Applied Human Anatomy and Biomechanics
Applied Human Anatomy and Biomechanics PEP 300
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Name Lab Section Muscle Actions Purpose To provide practice in the identification ofthe concentric and eccentric phases of muscular activity by visual observation of a series of exercises Eguipment Textbook class notes Procedures to be completed prior to lab Using your textbook the materials on reserve in the MathScience Library and LA pp 2425 complete the following x Define the following terms concentric tension muscle tension is suf cient to overcome a resistance and to move the ody segment of one attachment toward the segment of the other attachment the muscle actually shortens eccentric tension the tension the muscle develops while lengthening as it gives in to an external force that is greater than the contractile force the muscle is exerting isometricstatic tension tension of the muscle in partial or complete contraction without any appreciable change in length muscle does not cause movement nor does it give way to another force attempting to cause movement motive force a force that causes the desired motion resistive force a force that resists the desired motion functional muscle group a group of muscles that share a common action and together eveop eccentric concentric or isometric tension Procedures to be 39 during the lab session 1 Working with a partner provide the following information in the space provided for the initial from position 1 to 2 and return movement from position 2 to 1 in each of the 10 exercises Assume that all movements are performed slowly and under the control of muscular effort a articulation e functional muscle group b joint movement f type of contraction c motive force g body parts needing stabilization d resistive force during the entire exercise 2 Answer the questions at the end ofthe ab Exercises 1 FT 0 LEG CURL MACHINE 2 FORWARD ARM RAISE DUMBBELL INITIAL RETURN INITIAL RETURN knee a shoulder flexion extension b flexion extension muscle qravitv 0 muscle qravitv qravitv muscle d qravitv muscle knee flexors knee flexors e shoulder exors shoulder extensors concentric eccentric f concentric eccentric ankle hip pelvis trunk upper body 9 wrist finders trunk lower body elbow BENCH PRESS WIDE GRIP INITIAL RETURN INITIAL RETURN shoulder a elbow horizontal adduction horizontal abduction b extension flexion muscle qravitv 0 muscle qravitv qravitv muscle d qravitv muscle shld horiz adduct shld horiz abduct e elbow extensors elbow extensors concentric eccentric f concentric eccentric finqers wrist trunk HANGING LEG RAISES 5 BACK EXTENSIONS INITIAL RETURN INITIAL RETURN hip a lumbarspine flexion extension b extension flexion muscle aravitv 0 muscle aravitv Oravitv muscle d aravitv muscle hip exors hip exors e spinal extensors spinal extensors concentric eccentric f concentric eccentric knee pelvis ankle shoulder g knee pelvis ankle shoulder BACKWARD ARM RAISE DUMBBELL 7 QUADRICEP EXTENSION MACHINE INITIAL RETURN INITIAL RETURN shoulder a knee extension flexion b extension flexion muscle aravitv 0 muscle aravitv Oravitv muscle d aravitv muscle shoulder extensors shoulder extensors e knee extensors knee extensors concentric eccentric f concentric eccentric wrist finders elbow trunk lower bodv g ankle trunk upper bodv LAT PULL DOWN MACHINE INITIAL RETURN INITIAL RETURN shoulder a elbow adduction abduction b flexion extension muscle aravitv 0 muscle aravitv aravitv muscle d aravitv muscle shoulder adductors shoulder adductors e elbow exors elbow flexors concentric eccentric f concentric eccentric wrist finders trunk lower bodv 9 LEG PRESS INITIAL RETURN INITIAL RETURN knee a hi9 extension flexion b extension flexion muscle aravitv 0 muscle aravitv aravitv muscle d aravitv muscle knee extensors knee extensors e hib extensors hib extensors concentric shoulders trunk eccentric FRENCH CURL DUMBBELL o concentric eccentric INITIAL RETURN elbow extension flexion muscle gravitv Oravitv muscle elbow extensors elbow extensors concentric eccentric wrist ngers shoulder trunk Questions 1 N Write a sentence to describe the relationship between the motive force and the type of muscular action used to perform the exercises included in this lab When muscle produces the motive force what role does it play in the movement that is taking place When the motive force is muscle the type of tension developed by the muscle is concentric When the motive force is gravity the type of tension developed by the muscle is eccentric When muscle is the motive force muscle plays the role of mover agonist it causes the movement Write a sentence to describe the relationship between the resistive force and the type of muscular action used to perform the exercises included in this lab When muscle produces the resistive force what role does it play in the movement that is taking place When the resistive force is muscle the tension that the muscle develops is eccentric When the resistive force is gravity the tension developed in the muscle is concentric When muscle is the resistive force muscle controls the movement and is the antagonist To what functional muscle group does a muscle belong if it resists knee flexion knee extensors If it resists hip abduction hip adductors If it can help produce trunk flexion trunk flexors Je 01 0 Relationships between the motive and resistive forces and the types of muscular contraction were noted above Now write a sentence describing the relationship between the functional muscle group and the joint action during concentric muscle action Do the same for eccentric muscle action If concentric tension is being developed then the observed joint action is caused by tension being developed in the functional muscle group that shares the same name If eccentric tension is being developed then the observed joint action is controlled by tension being developed in the functional muscle group that has the opposite name Isometric action often occurs to stabilize or fixate a body segment This occurs under two conditions What are these conditions Give one example of each to demonstrate your understanding Isometric action is developed when muscles act to counteract each other or when muscle acts to counteract some external force EXAMPLE 1 During hanging leg raises 4 the rectus abdominis acts isometricaly to fixate the pelvis and keep it from rotating anteriory due to the concentric action of the hip flexors EXAMPLE 2 During fonvard arm raises 2 the wrist flexors act isometricaly to fixate the wrist and keep it from hyperextending due to the external pull of gravity Select two of the exercises from the lab and identify the functional muscle groups that are acting to stabilize the body parts you have listed for that exercise References Kreighbaum amp Barthels 1990 pp 6873 Illustrations adapted from this text Luttgens Deutsch amp Hamilton 1992 pp 4547 Lecture Notes Exercise Evaluation Instructions Read through the lecture while watching the PowerPoint slide show that accompanies these notes When you see the ltENTERgt prom pt press enter for the slide show so that you can progress through the show in a manner that corresponds to these notes SLIDE 1 Let s take some of the concepts that we have learned this semester and use them to help us evaluate exercises for training and for rehabilitation An exercise analysis serves to enhance the physical training of an individual by evaluating a particular exercise for speci city to a skill or sport for which an individual is training or rehabilitating We have already learned how to use a muscular analysis to help us determine which muscles an exercise is training and how those muscles are being used with regard to agonist function antagonist function neutralization and stabilization Now we want to apply some other concepts that we have learned this semester to exercise evaluation ltENTERgt SLIDE 2 The primary concept that we want to examine in this lecture is that of strength curve similarity This concept helps evaluate whether the principle of progressive overload is being applied appropriately throughout the range of motion in an exercise You have already been introduced to this concept in lab when you analyzed the horizontal and inclined crunch exercise Let s examine this concept in more detail ltENTERgt SLIDE 3 A strength curve is a plot of how maximum strength varies as a function of joint angle We previously used the concept of a strength curve to illustrate the torque output for a single muscle when we examined the biceps brachii and the brachioradialis From a practical perspective strength curves are most useful for muscle groups as opposed to individual muscles Obviously the strength curve for a muscle group is the cumulative effect of the strength curves of the individual muscles that make up the group As we have already seen these curves are in uenced by moment arm and length changes of the muscles Strength curves have been developed for numerous joints in the body Strength can be de ned in a number of ways We will de ne strength as the ability of a muscle group to develop torque against an unyielding resistance in a single contraction of unrestricted duration Before we discuss the concept of strength curve similarity let s review how the strength curve for an individual muscle is determined ltENTERgt SLIDE 4 Because a strength curve is a plot of how maximum strength torque varies as a function of joint angle then a strength curve can easily be generated if understand the factors that affect muscle torque throughout the ROM Earlier in the semester we also identi ed the two factors that affect torque production of a muscle as expressed by the equation TFd The rst factor is the muscle force Anything that affects muscle force output ultimately affects the torque output of that muscle as well ltENTERgt SLIDE 5 There are numerous factors that affect the force output of a muscle but only one of these factors changes predictably throughout the ROM 7 the forcelength relationship Therefore this is the only factor that can be used to predict and explain strength curves for muscles The forcelength relationship of the whole muscle is in uenced by the forcelength relationship of the its two tissue components 7 the muscle tissue and the connective tissue Before we can understand the forcelength relation of the whole muscle let s examine the individual components ltENTERgt SLIDE 6 The diagram on the slide presents the forcelength relationship for the muscle ber Muscle bers produce their greatest force at a length slightly greater than resting length 7 somewhere between 80120 of resting length Most muscles in the body operate within this range of lengths However when the muscle ber is shortened to a length that is less than this force output decreases due to overlap of the myosin and actin laments which reduces the number of crossbridges formed At lengths greater than this range force output of the ber also decreases because the myosin and actin laments are too far apart to allow all CBs to form ltENTERgt SLIDE 7 Therefore on this gure the forcelength relationship for the active component of the muscle organ the muscle tissue is depicted by this curve ltENTERgt ltENTERgt SLIDE 8 This curve ltENTERgt represents the forcelength relationship for the SEC and PEC components of the muscle These components develop tension when stretched due to elastic properties which assists to stop overlengthening of the muscles The force produced by CT depends on velocity of stretch A greater velocity will result in greater force production by the CT Force of CT varies across muscles due to differences in CT s resting lengths and the amount of CT in each muscle The SEC and PEC contribute 47 of passive torque produced in the midrange of movement The other half is produced by the joint capsule Because the SEC and PEC produce passive force they can protect joint by resisting at the ends of the ROM when muscle activation is delayed especially with an uneXpected perturbation ltENTERgt SLIDE 9 This curve ltENTERgt represents the total force output of the muscle organ as a function of length At short lengths the force produced in the muscle is due only to the active muscle contraction This force is then transferred to the SEC which then transfers the force to the bone At eXtreme lengths of the muscle the force in the