The dead don't teach. Future doctors study the human body only using dummies. Human anatomy: structure of internal organs Model of the human body for doctors what is it called

Andreas Vesalius made an anatomical revolution, not only creating amazing textbooks, but also raising talented students who continued breakthrough research. In this post we will get to the anatomical illustrations of the Baroque era and the stunning atlas of the Dutch anatomist Howard Bidloo, and also show illustrations from the first Russian anatomical atlas, which we received thanks to the courtesy of the staff medical library New York.

17th century: from blood circulation to the doctors of Peter the Great

The University of Padua in the 17th century maintained continuity, remaining something like the modern MIT, but for early modern anatomists.
The history of anatomy and anatomical illustration in the 17th century begins with Hieronymus Fabricius. He was a student of Fallopius and after graduating from university he also became a researcher and teacher. Among his achievements is a description of the fine structure of the organs of the digestive tract, larynx and brain. He first proposed a prototype for the division of the cortex cerebral hemispheres into lobes, highlighting the central sulcus. This scientist also discovered valves in the veins that prevent the blood from flowing back. In addition, Fabricius turned out to be a good popularizer - he was the first to begin the practice of anatomical theaters.
Fabricius worked extensively with animals, which gave him the opportunity to make contributions to zoology (he described the bursa of Fabricius, a key organ of the immune system of birds) and embryology (he described the stages of development of bird eggs and gave the name ovarium to the ovaries).
Fabricius, like many anatomists, worked on the atlas. Moreover, his approach was truly thorough. Firstly, he included in the atlas illustrations of not only human anatomy, but also animals. In addition, Fabricius decided that the work should be done in color and at a 1:1 scale. The atlas created under his leadership included about 300 illustrated tables, but after the death of the scientist they were lost for a while, and were rediscovered only in 1909 in the State Library of Venice. By that time, 169 tables remained intact.

Illustrations from Fabritius' tables (). The works correspond to the artistic level that painters of that time could demonstrate.

Fabricius, like his predecessors, managed to continue and develop the Italian anatomical school. Among his students and colleagues was Giulio Cesare Casseri. This scientist and professor of the same University of Padua was born in 1552 and died in 1616. He devoted the last years of his life to working on an atlas, which was called exactly the same as many other atlases of that time, “Tabulae Anatomicae”. He was assisted by the artist Odoardo Fialetti and the engraver Francesco Valesio. However, the work itself was published after the anatomist’s death, in 1627.

Illustrations from Casserio's tables ().

Fabricius and Casseri went down in the history of anatomical knowledge by the fact that both were teachers of William Harvey (our surname is better known in Harvey's transcription), who took the study of the structure of the human body to an even higher level. Harvey was born in England in 1578, but after studying at Cambridge he went to Padua. He was not a medical illustrator, but he focused on the fact that each organ of the human body is important not primarily because of how it looks or where it is located, but because of the function it performs. Thanks to his functional approach to anatomy, Harvey was able to describe the circulatory system. Before him, it was believed that blood is formed in the heart and with each contraction of the heart muscle is delivered to all organs. It never occurred to anyone that if this were actually true, about 250 liters of blood would have to be formed in the body every hour.

A prominent anatomical illustrator of the first half of the seventeenth century was Pietro da Cortona, also known as Pietro Berrettini.
Yes, Cortona was not an anatomist. Moreover, he is known as one of the key artists and architects of the Baroque era. And it must be said that his anatomical illustrations were not as impressive as his paintings:

Anatomical illustrations by Barrettini ().

Fresco “The Triumph of Divine Providence”, on which Barrettini worked from 1633 to 1639 ().

Barrettini's anatomical illustrations were probably made in 1618, during the early period of the master's work, based on autopsies carried out at the Hospital of the Holy Spirit in Rome. As in a number of other cases, engravings were made from them, which were not printed until 1741. Barrettini's works are interesting in compositional solutions and depictions of dissected bodies in lively poses against the backdrop of buildings and landscapes.

By the way, at that time artists turned to the theme of anatomy not only for depiction internal organs man, but also to demonstrate the process of dissection and the work of anatomical theaters. It is worth mentioning the famous painting by Rembrandt “The Anatomy Lesson of Doctor Tulp”:

Painting “The Anatomy Lesson of Doctor Tulp”, painted in 1632.

However, this story was popular:

Anatomy Lesson of Dr. Willem van der Meer An earlier painting showing a teaching dissection is “The Anatomy Lesson of Dr. William van der Meer,” painted by Michiel van Mierevelt in 1617.

The second half of the 17th century in the history of medical illustration is notable for the work of Howard Bidloo. He was born in 1649 in Amsterdam and trained as a doctor and anatomist at the University of Franeker in Holland, after which he went to teach anatomy techniques in The Hague. Bidloo’s book “Anatomy of the Human Body in 105 Tables Depicted from Life” became one of the most famous anatomical atlases of the 17th-18th centuries and was distinguished by the detail and accuracy of its illustrations. It was published in 1685, and was later translated into Russian by order of Peter I, who decided to develop medical education in Russia. Peter’s personal doctor was Bidloo’s nephew Nikolaas (Nikolai Lambertovich), who in 1707 founded Russia’s first hospital medical-surgical school and hospital in Lefortovo, the current Main Military Clinical Hospital named after N. N. Burdenko.

The illustrations from the Bidloo atlas show a tendency towards more accurate drawing of details than before and greater educational value of the material. The artistic component fades into the background, although it is still noticeable. Taken from here and here.

18th century: exhibits from the Kunstkamera, wax anatomical models and the first Russian atlas

One of the most talented and skillful anatomists in Italy at the beginning of the 18th century was Giovanni Domenico Santorini, who, unfortunately, did not live a very long life and became the author of only one fundamental work called “Anatomical Observations”. This is more of an anatomical textbook than an atlas - there are illustrations only in the appendix, but they deserve mention.

Illustrations from the book of Santorini. .

Frederik Ruysch, who invented the successful embalming technique, lived and worked in the Netherlands at that time. It will be interesting to the Russian reader because it was his preparations that formed the basis of the Kunstkamera collection. Ruysch knew Peter. The Tsar, while in the Netherlands, often attended his anatomical lectures and watched him perform dissections.
Ruysch made preparations and sketches, including children’s skeletons and organs. Like earlier authors from Italy, his works had not only a didactic, but also an artistic component. A bit strange, however.

