever arm. Torque is measured in units of force times distance, or newton-meters. Work. A force moving a resistance through a dis tance. The amount of work done by a force is the product of the amount of force in the direction of the displacement times the distance the resistance is moved. Regardless of the force applied to an object, no work is done without movement. If the magnitude or direction of the force changes, or the direction of
Three basic types of exercise are used in exercise research: isometric, isotonic, and isokinetic. Basic def initions are found in many places in exercise litera ture, as are certain physical quantities pertaining to each type of exercise. 15 Having defined these quan tities, specific exercises can now be discussed pre cisely. Each of these exercise types is examined in terms of the physical quantities that can be applied, that can be measured and compared, and that are not appropriate but are sometimes misused in the exercise literature.
Isometric
An isometric exercise is a static exercise. The mus cle contracts with little or no shortening. This type of exercise has been referred to as simply "an equal length exercise." :i Because nothing moves during an isometric exercise, no work is being done; because no work is done, the concepts of power and mechanical energy do not apply. Force, torque, and possibly time PHYSICAL THERAPY
Isotonic
An isotonic exercise is a dynamic exercise with a constant load or resistance. '' 4 ' b ' 7 The muscle shortens and the load is displaced. Work is done, because a force is moving a resistance through a distance. Be cause time is now involved, the quantities of velocity, acceleration, power, and mechanical energy have meaning. None of these quantities, however, is easily measured or calculated for an isotonic exercise, be cause most of the so-called isotonic exercises do not have a constant resistance and are, therefore, not truly isotonic. What is usually measured, or known, is the weight that provides the resistance and the number of repetitions done. An example of an exercise not being truly isotonic is use of a standard DeLorme boot to exercise the quadriceps muscles, as shown in the force diagram in Figure 1. Force (F), or the resistance that the quad riceps muscles must overcome, is the weight (W) that is perpendicular to the lever arm. The lever arm is a line drawn from the axis of rotation (the knee) to the point of application of the force (the foot). The length of the lever arm is r. The static resistance force as a function of the angle of flexion (0) is given by the simple equation F = (W)(cos 9). The weight of the leg is disregarded in this equation, and the speed of the exercise is assumed to be such that the dynamic forces are approximately equal to the static forces. For a numerical example, a weight of 100 newtons Volume 59 / Number 3, March 1979
Fig. I. Schematic for DeLorme boot exercise.
(about 10.2 kg or 22.5 lb) is used. The resistance is not constant and ranges from 0 newtons at 90 degrees of flexion to a maximum of 100 newtons at 0 degrees of flexion (Fig. 2). The equation for the work done between two angles of flexion 0\ and d 2 is Interval Work = (w)(r)(sin #i-sin d 2 ). In the two equations in this section, the resistance force is independent of the subject, but the amount of work done depends upon the length of the leg (r). Also shown in Figure 2 is the amount of work done
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Fig. 2. Resistance force and incremental work for DeLorme boot example.
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are the only physical quantities that can be measured during an isometric contraction. The laws of physics specify that because nothing moves (no acceleration), the resistance force equals the applied force. In reality, however, because some kind of strain gauge must be deformed slightly to measure the applied force, a small but usually negligible amount of work is done at the onset of the contraction. Other terms encountered with isometric exercises include BME (brief maximal exercise) and BRIME (brief repetitive isometric maximal exercise). "Maxi mal" is a fairly well defined and universal term, usually implying that the subject exerts the maximum force throughout the exercise. Any discussion of max imal efforts should, however, include comments on subject motivation. Additional terms encountered, such as strength, endurance, and fatigue, are subjective or "definable terms" and may have many different definitions. Therefore, comparisons or discussions of the defina ble terms should include precise definitions. Other wise, the reader may become confused by the results, misunderstand them, or be justified in questioning their validity.
function of an angle of flexion (6), is much more complicated but is given by the equation F = W cos 90° — 6
Fig. 3. Schematic for weight and pulley exercise.