muscle is almost exclusively elastic or passive Total force output is maximized at longer muscle lengths due to the elastic contribution but activation and initiation of movement is difficult because the active component has very low force producing potential ltENTERgt SLIDE 10 Now let s consider the practical application for this forcelength relationship The shortest length at which a muscle can produce active force is 60 of resting length Therefore a whole muscle can produce force and shorten to half its resting length not including its tendons The longest length at which a muscle can actively produce force is 15X its resting length or 160 of resting length Therefore the range of lengths that a muscle can actively produce force is 60l60 Passive force in the SEC and PEC is developed once a muscle is stretched beyond its resting length developing force at lengths up to 200 of resting length At lengths gt160 force production is entirely passive Maximum force produced by a muscle is the sum of the active and passive components and is produced at 110120 of resting length Most single joint muscles operate well within this range of 60160 of resting length ltENTERgt SLIDE 11 However multijoint muscles muscles that span more than one joint are not constrained to operate within this range They do not shorten below 60 but are much more susceptible to being placed in very shortened positions where force output can be severely compromised Multijoint muscles are also able to reach lengths of gt160 where they can develop greater force than they would be able to with the active tissue Therefore multijoint muscles have unique advantages and disadvantages in their contribution to human movement We will discuss these a little later ltENTERgt SLIDE 12 The second factor that affects torque production of a muscle as eXpressed by the equation TFd is moment arm The moment arm is determined by where the force is applied in the case of the muscle that would be its attachment site and the angle at which the force is applied in the case of muscle that would be its insertion angle Let s now review these two factors as they apply to the case of muscle torque ltENTERgt SLIDE 13 There are 4 points that I want to make with regard to the point of force application muscle attachment 1 Theoretically the further away from the axis of rotation the joint the muscle attaches the larger the moment arm can potentially be However in the case of muscles the further away the muscle attaches from the ioint the smaller the insertion angle for the muscle must become because of the longitudinal nature of our segments So the principle expressed in 1 does not typically hold up for muscle 2 V W V orce Unfortunately from a performance standpoint we are not able to alter muscle attachment sites so we are stuck with what we are born with However it is important that we understand that differences between people with regard to muscle torque output strength may be due in part to differences in attachment sites of the muscles In other words two people may have a biceps brachii with similar physiological neural and biomechanical characteristics and the difference in strength between the two people is simply due to structure In this case all the training in the world will not cause the one person to be stronger than the other person ltENTERgt 4 V SLIDE 14 There are 5 points that I want to make with regard to the angle of force application muscle insertion angle The closer the muscle insertion angle is to 90 degrees the larger the moment arm is 2 However most muscles in the body have muscle insertion angles that are less than 45 degrees so they are not designed to be very efficient with regard to torque production Muscle insertion angles are not typically constant for a given muscle through the ROM at a joint therefore muscle torque output or strength for a given muscle changes through the ROM Again we typically are not able to alter muscle insertion angles so we are stuck with what we are born with There is some evidence that insertion angles may change with hypertrophy but to what extent this occurs and what impact it ultimately has on function remains to be seen However it is important that we understand that differences between people with regard to muscle torque output strength may be due in part to differences in muscle insertion angles Let s now look at a couple of examples in the body to help us understand these points ltENTERgt V 3 V 4 V U V SLIDE 15 We will once again examine the case of the biceps brachii Let s rst remind ourselves of where the muscle insertion angle is Do you remember the de nition The muscle insertion angle is the proximal angle formed between the line of pull of the muscle and the mechanical axis of the segment to which the muscle attaches In the rst diagram the muscle insertion angle would be 30 For our discussion let s also de ne the joint angle As we learned at the beginning of the semester there are many different ways to identify segmental angles For the purposes of this discussion we will de ne the joint angle as the interior relative angle between the upper arm and the forearm In the rst diagram the joint angle as we have de ned it is 150 If you do not remember the de nition of a relative angle you may want to refresh your memory from the earlier lecture on Basic Kinematic Concepts Now can you draw a force vector and estimate the joint angle amp muscle insertion angle for each of the diagrams ltENTERgt SLIDE 16 Now that we have created a model for the biceps brachii through the ROM let s examine how the moment arm changes through this ROM We will then identify the key relationships for muscle forces in the body that will help us better understand their rotational function Can you draw in the moment arm for the biceps brachii force vector in each of the diagrams It has actually already been done for you but let s highlight it in red so that it is easier to see ltENTERgt Where in the ROM is the moment arm the greatest You should be able to tell that the moment arm is the largest in the middle diagram where the joint angle is 90 and the muscle insertion angle is 90 The angle that is important here is the MIA Just a few moments ago I reminded you of a point that you have learned several times this semester The closer the muscle insertion angle is to 90 the larger the moment arm is or the moment arm will be the largest when the force is applied perpendicular to the rotating body Therefore the rst relationship we want to identify is that the moment arm for a muscle is the largest when the MIA is 90 While this relationship is fundamental it does not do us much practical good if we do not know where this occurs in the ROM For the biceps brachii the MIA happens to be 90 when the joint angle is 90 This relationship is not necessarily true for every muscle While the fundamental relationship the closer the muscle insertion angle is to 90 the larger the moment arm is is true for all muscles regardless of where they are in the body the relationship between joint angle and MIA must be de ned for each muscle For the biceps brachii it just so happens that the moment arm is greatest at a joint angle of 90 and gets smaller as you move towards full exion or full extension because the muscle insertion angle is moving away from 90 Therefore as illustrated in these diagrams the strength torque output of the biceps brachii should be greatest at a joint angle of 90 SLIDE 17 However torque output is dependent on two things force and moment arm We have examined only the moment arm changes through the ROM Is there anything that would cause the force output of the muscle to change through the ROM as well and if so how would that force change Well of the seven factors that affect force output of a muscle the only one that will change in a systematic manner through the ROM is length Based on what we ve learned where would the length of the muscle be optimal for producing muscle force Well length for single joint muscles is optimal around the midpoint in the ROM which happens to be 90 in this example We know that the biceps brachii is a multijoint muscle but since the shoulder is in a fairly midrange position not too exed not too hyperextended we can assume that the biceps length will be optimal in the middle of the ROM You should begin to see that the position of the shoulder joint could have an in uence on the strength of the biceps brachii at the elbow We will discuss that a little later ltENTERgt SLIDE 18 So if we were to plot a torqueangle curve to illustrate how the torque output of the biceps brachii changes through the ROM we would plot something like this ltENTERgt Biceps brachii strength peaks at a joint angle of 90 because both the moment arm and the length of the muscle are optimal at 90 for torque output ltENTERgt SLIDE 19 Let s examine this relationship for another muscle Can you draw in a force vector to represent the pull of the brachioradialis on the forearm in each of the diagrams Where does the brachioradialis attach distally and how does it pull at the distal attachment Well it attaches on the styloid process of the radius and tends to pull the arm towards its proximal attachment on the lateral supracondylar ridge of the humerus ltENTERgt Can you draw the others ltENTERgt Now can you resolve the force vector for each diagram into its parallel and perpendicular components ltENTERgt From these diagrams can you tell me how the torque output of the brachioradialis changes through the ROM It does not look like the MIA nor the perpendicular component change much through the ROM so the moment arm would not change much either How about the effect of the length changes in the muscle on force output through the ROM Again the length would be optimal during the middle of the ROM especially since this muscle is a single joint muscle Therefore torque output should be a little higher through the middle of the ROM Can you summarize this in a torqueangle curve ltENTERgt SLIDE 20 The shape would be somewhat similar to the biceps brachii but the magnitude would be smaller since the size of the brachioradialis is smaller and the curve would be atter since there is no apparent change in the moment arm of this muscle through the ROM Earlier I told you that most muscles in the body have muscle insertion angles that are less than 45 degrees so they are not designed to be very efficient with regard to torque production The brachioradialis is an example of most muscles in the body the biceps brachii is not The MIA of the brachioradialis is closer to 20 and has about a 510 range through the ROM The changes in MIA for this muscle may not seem signi cant but there are numerous examples in the body of where changes in the MIA of this magnitude have signi cant functional implications ltENTERgt SLIDE 21 In summary the torque output of an individual muscle varies across the ROM of a joint The variation depends on the forcelength changes of the muscle and on the moment arm MIA changes of the muscle This variation differs across muscles and joints Now let s turn back to our discussion of strength curve similarity as a criterion in exercise evaluation ltENTERgt SLIDE 22 Remember that we stated earlier that from a practical perspective strength curves are most useful for muscle groups as opposed to individual muscles Obviously the strength curve for a muscle group is the cumulative effect of the strength curves of the individual muscles that make up the group As we have already seen these curves are in uenced by moment arm and length changes of the muscles Strength curves have been developed for numerous joints in the body On the slide is a strength curve for the shoulder exors Zero degrees indicates anatomical position According to the curve the shoulder exors have the greatest strength at zero degrees and get progressively weaker through the ROM This decrease is due to the way that the length of the muscles and the MIAs moment arms are changing through the ROM These strength curves are very useful in evaluating exercise effectiveness Let s look at an example of how we can use this curve to do this ltENTERgt SLIDE 23 On the slide are three diagrams that depict the concentric phase of the shoulder exor exercise To determine one aspect of exercise effectiveness we need to develop a torque angle curve for the resistive