Another prominent anatomist and physiologist of that time, Albrecht von Haller, lived and worked in Switzerland. He is famous for introducing the concept of irritability - the ability of muscles (and subsequently glands) to respond to nerve stimulation. He wrote several books on anatomy, for which detailed illustrations were made.

Illustrations from von Haller's books. .

The second half of the 18th century in physiology is remembered for the work of John Hunter in Scotland. He made a great contribution to the development of surgery, the description of the anatomy of teeth, the study of inflammatory processes and the processes of bone growth and healing. Hunter's most famous work was the book “Observations on certain parts of the animal oeconomy”

In the 18th century, the first anatomical atlas was created, one of the authors of which was the Russian doctor, anatomist and draftsman Martin Ilyich Shein. The atlas was called “Glossary, or illustrated index of all parts of the human body” (Syllabus, seu indexem omnium partius corporis humani figuris illustratus). One of its copies is kept in the library of the New York Academy of Medicine. The library staff kindly agreed to send us scans of several pages of the atlas, first published in 1757. This is probably the first time these illustrations have been published on the Internet.

Why know human anatomy

Once the great Leonardo da Vinci said great words: the highest failure is when theory is ahead of execution. Although this chapter is intended to serve as a kind of practical guide, it still makes sense to discuss the provisions of human anatomy in a more analytical manner. Although we do not expect this material to be a complete study on the topic. After all, entire volumes have been written about this subject. Let them serve as guides for serious students of the humanities who want to study anatomy in depth. Let's get started!

Students of the humanities department need to understand that in order to draw, sculpt and engage in three-dimensional modeling of the human figure, they also need to acquire certain knowledge of human anatomy. Given the lack of necessary knowledge in this area, it is easy to create ambiguous and incorrect depictions of forms. Surely you have seen this phenomenon more than once in images of people by novice artists. In their drawings, the arms and legs look more like sausages, and the body proportions are disturbed. The model looks, rather, assembled from some separate fragments that have nothing to do with each other.

Some people wonder why artists so often paint the human body naked. And everything is very simple. After all, the shape of the figure is hidden by clothes. And you need to start with a clear understanding of the basics of the human structure, without wasting time and nerves on the folds and details of clothing. The same situation applies to animation. It is much more beneficial for students to see how the body moves rather than having the action of muscles and bones obscured by drapery. Clothes animation, by the way, has new problems. But we will turn to them later.

PROPORTIONS

Throughout history, masters of the brush have tried to depict the human body in ideal proportions. Generally, the average height of a man or woman can be measured by taking seven head heights. As you can see on a two-dimensional surface, a figure with such a height falsely satisfies the concept of an ideal. And if we compare the same model shown in Figures 3-1 and 3-2, we will see that the woman in Figure 3-2, who is 8 heads tall, looks more graceful and slender.

If you are creating and animating ideal male and female figures, try modeling them at this height - 8 heads. Assuming you are using 2D or 3D templates, you need to first stretch their proportions and then use them as a guide. And if you are going to make a caricature, you need to try to make the heads larger, and the body only 5 heads high. As you may remember, superheroes are often depicted as both super tall and with very small heads.

Rice. 3-1 The figure is generally measured to be 7 head heights

Artists often specifically create a model according to the manner in which it will be viewed. A good example of this is Machelangelo's David. Since the statue was modeled to be very large, and it was also assumed that it would be viewed from below, the maestro sculpted a large head, because he knew that it should look normal in perspective.

Look at Figure 3-3 illustrating average width shoulders and height of the female torso. Modelappears to have a shoulder width of 2 and 2/3 of the head. A man has a shoulder width of 3 heads (Fig. 3-4). The distance measured from the top of the head to the crotch itself, for both men and women, is approximately 4 times the height of the head.

Rice. 3-2 The 8-head tall figure has a more majestic appearance

True, uh ThatIt may help to have an idea of ​​the general proportions first. It is still advisable to rely on your own view and your judgment as to what will look best. Everyone, gradually gaining experience, learns to measure proportions according to his common sense, and not to waste time to measure body proportions according to the rules.

Rice. 3-3 This -torso height andwoman shoulder width

For beginners, scientific knowledge of human body proportions and anatomy will be helpful, although this can become a hindrance when followed carelessly.

Rice. 3-4 This -torso heightand the width of a man's shoulders.

Try to create convincing models, thoroughly mastering their structure, and then eventually develop your own style. It has long been known that the works of artists who set aside standard ways of representing the human body often became more individual and interesting.

SKELETON

The skeleton plays the role of a kind of frame on which muscles with tendons, fat and skin are attached. The human body takes its shape from the skeleton. It is he who gives our bodies proportion . By the way, the skeleton is comparable to the same frame of a house. This is what protects and supports everything inside (we're talking about vital organs), while serving at the same time as support for the external parts, namely muscles, skin and fat.

The external contours of a person’s figure are also influenced by the mainskeletal structure. This point needs extra attention to be considered because in some areas the bones are sometimes not as obvious. Look at Figures 3-5 and 3-6, illustrating some parts of the body wheremore noticeable bones.

It will be difficult to create a model with convincing forms without studying the skeleton. At the figurewithoutwould be an unusual shape. Michelangelo shows us an example of this with his painting “The Last Judgment.” On it he depicted his skin, which was taken from him by St. Bartholomew (Fig. 3-7). We see a fine example of a figure without a skeleton.

Rice. 3-5 Some of the skeleton parts.

1. Scapula - Shoulder blade

2. Spine - Spine

It should be noted that artistic studies of the human skeleton are an order of magnitude simpler than medical studies. As a rule, students who do not pay attention or ignore the skeleton are quitelimited in describing conventional bumps or depressions when modeling human proportions. Onaspiring 3D modeler, nWithout being familiar with the basic structure, purpose, proportions and significance of the human skeleton, they will begin to consider it only asan additional burdensome factor that, it turns out, changes the contours of the body.

Rice. 3-6 This is part of the areas on the front and side of the figure where skeletal detail is visible.