for each 10-degree interval from 90 degrees to 0 degrees when the leg length is 45 cm, or 0.45 meters. The work per 10-degree interval is also not constant, but increases with decreasing flexion. If each repeti tion were timed as a function of angle, the average power could be computed. This calculation is not shown here. A second example of an exercise not being truly isotonic is when using the weight and pulley system in Figure 3. The static resistance force (F), as a
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Again, r is the length of the leg, this time from the axis of rotation (the knee) to the point of application of the resistance (a heel strap). The parameter (h) is the difference in height above the floor of the heel strap at 90 degrees of flexion and the pulley (A), as shown in Figure 3. The horizontal distance between these two points is d. For a numerical example, W is 100 newtons and r is 45 cm; h is 18 cm, and d is 15 cm. The resistance force as a function of the angle and the work done during each 10-degree interval are displayed in Figure 4. Again, the resistance force is not constant and the exercise is, therefore, not iso tonic. In this example, the maximum resistance force occurs at a flexion angle of 57.6 degrees. The location of this maximal force is not constant, however, and depends upon the leg length (r) and the parameters (h) and (d). A third example of an exercise that is not isotonic is the simple bench press with a barbell. Here, the resistance force is clearly a constant at the point of application and is equal to the weight of the barbell. The problem with studying this and similar examples is that, although the load is constant, the distribution of the load among the different muscles and muscle groups that act against the resistance varies through out the displacement of the load. No single muscle or muscle group acts on a constant resistance throughout the range of motion of the exercise. The purpose of the three examples provided is to show that, for most of the classical isotonic exercises, the resistance (load) for a specific muscle group varies with the displacement of the load. This point is important and should not be overlooked when mak ing comparisons based on isotonic exercises. The way that the resistance varies with position can differ from one exercise apparatus to another and even from one subject to another on the same exercise apparatus. Knowing that the distribution of the load was differ ent in two experiments may help to explain apparent discrepancies between the results of the two experi ments. Isokinetic
Flexion Angle
Fig. 4. Resistance force and incremental work for weight and pulley example.
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An isokinetic exercise is a dynamic, resistive exer cise that incorporates a full range of movement, with PHYSICAL THERAPY
* Cybex. Cybex Division of Lumex, Inc, Bayshore, NY 11706.
Volume 59 / Number 3, March 1979
or kinetic mechanical energy, but the dimensions, or units (newton-meters), are correct for energy. This energy is more properly a measure of the heat energy used by the body, or "muscular energy" expended, rather than a measure of mechanical energy. A common misuse of the term power in discussions of isokinetic exercises is in the expressions low power (low speed, high load) exercises and high power (high speed, low load) exercises. Work is the force on a load times the displacement of the load. High load is equivalent to high work, and low load is equivalent to low work, because the displacements are equal for a given exercise. Power is the rate at which work is done in one repetition divided by the time of one repetition. High work divided by long time (low speed, high load) and low work divided by snort time (high speed, low load) might very well be equal. A much simpler way of viewing this is to use one of the equivalent definitions for power: power equals torque times angular velocity. A high average torque times a low angular velocity could conceivably equal a low average torque times a high angular velocity. In one pilot study, the total work of the quadriceps muscle done in two minutes was the same for two groups of subjects, even though one group was exer cising at three times the velocity of the other group." The average power of the group doing the low-speed exercise was the same as the average power of the group doing the high speed exercise, because the average power would be the total work done in two minutes divided by 120 seconds. This equality will not be true in all, or even most, cases, but this example should illustrate that high power and low power are inappropriate terms for classifying isokinetic exer cises. Low and high speed or velocity are correct and sufficient terms for describing these exercises, and they necessarily imply high load and low load, re spectively, when dealing with maximal exercises. One further caution concerns the use of the quan tity peak torque. The peak torque achieved during one repetition of an exercise is a valid measurement, but its relationship to the average torque may not be consistent. Conclusions based on peak torque may not be the same as those based upon average torque. It is possible for peak torque to increase and average torque to decrease and vice versa. More probably, peak torque and average torque would both increase or both decrease, but not necessarily at the same rate. Percent increases or decreases in peak torque will not usually be the same as those in the average torque. When comparing results from different experiments, it is important to know and understand the quantities