force during the exercise In this case we know that the resistive force is the same throughout the exercise because the weight which is the resistive force of the dumbbell does not change Therefore any changes in torque through out the ROM will be due to changes in the moment arm Can you draw in the moment arm for the dumbbell in each of the 3 diagrams To do this draw in the axis of rotation the line of force and nally the moment arm ltENTERgt From these diagrams you can see that the resistive torque is zero at the beginning of the exercise increases as the arm moves to 90 of exion and then decreases as it continues from 90 towards 180 of exion ltENTERgt SLIDE 24 If we superimpose the torqueangle curve created by the resistive force through the ROM onto the strength curve of the shoulder exors we can see that they do not match up very well During the rst 90 of the ROM the resistance torque of the dumbbell is increasing as the strength of the exors decreases Therefore it is impossible to overload the shoulder exors appropriately through the rst half of the ROM There will be only one point in the ROM during which the overload is sufficient This occurs at the point where the lines intersect ltENTERgt Before this point there is no overload 7 the exercise is too dif cult Beyond this point the overload quickly exceeds the capability of the muscle and the individual will have to stop or they will cheat to continue through the ROM to a point where the muscles can once again move the resistive load This point is usually called the sticking point in the exercise ltENTERgt SLIDE 25 You can use a heavier or lighter dumbbell to shift this curve On this slide a heavier dumbbell has been used to shift the magnitude of the curve upward but no change in the shape of the curve occurs Therefore there is still only one point in the ROM ltENTERgt where the overload is suf cient for the muscle In this case it occurs in the beginning of the ROM The sticking point in this case would be earlier in the ROM ltENTERgt SLIDE 26 Let s go back to our original diagram When the curves run somewhat parallel to each other as they do in the latter half of the ROM ltENTERgt then the exercise appropriately overloads the muscle and the individual is able to work the muscle appropriately through this portion of the ROM Therefore this exercise is not very effective for training the shoulder exors in the rst 90 but has better effectiveness for training the shoulder exors through the last 90 ltENTERgt SLIDE 27 What happens when we have the person perform the exercise in a supine position lying on his back Well the moment arm is now largest at the beginning of the exercise and decreases as he exes to 90 After 90 the moment arm increases again but now the dumbbell is exerting a exor torque on the shoulder so it is no longer effective in training the shoulder exors 7 instead it would do the work for them and the shoulder extensors would have to resist the movement eccentrically Let s look at this using the torqueangle diagram ltENTERgt SLIDE 28 Now the resistive and muscle curves are parallel to each other indicating that from 0 to 90 this exercise can appropriately overload the shoulder exors provided the right dumbbell is selected This type of evaluation is the basis for the development of what are called variable resistance machines Variable resistance weight machines many of which are on the market are designed using special cams and pulley systems to match the resistive load to the strength curve of the muscle There is much debate about the value of this approach but it is certainly one factor that should be considered when evaluating exercises and selecting exercises for use in training and rehabilitation programs ltENTERgt SLIDE 29 In addition to using strength curve similarity to evaluate the effectiveness of exercises other biomechanical factors should be considered as well The progressive overload principle is the most important principle to adhere to with regard to muscular training Second but almost equal in importance is the principle of speci city which states that the exercise should be speci c to the skill or movement for which you are training If your primary goal for muscular training is for general health and physical tness then the speci city principle from a biomechanical standpoint is not so important However if training for performance enhancement in a particular skill speci city of training biomechanically is extremely important This speci city should be addressed in several ways As we have already stated speci city of muscle roles should also be considered Does the exercise use the muscles in the same way that they are used in the sport movement or skill In other words are the stabilizers the neutralizers the agonists and the antagonists being trained in the manner that they will be used in the sport or skill A muscular analysis helps us make this determination Is the ROM used in the exercise similar to the ROM used in the sport or skill This is important because using a similar ROM trains the muscle in a speci c forcelength range and allows the muscle to develop its force capabilities at lengths that are speci c to the skill Is the movement or contractile speed used in the exercise similar to the speeds used in the sport or skill Again this allows the performer to train on the portion of the force velocity curve that is important to the skill It also allows the user to train speci c to the muscular power demands muscle force produced at a given speed of the skill Again not all of these are critical for general physical tness though it is important to make sure that stabilizing and neutralizing muscles are being trained appropriately Whenever you select or prescribe exercise for an individual you should keep these factors in mind ltENTERgt SLIDE 30 0 Exercise evaluation is important to ensure appropriate physical training whether for performance enhancement injury prevention or injury rehabilitation ltENTERgt Exercise evaluation should focus on the progressive overload principle and the speci city principle ltENTERgt The importance of each principle depends on the goals of the exercise program Lecture Notes Vector Algebra Instructions Read through the lecture while watching the PowerPoint slide show that accompanies these notes When you see the ltENTERgt prom pt press enter for the slide show so that you can progress through the show in a manner that corresponds to these notes SLIDE 1 As we continue our study of biomechanics the next topic that we want to cover is vector algebra The word vector often instills fear in students in this course So I want to take a moment to explain to you Why we are going to learn vector algebra You already understand that one of our primary objectives in this course is to learn how and Why the body moves To understand that we are going to spend some time talking about forces Force is what is called a vector quantity so we have to learn how to represent and manipulate vector quantities The representation and manipulation of vector quantities falls under the realm of vector algebra We will spend two days of lecture on vector algebra At the end of the lecture time you will better understand forces and Why many of the trainingteaching techniques that you use work If it is any comfort our focus will be primarily qualitative 7 we will not learn the mathematical techniques of vector algebra So focus on the concepts and the application of those concepts as you learn this material ltENTERgt SLIDE 2 I just want to remind you where we are in the course outline We are still in Topic 11 7 Biomechanical Concepts Related to Human Movement ltENTERgt SLIDE 3 As we study the subdiscipline of biomechanics we are covering 3 main topics basic kinematic concepts vector algebra and basic kinetic concepts We are on our second topic This topic is timely as we get ready to study muscle attachments and actions in our lab sessions Understanding vectors will help you better understand the importance of muscle attachment sites in understanding the joint actions caused by individual muscle contractions Keep this application in mind as you learn this material ltENTERgt SLIDE 4 In the subtopic Vector Algebra we will cover 3 areas Introductory Concepts Vector Composition and Vector Resolution ltENTERgt SLIDE 5 Let s begin with Introductory Concepts ltENTERgt SLIDE 6 In this area we will learn relevant de nitions learn how to represent vector quantities so that we can analyze them and learn speci cally how to represent muscle force vectors ltENTERgt SLIDE 7 What is vector algebra Vector algebra is the process by which we add subtract multiply and divide vector quantities But what kinds of quantities are vector quantities and Why do we need a special process for dealing with them For our purposes we can divide physical quantities in the world into two major types vector quantities and scalar quantities To understand what a vector quantity is let s rst de ne scalar quantity ltENTERgt A scalar quantity is a physical quantity that can be completely de ned or expressed in terms of magnitude When you tell me how much magnitude there is you have expressed all the pertinent information about the quantity An example of a scalar quantity is mass If you state that an object has 50 kg of mass you have provided all the pertinent information about the object in terms of its mass This is not the case with vector quantities ltENTERgt A vector quantity is a physical quantity that is described in terms of both magnitude and direction Because we have to be concerned with direction we cannot simply add and subtract vector quantities in the same way that we do with scalar quantities An example of a vector quantity is force If two forces of 50 N in magnitude act on an object at the same time but in opposite directions then the net force that acts on the object is zero The directions cancel each other out and the forces have no effect on the motion of the object The forces do deform the object but that is a matter of study for deformable body mechanics Therefore we cannot simply add the magnitudes of the forces together but we must also consider the directions of the forces as well There are numerous vector quantities in the physical world but we will deal primarily with forces and torques this semester ltENTERgt SLIDE 8 The second area that we want to discuss under Introductory Concepts is Vector Representation To be able to deal with vector quantities conceptually or mathematically we must have a way to represent them that depicts both their magnitude and their direction Mathematically we use numerals to indicate the magnitude and we use signs minus signs and angles to depict their direction For example if we use the standard linear system that was introduced in Basic Kinematic Concepts then we would state that the person moved 50 m to indicate that a person was displaced 50 m to the left backward or in the x direction ltENTERgt to the left z direction ltENTERgt or downward y direction ltENTERgt Obviously we would have to know which of the three axes we were describing motion about to be able to interpret the data If the person did not move along one of the major axes but rather at an angle we might state that the person had displaced 50 min a direction of 40 degrees to indicate a CW rotation ltENTERgt SLIDE 9 Another way to represent vector quantities is graphically with an arrow ltENTERgt By using arrows to represent vector quantities we can draw diagrams of movement situations to help us systematically analyze the movement This is especially useful for analyzing forces ltENTERgt The arrow must depict both characteristics of the vector quantity 7 the magnitude and the direction ltENTERgt The magnitude of the vector quantity is depicted by the length of the arrow To be accurate in depicting magnitude you would have to set up a conversion scale much like what is used in road maps For example if you state that a 1 inch vector represents 50 N of force then you would draw a 2 inch vector to represent a 100 N force While we will not formally scale vectors this semester you should be comfortable with this concept so that you can estimate forces from vectors that are given to you or so that you can make general representations of force magnitudes when you are drawing and comparing two forces ltENTERgt The