1. Medial Malleolus of Tibia - middle malleolus of the tibia

2. Pubic Crest - pubic comb

3. Thoracic Arch - thoracic arch

4. Sternum - sternum

5. Clavicle - collarbone

6. Head of Ulna - head of the ulna

7. Superciliary Crest

8. Zygomatic Bone - cheekbone

9. Radius and Ulna - radius and ulna

10. Iliac Crest - iliac crest

11. Lateral Malleolus of Fibula - lateral malleolus of the fibula

12. Patella - patella

An experienced 3D modeler recognizes the importance of images of internal structure. Each component of the figure can be identified by identifying large skeletal details. It will become clear to an experienced animator that all movements are generated by the skeleton, which supports and moves the muscles. In Fig. 3-8 shown different types skeletons. Its main parts are the skull and spine, as well as the chest, pelvis, shoulders, arms and legs.

Rice. 3-7. The Last Judgment, fragment of a painting, St. Bartholomew flayed Michelangelo

SCULL

The human skull consists of 22 bones. In Fig. 3-9, illustrating the types of the skull, the most prominent bones are visible. You should be aware that the standard method for relative measurement of the human body is the height of the skull.

The jaw (lower) is ethe only movable bone of the skull. As for the remaining parts of the cranial bones, they are rigidly held together by fixed joints. The skull can be divided into 2 sections - the skull, the enclosing brain, and the facial bones.

The frontal bone, located at the front of the skull, forms the eyebrows with a protective curve above the eyes.

Among other prominent bones we will name the super ciliated bone, or the eyebrow ridge;zygomatic bone, or cheekbone;zygomatic bone, concavity below the orbit; lower crest of the nasal bone; lower jaw, or jaw bone.

Students of 3D modeling benefit from studying the skull. As layers of fat and muscle are stretchedrelatively thin layeralong the skull, its bone structure is more visible here than on other parts of the body (Fig. 3-10).

Rice. 3-8 Skeleton types

Rice. 3-9 Types of skull

1. Frontal Bone - frontal bone

2. Superciliary Bone

3. Orbit - eye socket

4. Nasal Bone - nasal bone

5. Zygomatic Bone - cheek bone

6. Canine Fossa - depression below the eye sockets

7. Maxilla - upper jaw

8. Mandibula - lower jaw

9. Zygomatic Arch - zygomatic arch

Rice. 3-10 The skull greatly influences the shape of the head

SKELETON TORSO

The upper and lower parts of the human torso can be divided into 4 sections. We are talking about the spine, chest, shoulder girdle and pelvic girdle (Fig. 3-11). All of them are grouped around the spinal column. The spine consists of 33 vertebrae. Nine of them, the lowest ones, are joined together to form the sacrum and coccyx. And the other 24 vertebrae are quite flexible (Fig. 3-12 and 3-13). Separating these vertebrae is a fibrous cushion of elastic cartilage that serves to cushion and allow movement between the vertebrae. Animators who are rigging or setting up a skeleton should take this into account to help them create multiple connected bones with properties that are similar to a real spine.

It is advisable to think about what causes the spinal column to bend. The coccyx and the arch of the sacrum in the back leave space for the internal organs within the pelvic girdle. If you take it higher, the spine bends below the ribs, which it, in fact, is designed to support.To support the breastsThe vertebral column behind the ribs bends towards the back. The cervical vertebrae curve forward under the skull, supporting it almost at its very center of gravity, so almost no effort is required to hold the head. It must be said that the shape of the spinal column regulates the main directions of the human body.

Let's look at the barrel-shaped chest, it decreases towards the top. Thanks to the 12 pairs of ribs and sternum, the lungs and heart covered by them are protected. Animators must remember that the ribcage is quite flexible, so it can expand and contract with breathing. Fashion designers should remember that the cartilage in front, at the junction of the seventh, eighth, ninth and tenth ribs,can often be visible on the bodyin the form of an arcunder the chest muscles (Fig. 3-14). By the way, this V-shape was called the pectoral arch. As you can see, the sternum consists of threebones,firmly attached. It can also be seen on the surface of the body as a groove separating the chest muscles (Fig. 3-14).With expansion and contraction of the chestit usually goes up and down.

Rice. 3-11 Skeleton of the upper body

1. Cranium - skull

2. Zygomatic Arch - zygomatic arch

3. Mandibula - lower jaw

4. Scapula - shoulder blade

5. Clavicle - collarbone

6. Sternum - sternum

7. Thorax - thorax (chest)

8. Iliac Crest - iliac crest

9. Pelvis - pelvis

10. Sacrum - sacrum (cross bone)

11. Coccyx - tailbone

12. Spine of the Scapula - collarbone

13. Thoracic Vertebrae - thoracic vertebrae

Rice. 3-12 The movable vertebrae of the spinal column allow a significant level of rotation and bending

The shoulder girdle has a collarbone and shoulder blades. Looking from above, we see that it has a slightly curved shape. And the clavicle from the outside will appear to have the appearance of an S-curve (Fig. 3-15). The collarbone, thanks to its ability to move, adds mobility to the arms.

Each shoulder blade is shaped like a triangular cup (Figure 3-15). and they are only indirectly attached to the trunk, adjacent to the collarbone. It must be said that the shape of the scapula should correspond to the shape of the chest along which it glides freely. In addition to this sliding in any direction, it can, being raised above the chest, protrude quite noticeably under the skin. We clearly see this when the hand is above the shoulder. In this case, the scapula is moved away from the chest.

Rice. 3-13 With the help of a group of powerful muscles located around the spine, a person can bend, twist and turn

Pelvic girdle, feeling a lack of mobility of the shoulder girdle, has strength and hardness. Therefore, its design is intended to transfer the weight of the torso to the legs, which bear the load.

The pelvis is the part of the body where the most important actions are born. From this area a huge amount of energy is transferred to the upper parts of the body. This is important to consider when animating the human body. Actions will be more convincing if you show the movements that come from the activity of the hips. When setting up a skeleton for animation, the parent bone must have its origin in the pelvis.

Rice. 3-14 The pectoral arch of the chest most often becomes part of the figure

Rice. 3-15 The forearm includes the collarbone (front) and scapula (back)

The sacrum is surrounded by 2 symmetrical pelvic bones. Often, an irregularly curved edge called the iliac crest is clearly visible above the surface of the skin (Figures 3-11 and 3-16). The pelvic bones are visible as wing-like structures, especially on thin figures.