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the muscle exerting the maximal force at all points in the range of motion:' With the isokinetic exercise, the speed of motion is a controlled variable not present in isometric or isotonic exercise. With an isokinetic exercise machine,* the angular velocity of the motion is specified and the resistance automatically accom modates to the exerted force so that the specified velocity is maintained. Isokinetic exercise is also called "accommodating resistance exercise." 5 The torque at the rotating joint, as a function of both time and angle of displacement, can be measured by using a pen recorder. When the length of the lever arm, the torque, and the angular velocity are known, the force at the point of application, the linear velocity, the work done during any increment of time or angle, and the instantaneous or average power can be cal culated. Because many physical quantities of isokinetic ex ercises can be specified, measured, calculated, and compared, terms describing these quantities should be used properly to prevent any confusion or misun derstanding. Definitions for all the pertinent physical quantities have been presented in an earlier section and will not be repeated except when necessary to clarify a particular point. A commonly misused term is acceleration, which is the rate of change of the velocity of some object with respect to time, whereas velocity is the rate of change of the displacement of that object with respect to time. A velocity can increase or decrease at some rate, but a velocity cannot be accelerated. An object can be accelerated but a velocity cannot. Other confusing terms describing isokinetic exer cise are work, power, and energy, with their relation ships to time. Work is force times distance, and power is the rate at which work is done. It is important not to confuse "the total amount of work done in a given time period" with average power, which is "the total amount of work done during a given time period divided by the time period." For example, suppose 50 newton-meters of work is done in 25 seconds. The total work done is 50 newton-meters, but the average power is 50 newton-meters divided by 25 seconds, or two newton-meters per second (two watts of average power for 25 seconds). Energy can be related to power in that average power for some time period multiplied by that length of time is an expression of energy. Using the same example as above two watts of power for 25 seconds is 50 newton-meters of energy. This use of the term energy does not fit the earlier definitions for potential
that are being compared and whether the comparison is appropriate. Concluding Remarks
1. Resnick R. Halliday D: Physics for Students of Science and Engineering: Part I. New York. John Wiley & Sons, Inc, 1960 2. Lissner HR. Williams M, LeVeau B: Biomechanics of Human Motion, ed. 2. Philadelphia. W B Saunders Co, 1977 3. Berger RA: Comparison of static and dynamic strength increases. Res Q Am Assoc Health Phys Ed 33(3):330-333, 1962 4. Miiller EA: Influence of training and of inactivity on muscle strength. Arch Phys Med Rehabil 51:449-462, 1970 5. Thistle HG, Hislop HJ, Moffroid M, et al: Isokinetic contraction: A new concept of resistive exercise. Arch Phys Med Rehabil 48: 279-282, 1966 6. Berger R: Effect of varied weight training programs on strength. Res Q Am Assoc Health Phys Ed 33(2): 168-181, 1962 7. Berger R A: Optimum repetitions for the development ofstrength. Res Q Am Assoc Health Phys Ed 33(3):334-338, 1962 8. Moffroid MA. Whipple RH: Specificity of speed of exercise. Phys Ther 50:1692-1700, 1970
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We have not discussed all the confusing or misused terms and expressions that exist in exercise literature. We have, however, defined most of the physical quantities encountered in exercise literature and pre sented several examples to illustrate and explain some of the most confusing or misused terms. These defi nitions and examples should help in understanding the articles and texts on exercise and exercise me chanics and make them more meaningful for all persons involved with physical exercises.
REFERENCES
PHYSICAL THERAPY