second characteristic 7 the direction 7 is represented by the arrow head of the vector Obviously this will be placed on the end of the vector that indicates the direction associated with the quantity ltENTERgt Because we will be dealing with force vectors quite a bit this semester I want to introduce two other characteristics of forces that should also be depicted on vectors ltENTERgt First is the point of force application When drawing a vector to represent a force the tail of the vector should be placed on the point of force application ltENTERgt Second a dashed line that runs towards infinity along the line of the vector should also be drawn to indicate the line of force for the force being analyzed This is also sometimes called the line of pull if the force being analyzed is a pulling force like a muscle force The importance of this characteristic will be explained better when we discuss torque in our next lecture Now let s look at some examples of vector representation ltENTERgt SLIDE 10 In the example depicted on the slide a vector is used to depict the velocity of the ball at one instant in time The magnitude is indicated by the length of the vector although we don t have a conversion scale available to us The direction could be stated as 30 degrees The quantity being depicted in this example is not force Why do we know that this is not a force vector ltENTERgt In the second example a vector is again being used to depict the velocity of the shot at one instant in time What would be the direction of this vector ltENTERgt SLIDE 11 On this slide the vector is being used to indicate the weight or gravity acting on the person walking up the hill The direction is down vertical since gravity always acts toward the center of the earth ltENTERgt SLIDE 12 Now let s turn our attention to using vectors to represent muscle forces since we will talk a lot about muscles this semester As with any other force a muscle force vector should represent the four characteristics of the force Let s start with point of force application ltENTERgt Where do you think you need to place the tail of the vector to accurately depict the muscle s point of force application Most students correctly answer at the point of attachment but which point of attachment We have already learned that when a muscle contracts it pulls towards its center exerting a force on all the bones that it attaches to So where do we place the vector Well it depends on which bone s motion you want to analyze In other words before you start you need to de ne your system What system s motion do you want to analyze Typically with muscles we assume that the distal bone is the one that will move and therefore we put the tail on the distal attachment site The distal bone is the one that usually moves because it is usually the one that is more free to move 7 in other words the magnitude of the m forces acting on the distal end are usually less than the magnitude of the other forces acting on the proximal end so the muscle s force is more able to overcome the other forces and cause movement More about this later For now we will assume the point of application is on the distal end but I want you to understand that the other end could move as well My purpose right now is to help you understand why muscles cause the joint actions that they do so we will keep it simple and assume the distal end is the moving end If I ask you to draw a muscle force vector on the rst exam you should assume the distal end is the moving end ltENTERgt What about the direction of the muscle force vector Most students initially answer towards the proximal attachment However this answer is not correct The direction that the force of a muscle acts will be in the direction that the muscle bers or the tendon bers come off the bone initially That is the key As we will see in an example in a minute the initial direction of the muscle or tendon bers is not always toward the other attachment point ltENTERgt The third characteristic is magnitude Again the length of the vector indicates the magnitude of the muscle force While you will not be asked to formally scale any vectors you should be able to estimate magnitudes of forces if given the appropriate information I will give you some examples of this later ltENTERgt The last characteristic is the line of force You should get in the habit of drawing this although its signi cance may not be clear We will talk more about this signi cance later Now let s look at some examples of drawing muscle force vectors ltENTERgt SLIDE 13 Let s start with the biceps brachii If we assume that the distal bone is the moving bone then the tail should be placed on the distal attachment of the muscle to represent the point of force application For the biceps brachii the distal attachment is the radial tuberosity ltENTERgt If you look at the picture you can get a general idea of the direction that the tendon bers run from this distal attachment so our vector should run in this general direction Can you draw the force vector ltENTERgt Did you get it right Now to illustrate the point that either end can move let s draw a force vector to represent the pull of the biceps brachii on the proximal bone Do you know what the proximal attachment of the biceps brachii is It actually has 2 7 the coracoid process and the supraglenoid tubercle of the scapula Did you know that the biceps brachii crossed the shoulder joint and could cause shoulder joint motion The only proximal attachment that we can see is on the diagram is the coracoid process so we will use this one for our example ltENTERgt The tail of the vector should be placed here Can you gure out what direction the vector should be drawn in ltENTERgt Did you get it right Notice that the two vectors do not directly oppose each other in direction even though they represent the force output of the same muscle This is because the direction is determined by the direction of the bers right at the attachment site not the direction of the bers in the belly of the muscle Also note that we would use the rst vector if we wanted to analyze the biceps brachii s effect on the radius or forearm and we would use the second vector if we wanted to analyze the biceps brachii s effect on the scapula Again you will assume unless told otherwise that the moving bone or the bone of interest is the distal bone ltENTERgt SLIDE 14 Next let s draw in a force vector to represent the pull of the brachialis Since we will assume that the distal bone is the moving bone then the tail should be placed on the distal attachment of the muscle to represent the point of force application Do you know where the distal attachment of the brachialis is It is on the coronoid process of the ulna ltENTERgt If you look at the picture you can get a general idea of the direction that the tendon bers run from this distal attachment so our vector should run in this general direction Can you draw the force vector ltENTERgt Did you get it right ltENTERgt SLIDE 15 Next let s draw in a force vector to represent the pull of the deltoid muscle Again for our purposes the tail should be placed on the distal attachment of the muscle to represent the point of force application Do you know where the distal attachment of the deltoid is It is on the deltoid tuberosity of the humerus ltENTERgt Although you can t see the actual attachment site on this picture you can get a general idea of the direction that the muscletendon bers run from this distal attachment if you can pick out which muscle is the deltoid muscle Do you know which one it is Our vector should run in the general direction of these bers at the distal attachment site Can you draw the force vector ltENTERgt Did you get it right Here is a good example of a muscle that does not pull towards its proximal attachment from its distal end Rather it pulls outward from the body This fact is critical when trying to understand the torque that a muscle produces and the joint actions that it causes We will learn more about torque production in our next lecture ltENTERgt SLIDE 16 Next let s draw in a force vector to represent the pull of the pectoralis major Where is the distal attachment of the pectoralis major It is on the lateral lip of the bicipital or intertubercular groove ltENTERgt Can you draw the force vector ltENTERgt Did you get it right ltENTERgt SLIDE 17 I want to use this muscle to make another point You may have heard people refer to the upper and lower pecs or the stemal and clavicular pecs Well the reason that people use those terms is because the pectoralis major can function as two separate muscles even though structurally it is bundled into one organ For now we won t discuss why that is the case but let s draw force vectors to represent the two functional units of this muscle At the distal attachment the bers do tend to run in several directions and if we divide the muscle into two parts based on its proximal attachment ltENTERgt we might think of the muscle as two separate muscles as shown on the slide ltENTERgt Now how would you draw force vectors to represent each of the components ltENTERgt Did you get it right ltENTERgt SLIDE 18 Finally let s look at one last muscle 7 the pectoralis minor Which end of the pectoralis minor is considered the more movable end The coracoid process of the scapula ltENTERgt Can you draw the force vector ltENTERgt Did you get it right When you consider the reverse action of this muscle it is also a respiration muscle If the scapula is xed then the pectoralis minor can pull on the rib cage and cause it to expand assisting in respiration ltENTERgt SLIDE 19 Now that you understand what vectors are and how to represent vector quantities graphically let s turn our discussion to how to manipulate vectors so that we can add amp subtract vector quantities The rst process we will discuss is vector composition ltENTERgt SLIDE 20 Vector composition is the process of determining a resultant vector by adding two or more vectors together ltENTERgt The new vector is called the resultant vector In the case of forces we may call it the resultant force or the net force Vector composition can be accomplished mathematically but our focus in this course will be on the graphical method of vector composition If you understand this concept then you will understand how altering the magnitude andor direction of one force within a system can completely change the net force that acts on the system ltENTERgt SLIDE 21 One graphical method of vector composition is sometimes called chaining or the headtotail method There are other graphical methods as well but this method can be used in any situation with as many vectors as presented During the next few slides I will walk you through the steps to take for this method We ll use two examples to illustrate as shown on the slide In the rst example we will add vectors P amp Q to determine the resultant In the second example we will multiply vector a times 3 which is another way of saying we will add a a a ltENTERgt The rst step is to select a vector to start with and draw it maintaining direction and magnitude This is shown in example 1 ltENTERgt and example 2 ltENTERgt It does not matter which vector you start with as I will show you in another example in a few minutes ltENTERgt SLIDE 22 The second step is to chain the tail of the next vector to the head of the rst maintaining direction and magnitude from original vector Again this is shown in example 1 ltENTERgt and example 2 ltENTERgt The two keys to this step are l the Q of the 2nd vector must connect to the w of the 1st thus the headtotail method and 2 you must maintain direction and magnitude of the vectors as you chain them ltENTERgt SLIDE 23 The third step is to continue to chain vectors in this manner until they are all chained This is shown in example 2 ltENTERgt There are no additional vectors to chain in example 1 You can do this for as many vectors as you have Again you must connect the vectors headto tail and maintain direction and magnitude of each vector ltENTERgt SLIDE 24 Once you have chained all the vectors together the 4th step is to draw in the resultant vector by connecting the tail of the rst vector in the chain to the head of the last vector in the chain This is shown for example 1 ltENTERgt and example 2 ltENTERgt ltENTERgt SLIDE 25 The last step is to gure