As for the sizes of the male and female pelvis, they differ. The female one is wider and shorter, while the male one is more massive, tall and angular (Fig. 3-17). Looking from the side, we see that the female pelvis is tilted more forward.

Rice. 3-16 The iliac crest of the pelvis is designed to form noticeably protruding bones

Rice. 3-17 The male pelvis is thicker and more angular than the female

HAND BONES

It is in the hand that the most mobile bones of the body are located. The range of gestures increases forearm dexterity and finger dexterity. Since their bones do not have to support the body, as those in the legs do, their shapes are more slender.

In Figure 3-18 we see the arm bones. The upper bone of the arm, called the humerus, has a ball-like shape at the top, which is built into the cavity of the scapula. Since the depth of the glenoid fossa is low and the connecting ligaments are quite loose, the hand has the greatest mobility in comparison with the other limbs.

Rice. 3-18 Hand bones

1. Clavicle - collarbone

2. Scapula - shoulder blade

3. Humerus - humerus

4. Medial Epicondyle - middle epicondyle

5. Lateral Epicondyle - lateral epicondyle

6. Capitulum - head (bones)

7. Radius - radius bone

8. Ulna - ulna bone

9. Carpals (8 bones) - wrist (eight bones)

10. Metacarpals (5 bones) - metacarpus (five bones)

11. Phalanges (14 knuckle bones) - phalanges (fourteen bones)

You see 2 arm bones below - the radius and ulna. The ulna is connected to the humerus using a hinge joint. The radius should rotate around the ulna (Figure 3-19). And this is achieved by bendinglower arm musclesand their stretching. The action of these two bones is clearly visible during the rotation of the palm from the "up" position to the "down" position of the palm. The position where the radius and ulna bones are parallel is called supination. Pronation occurs when the radius crosses the ulna (Fig. 3-20).

In terms of the surface characteristics of the arm bones, they may be noticeable in the shoulders, where the head of the humerus creates an internal bulge in the deltoid muscle. TOwhen the arm is bent,3 bumps may be visible in the elbow area.

Rice. 3-19 With the palm turned upward, the radius and ulna bones will become parallel. With the palm turned down, the radius crosses the ulna

1. Radius - radius bone

2. Ulna - ulna bone

Radius crosses Ulna - the radius crosses the ulna

The location of this weighty group of bones is at the end of the humerus and the beginning of the ulna. The rounded head of the ulna may be visible at the wrist.

The bones of the hand are usually divided into 3 groups: wrist, metacarpus and phalanges. Nand the wrist in two rowsThere are 8 bones of the hand. And their location makes it easier to bend your palms down and up. More limited is side-to-side movement.

The 5 bones of the metacarpus of the palm are connected to the 4 lower bones of the wrist. I must say that the 4 bones of the metacarpus that lead to the fingers are very hard. A thumb in the metacarpus, on the contrary, it has a joint that allows a large range of movement. This maneuverability, when animating the palms, could be used to your advantage to move in almost any directionthumb. By the way, the heads of the metacarpus bones are quite visible if you clench your palm into a fist. They disappear when the fingers of the palm are straightened.

Rice. 3-20 Surface properties of the lower part of the arm during pronation (talking about the rotation of the radius)

The 14 bones of the fingers are called phalanges. Gradually they become smaller in size and flatter in shape where the nails join.

When modeling hands, you should have an idea about the structure of its bones, because without such knowledge it is impossible to create an accurate model of hands. Let's note a common mistake when modeling - it's too small the size of the hands. As a rule, an open palm can cover 4/5 of the face. And you can easily talk about an amateur representation of the human body, just look at the ways in which hands are depicted.

LEGS BONES

By the way, the leg bones are somewhat similar to those in the arm. The leg has one upper bone - the femur, and 2 bones of the lower leg - we are talking about the tibia and fibula (Fig. 3-21). Just as there are joints in the shoulder and elbows, there are joints in the hip and knee. The hinge joint in the ankle (talking about the ankle joint) must correspond to a similar one in the wrist.

But the bones of the leg are heavier and stronger, and they have less freedom of movement than those in the arm. And all for the reason that the bones of the legs are designed to bear weight.

Rice. 3-21 Leg skeleton

1. Pelvis - pelvis

2. Great Trochanter - large swivel

3. Femur - femur

4. Patella - patella

5. Tibia - tibia

6. Fibula - fibula

The femur is helped to connect to the pelvis by a joint that allows limited movement in each direction. The visible bulge from the hip bones (Figure 3-21) marks the widest area of ​​the male thigh. In women, due to fat deposits, the widest part is lower.

The hinge joint in the knees is similar to the elbow, and only helps reverse movement, while the elbow joints of the hands allow only forward movement. The knee, viewed from the front and from the side, is placed in line with the hip joint. And its shape is somewhat triangular, its lower edge is the level of the knee joint.

Figure 3-22 shows the leg bones, how they are positioned, and their alignment. Bones are widest at the joint, and this is where they become visible on the surface.

The tibia in the lower leg is a massive bone that supports the weight of the femur. It must be said that its wide head is easy to see on the surface; its axis is formed by the crest of the tibia. As for the lower leg, this is one of the few places in the body where bones are hidden directly under the skin. And the fibula is thin because it does not bear weight, but its purpose is to attach muscles.

Rice. 3-22 The shape of the legs is influenced by boththe bend and location of the femur, as well as two more bones - the tibia and fibula

We will see the head of the fibula on the outer surface below the knee. Its end is immediately noticeable, protruding outward and forming the outer ankle (we are talking about ankle joint). The inner ankle is placed above the outer ankle (Figure 3-23).

Rice. 3-23 Inner ankle higher than outer

The shape of a person’s legs almost entirely determines its skeleton (Fig. 3-24). And the muscles with ligaments covering the legs do not significantly affect its shape. The inner part of the legs is rounded, while the outer leg, on the contrary, is flatter. The body's weight is supported by a primary longitudinal arch from the heels to the toes, as well as a secondary transverse arch through the instep (Fig. 3-25).

Rice. 3-24 Foot bones

1. Phalanges (14 bones) - phalanges (fourteen bones)

2. Metacarpals (5 bones) - metacarpus (five bones)

3. Tarsals (7 bones) - tarsus (seven bones)

Rice. 3-25 Curves of the feet

1. Transverse Arch

2. Longitudinal Arch - longitudinal arch

The foot is divided into 3 groups of bones (Fig. 3-24). Take the tarsus, a group of 7 bones that form the heel and part of the instep. The rise is made up of 5 metatarsal bones. And the toes make up 14 segmented phalanges.

The heel tarsus is the largest bone in the foot and bears the force from the weight of the torso on the back side of the longitudinal arch of the feet. The remaining 5 small tarsal bones are collected together at the top of the arch. There is room for movement between the tarsus and metatarsus, and this creates an elastic structure rather than a rigid one. As a result, the impacts from walking, or jumping and running are distributed throughout the structure of the feet.

The metacarpus of the hands correspond to 5 metacarpus of each foot, whose lower sides are curved, ending at their ends in a longitudinal arc. The metatarsus and are held together by strong ligaments (Fig. 3-26).

14 phalanges, 2 for the big toes and 3 for the other toes. They are shorter in length than the phalanges of the fingers. Thinner and smaller toes. At the ends of the toes, in the mass where the nails grow, there is a flattened shape.

Rice. 3-26 Leg ligaments

MUSCLES

The superficial forms of the body are formed mainly by different muscle groups. During human activity, surface contours will change as muscles contract (thicken), expand, and twist.

Muscles are made up of parallel short fibers that attach to bones or other tissues using tendons. We are talking about rigid inelastic fibers placedalong the edges of widemuscles and at the ends of the long ones.

Muscles contracting pull the bones, and secure against movement skeleton . But a fact that is very interesting for animators is that none of the individual muscles will act alone. When muscles contract (squeeze), others become active in order to regulate the action of the contracting muscle. Antagonistic muscles make it possible to perform complex actions, allowing different parts the torso return to their previous state.

Women have the same muscles as men. Where they differ is that women have smaller muscles and, as a rule, are not as developed. But women's muscles are also covered by a thicker layer of fat, which tends to hide their contours. It is worth recalling that studying muscles is a much more complex process than recognizing the skeleton.

MUSCLES OF THE HEAD

The muscles of the head, unlike other parts of the body, are relatively thin. This is a Thai skull whose bones greatly influence the shape of the head.

Those interested in facial animation will have to spend a lot of time learning about these muscles and the methods they use to change facial expressions. Chapter 9, which covers facial animation, identifies the most important muscles that are responsible for speech and other expressions. And, by the way, studying them is more important for animators than for modelers. During the facial modeling process, great value has a study of the structure of the skull.

In Figure 3-27 we see the most distinctive muscles of the head. Temporalis and masticatory muscles, nthe largest of this muscle group,act on the lower jaw. With the help of the muscles of the neck, the lower jaw is lowered.

A number of facial muscles are endowed with differences, having no connections with bones. They are attached to ligaments or skin, or connected to other muscles. A number of other muscles originate from the bone, but end on the skin, or fascia (we are talking about connective tissue), cartilage or fibers of other muscles.

Rice. 3-27 Head muscles

1. Apicranial Aponeurosis - tendon helmet

2. Frontalis - frontal

3. Temporalis - temporal

4. Orbicularis Oculi - circular muscle of the eye

5. Corrugator - a muscle that causes skin wrinkling

6. Procerus - alar part of the nasal muscle

7. Nasalis - levator labii superioris nasalis muscle

8. Quadratus Labii superioris

9. Zygomaticus Major - large zygomatic

10. Caninus

11. Orbicularis Oris - circular muscle of the mouth

12. Buccinator - buccal

13. Depressor Labii Interioris

14. Triangularis - triangular muscle, triceps

15. Occipitalis - occipital

16. Masseter - chewing muscle

17. Mentalis - mentalis muscle

NECK MUSCLES

The neck can be divided into 2 separate sets of muscles. One of them is designed to regulate the movement of the lower jaw, while the others act on the skull.

The muscles of the neck that influence the base of the tongue and the process of lowering the jaw are called digastric, omohyoid and sternohyoid muscles (Fig. 3-28).

The influence on the skull and vertebrae of the neck is exerted bythe extensor muscles of the neck, the muscles that elevate the scapula, as well as the scalene, trapezius and sternomastoid muscles (Fig. 3-28). The main task of the neck extensor muscle is to tilt the head back and to the side.Help tilt the skull to the side and mmuscles that elevate the scapula. The main one, responsible for tilting the head to the side, is the staircase. Accessionto the first ribThis deeply located muscle makes it possible to apply serious force to the skull.

Rice. 3-28 Neck muscles

1. Trapezius - trapezius muscles

2. Splenius - extensor muscles of the neck

3. Sternomastoid - sternomastoid muscle

4. Levator Scapulae - muscles that lift the scapula

5. Thyroid Cartilage (Adam’s Apple) - cartilage of the thyroid gland (Adam’s apple)

6. Scalenus - scalene muscle

7. Omohyoid - omohyoid muscle

8. Sternohyoid - sternohyoid muscle

9. Clavicular Head of Sternomastoid - clavicular head of the sternomastoid muscles

10. Digastricus - digastric muscle

Often visible on the surface of the necktrapezius and sternomastoid muscles, not likethe neck extensor muscle, the levator scapulae muscle and the scalene muscle, which, as a rule, are not visible on the surface, except when the head is tilted a considerable distance to the side (Fig. 3-29).Trapezius muscles, viewed from behind and from the front, appear as inclined planes. The sternomastoid muscle will be clearly visible if the head is turned to the side. The purpose of the trapezius and sternomastoid muscles is to tilt the skull back and rotate the head. Alone, they help tilt the skull to the side. The 2 sternomastoid muscles are attached by ligaments to the dimple in the neck, creating a V-shape that is almost always visible.

Rice. 3-29 The two most visible muscles of the neck

TORSO MUSCLES

The result of the vertical position of the torso is itsstructural feature. The human shoulders, unlike other mammals, do not have to support either the head or the chest, so they are separated by a certain distance in order to improve the functionality of the arms. The chest cavity is distinguished not by its depth, but by its width.

The upper and lower parts of the body are affected byve muscle groups. The upper one affects the upper arms and shoulders, while the lower group of muscles, located from the chest to the pelvis, controls movements at the waist. Figure 3-30 illustrates the superficial muscles of the body.