out which end of the resultant vector is the head so that you indicate the direction of the resultant vector appropriately This is where the headtotail technique changes In this step the head of the resultant vector will be the end that is connected to the head of the last vector In other words headtohead This is shown in example 1 ltENTERgt and example 2 ltENTERgt It is very important that you get this step correct or you will end up with a wrong answer You will have the magnitude correct but you will have the direction wrong ltENTERgt SLIDE 26 If I tell you that vector P has a magnitude of 50 N can you estimate the magnitude of the resultant vector in example 1 Maybe 110120 N Can you see that ltENTERgt On the next 3 slides I want to make three other points about vector composition ltENTERgt SLIDE 27 As I told you earlier it does not matter which vector you start with nor does it matter what order you chain the vectors in The key is that you connect your vectors headtotail while chaining them and that you maintain magnitude and direction As an example let s chain the 4 vectors shown in the gure in a different order starting with a different vector ltENTERgt This time I started with C then B then A and nally D Notice that for each vector I maintained both magnitude and direction Can you draw in the resultant vector Try it and then when you are ready press the space bar to see if you got it right ltENTERgt Notice that the resultant R for this order of chaining is the same in magnitude and direction as the resultant R in the rst order of chaining It doesn t matter what order you use ltENTERgt If A50 N of force what would you estimate the magnitude of R to be Maybe 100 N Can you see that ltENTERgt How would you state the direction of R Well if we use an absolute reference system where the right horizontal is 0 degrees we would say that R is 100 N at about 70 degrees ltENTERgt Again it is important that you know what reference system is being used Relative systems are used primarily for body segment positions and displacements Otherwise an absolute system is the one usually used ltENTERgt SLIDE 28 Point 2 The same R can be achieved from an in nite combination of vectors In the three examples shown on the slide the same R is shown as a resultant of three different combinations of vectors This is true in human movement as well when trying to analyze forces The same resultant force can be achieved by the body with an in nite combination of force applications In human movement we can get the right outcome resultant force with numerous combinations of force applications 7 some of which may be safe and some which may be unsafe That is one reason that you should consider the process or technique one uses to produce the force rather than just consider the outcome Good outcomes can be accomplished with poor and unsafe techniques ltENTERgt SLIDE 29 Point 3 The magnitude of R is dependent on the direction of the components not just their magnitude In the three examples shown on the slide vectors F and P have the same magnitude in each example However the magnitude of the resultant vector R is different in each of the examples because the directions of F and P change Don t forget that magnitude of R is dependent on the direction as well as the 39 39 of the l vectors 39 that is why we have to treat vector quantities differently ltENTERgt If F300 N of force what would you estimate the magnitude of R to be Well in 1 it would be N650 N in 2 it would be N500 N and in 3 it would be N350 N ltENTERgt How would you state the direction of R Using an absolute system where the right horizontal is 0 degrees and counter clockwise is considered the positive direction in l the direction would be 280 in 2 the direction would be 260 and in 3 the direction would be 270 Let s look at a couple of other examples of vector composition ltENTERgt SLIDE 30 Do you understand this example Ask me questions if you don t ltENTERgt SLIDE 31 Do you understand this example ltENTERgt If Q50 N of force what would you estimate the magnitude of R to be ltENTERgt How would you state the direction of R Would you use an absolute or a relative system Ask me questions if you are having trouble answering any of these questions ltENTERgt SLIDE 32 Do you understand this example This should look somewhat familiar from earlier in the lecture ltENTERgt SLIDE 33 The last area we want to cover under the topic of vector algebra is Vector Resolution ltENTERgt SLIDE 34 Vector resolution is taking a resultant vector and breaking it down into 2 or more component vectors ltENTERgt SLIDE 35 Conceptually it is similar to the process in regular algebra where you might try to nd a combination of addends that add back up to some given sum For example for the number 8 four different combinations of addends are shown that add back up to the number 8 You can see that there is an in nite number of addend combinations that will add back up to 8 and if you wanted to you could spend your whole lifetime listing these combinations In vector algebra we do not use the term addends but rather we use the term components ltENTERgt For any given R resultant vector there is an in nite number of combinations of component vectors that add back up to R ltENTERgt On the slide you see three examples of component combinations that add back up to the pink R Note that the pink R is the same vector in all three examples 7 the same magnitude and the same direction But I have presented three different ways that you could resolve break down the vector in pairs of components that are valid components of R By valid I mean that they would add back up to R vector composition These examples only show pairs of vector components 7 you could come up with combinations of 3 4 5 etc vector components that add back up to R much like what we showed for the number 8 ltENTERgt SLIDE 36 The question is How do we know which components to resolve for Which combination do we try to obtain In other words for the number 8 how do we know whether we are after 44 or 1322 Well we are going to keep things simple in this class when it comes to vector resolution ltENTERgt When I ask you to resolve a resultant vector you will always deal in pairs of vectors or in two dimensions We will discuss resolution in three dimensions and I want you to be able to think about it this way but the actual skill of vector resolution will only involve pairs of vectors not combinations of 3 4 5 etc vectors ltENTERgt Second for the pairs that you work with you will only resolve for vectors that are orthogonal to each other Orthogonal means at right angles or perpendicular ltENTERgt In the pictures shown on the slide both represent combination pairs that are components of R the pink vector However only the bottom represents a combination pair that is orthogonal to each other Again for any given R there are numerous combination pairs that are orthogonal to each other ltENTERgt For example this third combination pair represents a second orthogonal pair that adds back up to R So how do we know which orthogonal pairs to resolve for ltENTERgt SLIDE 37 In many cases the orthogonal pair that we will resolve for is the orthogonal pair that lies along the horizontal and vertical axes ltENTERgt An example of this is shown in the diagram The resultant force that the foot exerts into the ground is labeled 0 This force has been resolved into X and Y horizontal and vertical components Can you think why we might want to do this Can you pick out the orthogonal combination on the previous slide ltENTERgt There will be exceptions to this rule 7 in other words there will be times when we do not necessarily want to resolve for horizontal and vertical components Resolution is always done so that we can get more meaningful information so you must determine what is meaningful for a given situation For most of these exceptions it will be obvious to you the reference that you should use to create your orthogonal resolution If it is not obvious then I will provide you with some guidelines for the resolution This will be true especially for muscles and we will do some examples in a few moments We will also talk about one other exception to this rule But before we talk about the exceptions let s nd out how to resolve vectors graphically using horizontal and vertical combination pairs ltENTERgt SLIDE 38 Graphical resolution of vectors is fairly simple All you have to do is draw a rectangle around R which includes R as the diagonal of the rectangle The idea of a rectangle implies orthogonal combination pairs Obviously if you are using the horizontal and vertical as your reference then one side of the rectangle must lie on the horizontal axis and one side of your rectangle must lie on the vertical axis The direction of these components is determined by the direction of the resultant vector Remember in the end your rectangle must enclose your resultant vector and the resultant vector must form the diagonal of the rectangle Two examples have been done on the slide for you ltENTERgt SLIDE 39 Can you resolve this vector into its horizontal and vertical components Try to do it and then move through the slide show to see if you did it correctly ltENTERgt ltENTERgt If V is 200 ms what is the magnitude ofVV and Vh VV is 100 ms and Vh is 150 ms Can you see that ltENTERgt Why might you want to do this Well in this case how much of the velocity vector is vertical indicates the hang time and distance of the punt while the horizontal velocity vector indicates horizontal distance covered by the punt Depending on the situation in the football game different combinations of horizontal and vertical velocity are necessary Analysis of the punt in a given situation might help us alter the punter s technique in a way that is more favorable for the given situation For example if you wanted more hang time how might you alter the technique of the punter Have himher contact the ball later in the ROM when the foot is higher off the ground Note that for any combination of horizontal and vertical velocity the magnitude of the resultant velocity might stay the same The only thing that might change is the direction of the resultant and thus the magnitudes of the components ltENTERgt SLIDE 40 Can you resolve this vector into its horizontal and vertical components Try to do it and then move through the slide show to see if you did it correctly ltENTERgt ltENTERgt SLIDE 41 Now let s move to resolution of muscle force vectors Our focus today will be on learning the technique of vector resolution for muscles While we will discuss the application of this process why we want to learn to do this on the rst exam you will be tested only on your ability to perform the technique The application will come later ltENTERgt As I told you earlier the direction of resolution should be in the direction of interest In the previous examples the reason we used a horizontal and vertical reference is because those were the directions that would provide the most meaningful information to us The same is true for muscles In the case of the shoulder girdle horizontal and vertical directions are still the directions that provide the most meaningful information to us because these are the directions that are associated with the linear scapular movements that we have learned The vertical linear motions are elevation and depression and the horizontal linear motions are protraction and retraction Notice that I have used the word linear here That is because resolution provides us information primarily about linear motions The scapula does move angularly upward amp downward rotation but resolution will not be used to give us insight into that We will talk about angular motions created by muscle forces in our next lecture So can you resolve this muscle s force vector into horizontal and vertical components ltENTERgt SLIDE 42 Well the steps for resolution of shoulder girdle vectors are listed on the slide 1 Draw line of pull for the muscle force Can you do that using the guidelines that were presented earlier in the lecture ltENTERgt 2 Draw vertical component Can you do this ltENTERgt 3 Draw horizontal component Can you do this It doesn t really matter whether you draw the horizontal or vertical component rst but my experience has been that most students nd it easier to draw the vertical rst Do whichever