The trapezius muscle is diamond-shaped, extending from the base of the skull to the middle of the back. The upper lobe of the trapezius muscle itself is located vertically in relation to the base on back side neck. The middle part is a thick and distorted bulge located on the top of the shoulders. As for the lower segment, while remaining more or less thick, it corresponds to the shape of the human chest and the edge of the shoulder blades.Trapezius muscles, withturning towards the middle, acceptsin the tendon areaflat arrow shape. By the way, in this zone, vertebrae will be visible on the surface of the body (Fig. 3-31). Thanks to trapezius muscle, you can bend your head back, raise and hold your shoulders, and rotate your shoulder blades.

Rice. 3-30 Torso muscles

Sternomastoid - sternomastoid muscle

Trapezius - trapezius muscles

Spine of Scapula

Deltoid - deltoid muscle

Infraspinatus - infraspinatus muscle

Teres Minor - teres minor muscle

Teres Major - teres major muscle

Pесtoralis Major - large chest

Serratus - serratus muscle

External Oblique - external oblique abdominal muscle

Flank Pad of the External Oblique

Rectus Abdominus - rectus abdominis muscle

Gluteus Maximus - large sciatic muscle

Sartorius - sartorius muscle

Tensor Fasciae Latae - hip abductors

Latissimus Dorsi - latissimus dorsi muscles

Anterior Superior Iliac Spine - anterior Superior Iliac Spine

Gluteus Medius - middle ischial muscles

Great Trochanter - large swivel

Rice. 3-31 Vertebral protuberances become visible in the middle of the trapezius muscle

Majoritymuscles,visible in the form of stripes, these are the serratus muscles. We are talking about a long and deeply located muscle that pulls the scapula forward and raises its lower angle. This function assists in various hand movements. Each of the 4 fleshy points on both sides of the torso is more visible if the arm is raised.

The pectoralis major muscles are formed by a triangular muscle on the chest attached to the sternum and collarbone. Thick fibers, converging below the armpit, join the upper bones of the arm. The main task is to bring your hand forward. More often, the contours of the muscle are visible in men; as for women, in the latter they are completely covered by the chest (Fig. 3-32).

Rice. 3-32 Breasts are directed slightly in different directions with nipples coming from the center

The second triangular-shaped muscle that appears on the back and extends to the side is the latissimus dorsi. Fibers similar to the pectoral muscles are twisted before moving to the outside of the arm bones. The latissimus dorsi muscles are capable of pulling the arm back. As for pectoral muscles and the teres major muscle, they pull the arm down and toward the body together.

In the shoulder girdle they begin and connect to the humerus 4muscle groups, we are talking about the deltoid, infraspinatus, teres major and teres minor muscles (Fig. 3-33). They assist each other in stretching their arms.

Fig. 3-33 A number of muscles located closer to the surface are visible on the back in the upper and lower torso

1. Spine of Scapula

3. Infraspinatus - infraspinatus muscle

4. Teres Major - teres major muscle

5. Latissimus Dorsi - latissimus dorsi muscles

6. Trapezius - trapezius muscles

7. Gluteus Maximus - large sciatic muscle

The lower set of muscles includes the external oblique and rectus abdominis. The first of these, the external oblique, becomes most noticeable at the base of the thighs. This was called the flank pad (Figure 3-34). We are talking about one of the most prominent muscles in Roman and Greek sculptures.

Rice. 3-34 Visible muscles of the lower front part of the human torso

1. Rectus Abdominus - rectus abdominis muscle

2. Flank Pad of the External Oblique – Flank Pad of the external oblique muscle

It must be said that the rectus abdominis muscle is covered with a thin layer of veins. The rectus muscle is the thickest muscle around the navel. This is characterized in well-developed bodies by two rows of 4 fleshy pads, each row separated by horizontal tendons. And vertical tendon grooves are laid between each of the four groups of boundaries. If we talk about the rectus abdominis muscle, it goes around the body at the waistfront. Between bgreat ischial andThe middle ischial muscle is located in the socket of the thigh (Fig. 3-35). We will learn more about these muscles by looking at them later, along with the muscles of the legs.

Rice. 3-35 Between the gluteal muscles there is a noticeable thigh dimple.

1. Gluteus Medius - middle ischial muscles

2. Dimple of the thigh

3. Gluteus Maximus - large sciatic muscle

MUSCLES OF THE ARM

The muscles of the arm are divided into 2 sets. The upper one controls the elbow joint, while the lower group controls the wrist joint. If you imagine your arm hanging at the side of your torso, the set of muscles in your upper arm will be located on the outside of your arms. These muscles act as flexors and extensions, that is, to be able to raise the lower part of the arms. Sets of muscles in the lower arms are placed nearby to control the wrist joint, supportingat right angles to the elbowwrist. Figure 3-36 illustrates some familiar sets of arm muscles.

The deltoid muscle is considered a muscle of both the arm and shoulder. With the help of this heavy, triangular-shaped muscle, the arm moves backward.

There are 2 on the top of the handwell-known muscle groups, we are talking about the triceps muscle and biceps. The triceps muscle gets its name from the long lateral and middle chapters. They are located at the end of the humerus (upper arm bone), and extend to its full length - to the elbow. They appear in a relaxed state on the surface as one muscle, and when tense, they become more distinct. Speaking of biceps, let us clarify that we are talking about long muscles that taper at the ends. Their name comes from the two heads arising from two separate points on the scapula. The biceps flexes the arm at the elbow for efforts such as lifting weights. As for the triceps muscle, we are talking about an extensor muscle that acts as a counterforce to the biceps.

Here is another muscle located between the biceps and triceps muscles, we are talking about the brachialis muscle. Working with the biceps, it acts like a flexor muscle of the forearm. It is rarely visible on the surface.

The lower arm muscles are divided into groups, we are talking about flexor and extensor muscles that control the work of the arms and wrist. These muscles also rotate the forearm and operate with finger movements. They, like flexor muscles, pull the fingers together in order to turn them into a fist. And when the extensor muscles act, they straighten these fingers, on the contrary. And two more muscles, we are talking about the supinator longus and pronator teres, stretchin a circular motionradius to the ulna. Despite the presence of 13 muscles in the forearm, it feels like there are only three - the supinator longus and the flexor carpi muscle.

Rice. 3-36 Arm muscles

1. Supinator Longus - long instep support

2. Deltoid - deltoid muscle

4. Biceps - biceps

5. Pronator Teres - round pronator

6. Flexor Carpi Radialis - flexor carpi radialis

7. Extensor Capri Radialis - extensor carpi radialis

8. Fexor Capri Ulnaris - flexor carpi ulnaris

9. Annualar Ligaments - Annualar ligaments

10 Brachialis - brachial muscle

11. Supinator Longus - long instep support

LEGS MUSCLES

The pelvis is the basis for supporting the mass of the upper torso. And it is designed to have a fixed base for the legs to move around. This helps to transfer the inverse kinematics (IK) of the entire structure, where the parent (talking about the pelvis) and pelvic (right and left) bones are unaffected by the IK, helping to stabilize the forces of the IK-controlled legs.

Figure 3-37 clearly shows a number of the major muscles of the leg. Here are the middle sciatic and large sciatic muscles, they begin the contours of the leg. The sciatic major muscle is the largest and strongest muscle in our body. It is designed to act as an extensor muscle, which is used for activities such as, say, running, walking or jumping. In addition, it helps to maintain an upright body position. She has a rectangular shape on the surface of her buttocks. And this happens not at all because of the shape of the muscle, but because of the rather deep lining of fatty tissue.

The movements and position of the leg are commanded by 3 ka set of muscles on the thigh, or the upper part of the leg. Astraightens the leg at the kneegroup of the anterior side, which includes the rectus femoris, vastus lateralis, vastus intermedius and sartorius muscles.When the leg is tense,the rectus femoris and vastus lateralis muscles, as well as the vastus femoris. The lower part of the vastus medialis muscle can often be seen as a tear shaped muscle above the knee. These three muscles act as extensor muscles for the lower leg at the knee. As for the rectus femoris muscle, it is the main hip flexor muscle in the hip joint. And speaking of the sartorius muscle, it looks like a thick, long strip that runs diagonally across the front of the leg to end below the knee, where it connects to the tibia. This muscle does not particularly affect the superficial forms of the legs. Its task is to bend the leg at the hip and knee.

Rice. 3-37 Leg muscles

1 Sartorius - sartorius muscle

2. Rectus femoris - rectus femoris muscle

3. Vastus Medialis - vastus medialis muscle

4. Patella - patella

5. Tibialis Anterior - tibialis anterior muscle

6. Peronaeus Longus - long peroneal muscle

7. Extensor Digitorum Longus - extensor digitorum longus

8. Medial Malleolus of Tibia

9. Gluteus Medius - middle ischial muscles

10. Gluteus Maximus - large sciatic muscle

11. Great Trochanter - large skewer

12. Semimembranosus - semimembranosus muscle

13. Biceps Femoris - 2nd head muscle of the thigh

14. Semitendinosus - semitendinosus muscle

15. Gastrocnemius - gastrocnemius muscle

16. Extensor Digitorum Longus - long extensor finger

17. Peronaeus Brevis - short leg muscle

18. Achilles’ Tendon - Achilles tendon

19. Vastus Lateralis - vastus lateralis muscle

20. Soleus - soleus muscles

21. Medial Malleolus of Tibia - inner surface of the tibia

The posterior muscles of the thigh are considered to beThe vugicetus femoris, semimembranosus, and semitendinosus muscles are sometimes referred to as the hamstrings. They act as flexor muscles to act as counteracts to the extensor muscles of the anterior part, bendingbackleg at the knee. Both the tendons and the lower fibers of the semitendinosus and biceps femoris muscles can be clearly visible on the outside of the knee joint. They all appear as one piece above the knee.

Upper leg muscle groups, ostanding inside, pull the leg inward, towards the center of gravity of the body. Such musclesdue to fat depositsrarely visible on the surface in this area separately .

Ankle jointcontrol 2 sets of muscles. The anterior band, located on either side of the tibia, bends the leg and straightens the toes. With the help of the opposite group, the foot is straightened and the toes are bent. We can clearly see the heavy upper part of the tibialis anterior muscle on the surface. The tendons that cross the ankle are also noticeable.Extensor digitorum longusand on the outside of the legs straightens or contracts the toes, tensing the peroneus longus muscle higher up on the foot. If we talk about the calf muscles, or calves, then these are the main muscles that make up the shape of the back of the lower leg. More often their 2 heads appear in one mass. And the soleus is another calf muscle that works with the calf muscles to straighten the foot and keep the body upright. Both the gastrocnemius and soleus muscles are attached to the thick Achilles tendon, which in turn is connected to the heel bone.

The biology classroom, lined with model skeletons, frogs preserved in alcohol, and exotic plants, invariably attracts the interest of children. Another thing is that interest does not always extend beyond these unusual objects and is rarely transferred to the object itself.

But to help teachers and lecturers today, a huge number of games and applications have been created, with which previously unimaginable experiences become available. Here are the best ones.

This great app partially solves the age-old ethical problem surrounding animal testing. Frog Dissection allows you to perform a 3D dissection of a frog, which is painfully reminiscent of a real dissection. The program has detailed instructions on conducting an experiment, an anatomical comparison of a frog and a human, and a whole set necessary tools, which are displayed at the top of the screen: a scalpel, tweezers, a pin... In addition, the application allows you to study each dissected organ in detail. So with Frog Dissection, first-year students who are part-time members of animal protection organizations can safely dissect virtual frogs and receive their treasured credits. No animal will be harmed during this experience. Frog Dissection can be downloaded from iTunes for $3.99.

Despite the fact that today there are a huge number of anatomical atlases and encyclopedias created for both schoolchildren and medical students, the 3D Human Anatomy application, created by the Japanese company teamLabBody, is one of the best interactive anatomy today that allows you to study three-dimensional model of the human body.