works best for you 4 Complete the rectangle to assure proper magnitudes of components Can you do this ltENTERgt SLIDE 43 What are the linear effects produced by this muscle From the component vectors you should be able to tell that this muscle will elevate and retract the scapula Is it a stronger retractor or a stronger elevator Since the horizontal retraction component is larger than the vertical elevator component it is a stronger retractor Do you know what muscle this is Can you determine how the function of this muscle would change if the person had broader shoulders 7 in other words if the scapula were further away from the vertebral column Let s take a moment to explore this ltENTERgt SLIDE 44 If we moved the scapula away from the vertebral column ltENTERgt and then drew in the muscle and its force vector ltENTERgt we can see that the force vector pulls a little more horizontally than before ltENTERgt To make the difference more evident let s resolve the new muscle vector and compare it to the previous components ltENTERgt The yellow represents the new components and the blue represents the old components You can see that the retraction component is a little larger and the elevation component is a little smaller So all other things being equal a person with broader shoulders would have stronger retraction capability than a person with narrower shoulders Of course broader shoulders would change other muscle lines of pull as well so we cannot make a de nitive statement here However the point that I want you to understand is that small structural differences have an impact on the mechanics of musc e function and in part explain the differences we see between people Remember we are as different on the inside as we are on the outside Now back to our original vector resolution of the rhomboids ltENTERgt SLIDE 45 If the resultant force is 100 N how much force is acting to elevate the scapula Approximately 50 N How much force is acting to retract the scapula Approximately 70 N Notice that the components do not add back up to the resultant in the regular algebraic sense 70 N 50 N 120 N The components add back up to a sum larger than the resultant This is always the case Remember these are vector quantities not scalar quantities The components do add up to 100 N but only using vector addition composition So when I ask you to estimate component vectors do not force them to add back up to the resultant vector in the traditional algebraic sense Estimate the magnitudes of the components using the scale that you are given ltENTERgt SLIDE 46 We will now move on to resolution of muscle force vectors other than shoulder girdle muscles The horizontal and vertical reference does not generally work for other muscles in the body Instead the reference that we use for resolution of muscle forces other than shoulder girdle muscles is the mechanical axis of the bone to which the muscle attaches The mechanical axis is essentially the longitudinal axis of the bone or segment If you use this de nition you can draw a mechanical axis for any bone in the body The mechanical axis then serves as your reference for resolution of muscle force vectors You will resolve muscle force vectors in directions that run tangential parallel and normal perpendicular to the mechanical axis of the bone That is because we are interested in how the bone slides linear motion parallel and perpendicular to this axis Let s look at some examples of this ltENTERgt SLIDE 47 Remember for muscles we are often interested in the rotational effects of the muscle on a given bone For example does the muscle cause exion or extension of the bone about the joint The techniques that we are learning right now help us understand the translational linear effects of the muscle on the bone 7 we will discuss rotational effects later In this example the resultant muscle force vector has already been drawn for you and you are being asked to resolve this muscle force vector Do you know which muscle is pictured here The biceps femoris 7 one of the three hamstring muscles The rst step in the resolution process ltENTERgt is to draw a line to represent the mechanical axis of the bone This is going to be your reference for the vector resolution You might ask Which bone Well since we have drawn our force vector with the tail on the distal bone then it must be the distal bone whose motion we are interested in Remember for now we assume that the distal bone is the moving bone Therefore that is the bone that we want to draw the mechanical axis for So can you draw the mechanical axis for the tibia bula complex ltENTERgt Did you get it right ltENTERgt SLIDE 48 The second step is to draw in the normal perpendicular component You want to draw a component vector that runs perpendicular to the mechanical axis of the bone Remember your end result is going to be a rectangle that encloses the resultant muscle force vector Can you draw the normal component ltENTERgt Did you get it right ltENTERgt SLIDE 49 The third step is to draw in the tangential parallel component You want to draw in a component that runs parallel to the mechanical axis of the bone Remember your end result is going to be a rectangle that encloses the resultant muscle force vector Can you draw the tangential component ltENTERgt Did you get it right It really does not matter whether you draw in the tangential or normal component rst but in my experience students usually nd it easier to draw in the normal component rst Again do whichever works best for you ltENTERgt SLIDE 50 The fourth step is to complete the rectangle to make sure that you have the lengths of your component vectors correct ltENTERgt You have now resolved a muscle force vector using the mechanical axis of the bone as your reference Any questions ltENTERgt SLIDE 51 How would you express the direction of the resultant muscle force Well to answer this question we need to know which reference system is most appropriate to you 7 a relative system or an absolute system Since we are dealing with motion of body segments a relative system is more appropriate However this relative reference system is a little different than the one we discussed earlier for describing joint ROM In this system the mechanical axis is your reference point and the proximal end of the axis is considered 0 Once you establish this then you identify the position of the resultant muscle force vector relative to this zero point In this example let s extend the mechanical axis a little further proximally and label it 0 ltENTERgt Now can you locate the angle for the resultant muscle force vector ltENTERgt What is the magnitude of this angle It is 8085quot This angle is called the muscle insertion angle This will be the angle that you use to describe the direction of the resultant muscle force vector in future problems How would you express the direction of the components Well at the simplest level you would say that the forces act normal perpendicular and tangential parallel to the tibia But let s put that in context by answering the question on the next slide ltENTERgt SLIDE 52 What are the linear effects produced by this muscle Remember we use vector resolution to help us understand how muscles move bones linearly While this is not how we often think of muscles pulling bones it is an important part of muscle function and has implications for joint stability and injury prevention Look at the normal and tangential components of the pull of the biceps femoris Can you describe the linear effects of the biceps femoris on the tibia bula complex and the knee joint If we look at the tangential component we can see that the muscle tends to pull the tibia bula into the femur squeezing the joint together This is called compression thus the muscle has a compressive effect on the knee joint Is this good or bad Well it certainly depends on what other forces are doing about the knee joint so we cannot really answer this question but as a general rule compression of a joint has the bene cial effect of stabilizing the joint How about the normal component It tends to pull the tibia bula in a way that makes it want to slide off of the femur This is called a shear force thus the muscle tends to have a shear effect on the joint The shear effect is in the posterior direction Is this good or bad Again it certainly depends on what other forces are doing about the knee joint so we cannot really answer this question However by itself this shear effect would not be desirable because as it attempts to slide the tibia bula off the femur it would tend to stress the soft tissues around the joint For now you do not have to worry about understanding the applications of this vector resolution process but you must be able to resolve muscle force vectors ltENTERgt SLIDE 53 If the resultant muscle force is 500 N what is the magnitude of the components The tangential component is 100 N and the normal component is N450 N Are you getting tired of this type of question I hope so and I hope that means that you have this concept down Let s look at another example of resolving muscle force vectors parallel and perpendicular to the mechanical axis of the bone ltENTERgt SLIDE 54 This diagram is another view of the biceps femoris muscle However the difference here is that the leg is not exed as far in this example as in the previous example That will change the linear effects of the muscle Let s resolve the muscle vector to see how ltENTERgt The rst step is to draw a line to represent the mechanical axis of the bone Can you do it ltENTERgt Did you get it right ltENTERgt SLIDE 55 The second step is to draw in the normal component Can you do it ltENTERgt Did you get it right ltENTERgt SLIDE 56 The third step is to draw in the tangential component Can you do it ltENTERgt Did you get it right ltENTERgt SLIDE 57 The fourth step is to complete the rectangle to make sure that you have the lengths of your vectors correct ltENTERgt ltENTERgt SLIDE 58 How would you express the direction of the resultant muscle force Extend the mechanical axis and mark the proximal end as 0 degrees Then estimate the muscle insertion angle Can you do it ltENTERgt The muscle insertion angle is 45 degrees Given our discussion about the linear effects in the previous example how would you express the direction of the components The normal component still exerts a posterior shear force about the knee joint and the tangential component still exerts a compressive force about the knee joint However there is a difference between this example and the previous example Can you gure out what it is ltENTERgt SLIDE 59 The difference is in the 39 39 ofthe 1 While the 439 quot 39 effect is the same for the normal and tangential components in both examples the magnitudes of the shear and compressive forces are different in the two examples even though the resultant vector for the biceps femoris is the same magnitude in each The difference between these two examples is in the direction of R which does affect component magnitudes The practical application of this knowledge is that muscle function in terms of linear effects does change throughout the ROM at a joint as the muscle insertion angle changes We will talk more about this in the future ltENTERgt SLIDE 60 Now I am going to present several other examples of vector resolution in various contexts Please make sure that you understand how to resolve the vectors as shown in each example In the example shown on this slide the red vector represents the weight of the person as heshe walks up the hill We know that weight always acts vertically and acts at the COG of the person So the vector is drawn accordingly We want to resolve this vector but can you gure out which directions would provide us with the most important information The answer is that we want to resolve the vector in the directions that run parallel and perpendicular to the surface that she is walking on Can you do this ltENTERgt Did you get it right Why do you think these directions are most appropriate Well the component parallel to the slope gives us information about how gravity is opposing our motion up the hill and helps us understand why walking uphill is harder The component perpendicular to the slope will help better understand the friction that is acting on the person The connection between gravity and friction may not be apparent to you right now but suf ce it to say that that is the application ltENTERgt SLIDE 61 In this example the force that is being exerted on the box is resolved into horizontal and vertical components Why do you think these directions are most appropriate Well the horizontal component gives us information about the forces that are acting to slide the box horizontally Can you gure out how to make the horizontal component larger Pull harder or pull at a lower angle The vertical component helps us better understand the friction that is acting on the box Again the connection between gravity and friction may not be apparent to you right now but suf ce it to say that that is the application ltENTERgt SLIDE 62 In this example the force vector for the biceps brachii has been resolved normal and tangential to the mechanical axis of the bone in three different joint positions A15 D75 and F120 ltENTERgt Can you describe the differences in the normal component The normal component is fairly small in A and much larger in D and F with approximately the same magnitude in D and F In all three positions the perpendicular component is directed anteriorly thus it exerts an anterior shear on the joint ltENTERgt SLIDE 63 Can you describe the differences in the tangential component The tangential component is fairly large in A and much smaller in D and F In A and D the direction of the component is towards the elbow joint while in F the direction of the component is away from the elbow joint towards the wrist joint Therefore in A and D it exerts a compressive effect on the joint and in F it exerts a tensile pulling apart effect on the joint ltENTERgt Can you describe the differences in the muscle insertion angle ltENTERgt In A the muscle insertion angle MIA is 30 in D 80 and in F 110 ltENTERgt SLIDE 64 In this example the force vector for the deltoid muscle has been resolved normal and tangential to the bone It just so happens that these directions coincide with the horizontal and vertical as well but the reference is still the mechanical axis of the bone Can you describe the linear effects of this muscle The tangential component exerts a compressive force on the shoulder joint while the normal component exerts a superior shear force on the joint The muscle insertion angle has been identi ed for you and is 20 ltENTERgt SLIDE 65 In this example the force vector for the weight of the forearm has been resolved normal and tangential to the mechanical axis of the bone in two different joint positions B30 and F120 Note that we have used the same reference in this example as we do for muscles This is because we want to understand the linear effects about the elbow joint How would you describe the linear effects of the weight of the forearm on the elbow joint In B and F the normal component exerts a posterior shear although it is much larger in F The tangential component is directed away from the elbow in B and towards the elbow in F If you think back to the resolution of the biceps brachii you can see how the biceps brachii works to offset the pull of gravity or the weight of the forearm Can you see that ltENTERgt SLIDE 66 Finally this is a gure that illustrates the lumbosacral joint with three different sacral angles 7 30 45 and 60 The sacral angle represents the tilt of the sacrum and thus the tilt of the lumbar spine in the sagittal plane The W vector represents the weight of the body above the lumbosacral joint This weight vector has been resolved normal and tangential to the sacral joint surface to determine the effects of the weight on the lumbosacral joint You can see that as the sacral angle gets larger the shear effect gets greater which means that certain tissues around the joint will be put under greater stress Conversely the compressive effect is greater at smaller sacral angles which means that other tissues are put under greater stress at smaller sacral angles Again I do not eXpect you to learn the applications at this time but I do eXpect you to be able to resolve any vector I give you into appropriate component vectors ltENTERgt SLIDE 67 After this lecture you should understand the value of vector analysis For this class we will use vector analysis to help us better understand forces and their effects We will use these concepts throughout the rest of the semester as we discuss human movement and how to alter it to enhance performance and prevent injury ltENTERgt SLIDE 68 For the neXt lecture unit we will cover Lecture Topic 2 Subtopic C 7 Basic Kinetic Concepts Lecture Notes Movement Terminology Instructions Read through the lecture while watching the PowerPoint slide show that accompanies these notes When you see the ltENTERgt prom pt press enter for the slide show so that you can progress through the show in a manner that corresponds to these notes SLIDE 1 It is important to begin our semester by getting familiar with the movement terminology that will be very important to you this semester and throughout your careers It is important that you understand and learn appropriate terminology so that you can communicate accurately with students and colleagues Within the profession Imagine if some of us called blue what we universally acknowledge as blue While others of us called it red and others of us called it green we would never be able to communicate So it is with movement terminology The purpose of this lab is to review and learn in more detail the terminology used to describe motion of the body s segments ltENTERgt SLIDE 2 This slide show and the rst laboratory are designed to cover content biomechanics related to Movement Terminology Most of the content in this topic will be covered in lab but this slide show is designed to review some old material from Human Anatomy and to present some new ideas to prepare you for the Movement Terminology Laboratory You should have read the material listed on slide one before watching this slide show You should also have completed the preliminary tasks described in Laboratory 1 7 Movement Terminology ltENTERgt SLIDE 3 In this lecture and lab we will review 5 areas that you should already be familiar with from your Human Anatomy course ltENTERgt 1 Types of motion ltENTERgt 2 Reference systems ltENTERgt 3 Fundamental movements in the sagittal plane ltENTERgt 4 Fundamental movements in the frontal plane and ltENTERgt 5 Fundamental movements in the transverse plane We will begin our review with Types of Motion ltENTERgt SLIDE 4 We have already been using the term human movement or human motion Before we go any further we need to de ne what is meant by the word motion What is motion ltENTERgt Motion is de ned as a change in position with respect to some reference frame ltENTERgt What causes motion As we have already stated several times ltENTERgt FORCE We will rst learn how to describe motion of human body segments and then we will study the forces behind human motion so that we can alter movement in a safe effective and efficient manner ltENTERgt SLIDE 5 Now we can turn our attention to our rst topic 7 Types of Motion There are two basic types of motion in the physical world It is very important that you know which type of motion you are trying to analyze before you begin The rst type of motion is linear motion ltENTERgt Your textbook gives you a rather wordy de nition of linear motion and While it is a good de nition I am going to simplify it even further Linear motion can be de ned as a point moving in a line On the slide you can see two examples of linear motion ltENTERgt The rst example is of the gymnast moving linearly through the air The point of interest that is moving is the center of gravity COG of her body ltENTERgt In the second example the ball is moving linearly through space The poin of interest that is moving is the COG of the ball It is important to understand that when you observe and analyze linear motion you should consider your object as a single point and focus on this point We call this a point model ltENTERgt By focusing on a point of interest you are able to remove from consideration any distracting movements For example by focusing on the gymnast s COG you can ignore the movements of her legs and arms While these movements may ultimately be of interest you must rst be able to describe whether she is traveling far enough horizontally and vertically linearly to complete the skill If she is but she is not successful then that will point you to one type of problem If she is not then your focus will be on a different type of problem Back to our de nition We de ned linear motion as a point moving in a line We now understand the importance of treating the object as a point The second thing we need to focus on are the words moving in a line Linear motion can be ltENTERgt rectilinear where the object moves in a straight line or ltENTERgt curvilinear where the object moves in a curved line Can you nd examples of each of these in the diagrams on the slide ltENTERgt Another word for linear motion is translation If I ask you how the body translated I am essentially asking you how the body moved linearly ltENTERgt What role does the COG play in linear motion Well as in these two examples the COG is usually what we use to represent the point of interest Can you think of an example where this is not the case ltENTERgt SLIDE 6 The second type of motion is angular motion ltENTERgt To be able to describe angular motion we use what is called a link model ltENTERgt The system or object of interest is represented as a rigid link or rigid body and graphically we do this with a line In the rst example the system of interest is the lower leg In the second example the system of interest is the entire body of the gymnast ltENTERgt Again your textbook gives you a rather wordy de nition of angular motion so I am going to simplify it for you Where linear motion was de ned as a point moving in a line angular motion is de ned as a line moving around a point ltENTERgt This point is called the axis of rotation On the slide there are two examples of angular motion ltENTERgt In the rst example the runner s leg the line moves around his knee joint the point or axis ltENTERgt In the second example the gymnast s body the line moves around the bar the point or axis Again it is important to understand that when you observe and analyze angular motion you should consider your object as a single line and focus on this line There may be other lines moving in other words other things rotating There may even be linear motion going on but you must decide what you are most interested in and focus on that movement only While these other movements may ultimately be of interest you must approach your analysis systematically stepbystep The rst part of this process is describing the movement of interest There are several other points we need to make ltENTERgt First the axis may be xed or moving In the example of the runner the axis the joint is moving linearly through space while simultaneously serving as an axis of rotation for the lower leg In the example of the gymnast the axis the bar is xed ltENTERgt Another word for angular motion is rotation so we will tend to use these words synonymously ltENTERgt What role does the COG play in linear motion Well the COG plays 2 roles in angular motion In cases where the system is free to rotate about itself the COG actually serves as the axis of rotation In cases where the system is xed to some other object to create an axis of rotation the COG is the point we use to connect to the axis of rotation so that we can determine the length of our rigid link ltENTERgt This concept is extremely important in quantitative analyses and is also helpful to visualize in qualitative analyses where an approximation of the length of the rotating link is important ltENTERgt SLIDE 7 In most instances of human motion both types of motion are occurring simultaneously general motion A kinematic analysis may describe one or both types of motion It is important to know which type of motion is being analyzed Oftentimes we analyze the angular motion of body segments to understand the linear motion of the body as a whole Translation of the body as a whole during gait occurs by virtue of rotational motions taking place at the hip knee and ankle around imaginary ML axes of rotation On the slide are two examples of general motion In the example of the gymnast the COG of the gymnast is moving curvilinearly as we discussed earlier At the same time the upper and lower body of the gymnast are rotating around the COG as she moves through the air linearly Can you describe the linear and angular motion of the ball once it leaves the pitcher s hand Can you describe any linear movements of the runner and the gymnast on the high bar on the previous slide where we discussed angular motion ltENTERgt SLIDE 8 To develop language so that we can observe and describe any type of motion a reference system must be established remember the de nition of motion 7 a change in position with respect to some reference frame Since there are numerous positions and movements the human body can adopt and perform the reference or baseline position is used to reduce confusion de ne positional and motion terms identify position of the segment in space and identify whether motion has occurred The reference system is arbitrarily established however it must be speci ed so that terminology and description of motion is understood In functional anatomy the reference system includes a starting position and the reference frame imposed on this starting position In your Human Anatomy course you learned about two starting positions that are used to de ne movement terminology in the human body the Fundamental Standing Position and the Anatomical Standing Position Qualitatively the Anatomical Standing Position is an upright standing posture in which all joints except the ankle are extended so that all body segments form a straight line The head faces forward the arms are at the side of the trunk with the palms facing forward the radioulnar joint or forearm is in a supinated position and the legs are together with the feet pointing forward All segmental movement descriptions are de ned and made relative to this starting position The Fundamental Standing Position is exactly like the anatomical position except that the palms face the body the radioulnar joint or forearm is in a neutral position ltENTERgt We can also describe these positions more quantitatively Both of these positions are described using a relative systems more on that in a later lecture ltENTERgt In both positions all joints are considered to be in a zero degree position except the ankle and the forearm In both positions the ankle is considered to be at 90 degrees In the Fundamental position the forearm is at 0 degrees or neutral but in the Anatomical position the forearm is supinated 90 degrees With these starting positions we can now establish a more precise reference system for de ning movement terminology ltENTERgt SLIDE 9 The reference frame imposed on the reference position consists of the 3 cardinal planes and their associated axes Basically a plane can be described as a pane of glass that the divides the body or a segment into two parts The cardinal planes cut the body exactly in half Each cardinal plane is associated with an in nite number of planes that pass through the body sort of like a stack of paper in which the cardinal plane is the sheet of paper that is in the middle of the stack The intersection of the cardinal planes while in anatomical position is called the center of gravity Each plane has its own axis of rotation By de nition the axis runs perpendicular to the plane Body segments or bones can move linearly in a plane if it actually moves parallel to the plane Rotational movement also occurs in the plane or parallel to the plane and around its associated axis The joint that is in the center of the surrounding moving segments is the axis A movement term for the body or a segment is de ned according to which of the three planes it is moving in It is important to know that these terms are derived from the knowledge of planes and axes and are de ned according to the orientation of these planes and axes to the body Any position can be described by identifying the distance the object line or point is from each of the three axes In advanced movement analysis the planes and axes become the basis for quantitative analysis and thus the dominant system for research ltENTERgt The rst plane that we will de ne is the sagittal plane which divides the body into right and left portions There are an in nite number of these planes that pass through the body sort of like a stack of notebook paper Therefore the sagittal plane passes through each and every joint in the body The axis that runs perpendicular to the sagittal plane is the mediolateral ML axis When a segment rotates in the sagittal plane it must spin around the ML axis Try spinning or rotating your head about an ML axis that runs through your neck Can you gure out what sagittal plane motion of the head is ltENTERgt Other names for the ML axis are the frontal axis the bilateral axis and the transverse axis I will use ML axis in my lecture and on exams ltENTERgt SLIDE 10 The second plane that we will de ne is the frontal plane which divides the body into front and back portions Again there are an in nite number of these planes that pass through the body so that a frontal plane passes through each and every joint in the body The axis that runs perpendicular to the frontal plane is the anteroposterior AP axis When a segment rotates in the frontal plane it must spin around the AP axis Try spinning or rotating your head about an AP axis that runs through your neck Can you gure out what sagittal plane motion of the head is ltENTERgt Another name for the AP axis is the sagittal axis though I will use AP axis in my lecture and on exams ltENTERgt SLIDE 11 The third plane that we will de ne is the transverse plane which divides the body into upper and lower portions Again there are an in nite number of these planes that pass through the body so that the transverse plane passes through each and every joint in the body The axis that runs perpendicular to the transverse plane is the superiorinferior SI axis When a segment rotates in the transverse plane it must spin around the SI axis Try spinning or rotating your head about an SI axis that runs through your neck Can you gure out what transverse plane motion of the head is ltENTERgt Other names for the SI axis are the longitudinal axis and the vertical axis I will use SI axis in my lecture and on exams ltENTERgt SLIDE 12 We will now de ne the fundamental movements associated with each plane The movements that we will describe for each plane are all rotational movements That means that we must consider a segment as a line which rotates about some imaginary point or axis In the human body these axes are represented by the joints For each plane I am rst going to identify the fundamental movements associated with that plane Then I will identify alternative names for these movements at various joints Remember that all movements are de ned starting from anatomical position You will have an opportunity in lab to practice all of these movements ltENTERgt SLIDE 13 In the sagittal plane the fundamental movements are exion ltENTERgt extension ltENTERgt and hyperextension ltENTERgt You should have already de ned these for your lab Again you can picture these movements if you imagine a sheet of paper running through your head in the same way the sagittal plane runs through your body Now place a pencil through your neck the joint axis for rotation of the head to simulate the ML axis for the sagittal plane Try to rotate your head around the pencil axis in the paper or parallel to the sagittal plane Can you gure out which movements of the head are sagittal plane movements Coupled with the de nitions you already have can you speci cally identify which movement is exion which is extension and which is hyperextension One point I want to make is that hyperextension can be a normal movement as it is at the spine shoulder and hip Hyperextension simply refers to posterior movement beyond anatomical position It is not necessarily an abnormal movement unless of course you continue to hyperextend beyond the normal range of motion ROM for hyperextension or attempt to hyperextend a joint that does not permit hyperextension ltENTERgt Hyper exion is a term that is used to describe exion of the shoulder beyond 180 ltENTERgt ltENTERgt Plantar exion and dorsi exion are the terms used for extension and exion at the ankle respectively ltENTERgt One last point I would like to make is that you should not use exion and extension to refer to muscle contraction as in I exed my biceps brachii Muscles do not ex they contract When they contract they may cause exion of a particular joint but exion is a joint action not a muscle contraction ltENTERgt SLIDE 14 In the frontal plane the fundamental movements are abduction ltENTERgt and adduction ltENTERgt Again you should have already de ned these for your lab Again you can picture these movements if you imagine a sheet of paper running through your head in the same way the frontal plane runs through your body Now place a pencil through your neck the joint axis for rotation of the head to simulate the AP axis for the frontal plane Try to rotate your head around the pencil axis in the paper or parallel to the fronttal plane Can you gure out which movements of the head are frontal plane movements Coupled with the de nitions you already have can you speci cally identify which movement is abduction and which is adduction ltENTERgt ltENTERgt Left and right lateral exion are the terms used for frontal plane rotations of the spine as shown in the diagram ltENTERgt Hyperabduction is a term that is used to describe abduction of the shoulder beyond 180 ltENTERgt Hyperadduction is a term that is used to describe adduction of the shoulder and hip beyond anatomical position This movement is possible only when the shoulder or hip is slightly exed rst to put the arm or leg in front of the trunk ltENTERgt ltENTERgt Radial and ulnar deviation are the terms used for abduction and adduction at the wrist respectively ltENTERgt ltENTERgt Finally inversion and eversion are the terms used for frontal plane motion at the subtalar joint These movements do not occur at the ankle joint ltENTERgt As you begin to learn these movements for each joint and practice observing them on your partner in lab remember that you should always look at the plane and down the axis associated with that plane In other words when trying to observe frontal plane movements you should place yourself in front of or behind the person as shown in the picture on the slide When you do this you are looking at the frontal plane and right down the AP axis associated with the frontal plane This will place you in the best position for observing movements in that plane This same principle is true for the other planes as well ltENTERgt SLIDE 15 In the transverse plane the fundamental movements are ltENTERgt medial and lateral rotation Medial rotation is often called inward or internal rotation and lateral rotation is often called outward or external rotation Again you should have already de ned these for your lab You can picture these movements if you imagine a sheet of paper running through your head in the same way the transverse plane runs through your body Now place a pencil through your neck the joint axis for rotation of the head to simulate the SI axis for the transverse plane Try to rotate your head around the pencil axis in the paper or parallel to the transverse plane Can you gure out which movements of the head are transverse plane movements Coupled with the de nitions you already have can you speci cally identify which movement is medial rotation and which is lateral rotation ltENTERgt That may be a little tricky since we don t use the terms medial and lateral rotation to describe head motions Instead left and right rotation are the terms used for transverse plane rotation at the spine ltENTERgt Supination and pronation are the terms used for lateral and medial rotation at the radioulnar joint respectively These movements do not occur at the elbow joint These movements are de ned with the forearm in the neutral position middle picture of the handforearm shown ltENTERgt SLIDE 16 Two other transverse plane movements that can occur at the shoulder and hip joints are horizontal abduction and adduction ltENTERgt You must rst ex the shoulder or the hip to 90 then move the arm or leg in the transverse plane ltENTERgt