Leafsnap is a unique digital tree recognizer that will certainly appeal to all botanists (in the truest sense of the word) and nature lovers. The principle of operation of the application is quite simple: to understand what plant is in front of you, just take a photo of its leaf. After this, the application launches a special algorithm for comparing the shape of the leaf with those stored in its memory (something like a mechanism for recognizing people’s faces). Along with the conclusion about the supposed “carrier” of the leaf, the application will provide a bunch of information about this plant - place of growth, flowering characteristics, etc. If the image quality makes it difficult for the program to come to a final conclusion, it will prompt you possible options with a detailed description. Then it’s up to you. Overall, a very educational application that helps you learn a little more about the world around you without any extra effort. By the way, each photo received in the application ends up in a specially developed database of the flora of a particular area and helps scientists in researching new plant species and replenishing information about already known ones. The application can be downloaded for free on the App Store.

A fun app for kids that makes it easy to take exciting journeys through the human body. And not just travel, but rocket travel through 3D models of various organs and systems of our body: you can “ride” through the vessels, see how the brain receives and sends signals and where the food we eat goes. The child has the opportunity to stop anywhere and look around. The application allows you to enlarge images of the skeleton, muscles, internal organs, nerves and blood vessels and study their location and principles of operation. Do you want to know how the bones of the skull are attached to each other, which muscles work harder than others in the body, or where the name iris comes from? My Incredible Body has answers to these questions and many more. The program contains short videos that depict the breathing process, the joint work of muscles, the functioning of the hearing aid, etc. In general, to get to know the body it is great option, especially since the price in the App Store is $2.69.

This is not even an application, it is a pocket tip, which presents short articles on the main topics: “Cell”, “Root”, “Algae”, “Class Insects”, “Subclass Fish”, “Class Mammals”, “Evolution of the Animal World” , " general review human body, etc. Nothing new or surprising, but to repeat some basic things that have been lost in memory, it will do just fine. Strict, concise and free.

Another app for your first acquaintance with the human body. Human Body is a cross between a game and an encyclopedia. Every process of the human body is presented interactively and described in detail: the heart beats, the intestines gurgle, the lungs breathe, the eyes examine, etc. The application took 1st place in the App Store educational charts in 146 countries and was named one of the best App Store applications in 2013. Here's a quote from the product description on iTunes:

Human Body is designed for children to help them learn what we are made of and how we work.

In the application, you can choose one of four avatars, an example of which will demonstrate the work of our body. There is no special rules and levels - the basis of everything is the curiosity of a child, who can ask the application any questions about our body. How do we breathe? How do we see? And so on. The app features animations and interactive representations of our body's six systems: skeletal, muscular, nervous, cardiovascular, respiratory and digestive. Included with the app you download a free PDF book on human anatomy with detailed articles and discussion questions. The app is available on iTunes for $2.99.

This is another app from the Brooklyn studio of educational app developers Tinybop, but this time for studying botany. Did you want to know the secrets of the green kingdom? Plants will help both children and those who simply want to learn more about the ecosystems of our planet. The application is an interactive diorama in which the player is a king and god, able to control the weather, start forest fires and observe animals in their natural environment. In the process of such creativity, the user is given the opportunity to get acquainted with various plants and animals in a virtual sandbox that replicates their natural habitat. The application contains ecosystems of forest and desert areas, tundra and grasslands. Soon the developers promise to introduce the ecosystems of taiga, tropical savannah and mangrove forests. However, it's not a matter of quantity here. Getting to know the life cycle of at least one biome is already an achievement, but such experience will help you understand much better how our planet lives and how interconnected everything is in nature. The application is available in the App Store, its price is $2.99.

That is why the science of mechanics is so noble
and more useful than all other sciences, which,
as it turns out, all living beings,
having the ability to move,
act according to its laws.

Leonardo da Vinci

Know yourself!

The human locomotor system is a self-propelled mechanism consisting of 600 muscles, 200 bones, and several hundred tendons. These numbers are approximate because some bones (e.g., spinal column, rib cage) are fused together, and many muscles have multiple heads (e.g., biceps brachii, quadriceps femoris) or are divided into multiple bundles (deltoid, pectoralis major, rectus abdominis, latissimus dorsi and many others). It is believed that human motor activity is comparable in complexity to the human brain - the most perfect creation of nature. And just as the study of the brain begins with the study of its elements (neurons), so in biomechanics, first of all, the properties of the elements of the motor apparatus are studied.

The motor system consists of links. Linkcalled the part of the body located between two adjacent joints or between a joint and the distal end. For example, the parts of the body are: hand, forearm, shoulder, head, etc.

GEOMETRY OF HUMAN BODY MASSES

The geometry of masses is the distribution of masses between the links of the body and within the links. The geometry of masses is quantitatively described by mass-inertial characteristics. The most important of them are mass, radius of inertia, moment of inertia and coordinates of the center of mass.

Weight (T)is the amount of substance (in kilograms),contained in the body or individual link.

At the same time, mass is a quantitative measure of the inertia of a body in relation to the force acting on it. The greater the mass, the more inert the body and the more difficult it is to remove it from a state of rest or change its movement.

Mass determines the gravitational properties of a body. Body weight (in Newtons)

acceleration of a freely falling body.

Mass characterizes the inertia of a body during translational motion. During rotation, inertia depends not only on mass, but also on how it is distributed relative to the axis of rotation. The greater the distance from the link to the axis of rotation, the greater the contribution of this link to the inertia of the body. A quantitative measure of the inertia of a body at rotational movement serves moment of inertia:

Where R in — radius of inertia - the average distance from the axis of rotation (for example, from the axis of a joint) to the material points of the body.

Center of mass is the point where the lines of action of all forces that lead the body to translational motion and do not cause rotation of the body intersect. In a gravitational field (when gravity acts), the center of mass coincides with the center of gravity. The center of gravity is the point to which the resultant forces of gravity of all parts of the body are applied. The position of the overall center of mass of the body is determined by where the centers of mass of the individual links are located. And this depends on the posture, i.e. on how the parts of the body are located relative to each other in space.

There are about 70 links in the human body. But so detailed description mass geometry is most often not required. To solve most practical problems, a 15-link model of the human body is sufficient (Fig. 7). It is clear that in the 15-link model, some links consist of several elementary links. Therefore, it is more correct to call such enlarged links segments.

Numbers in Fig. 7 are true for the “average person” and are obtained by averaging the results of a study of many people. Individual characteristics of a person, and primarily the mass and length of the body, influence the geometry of the masses.

Rice. 7. 15 - link model of the human body: on the right - the method of dividing the body into segments and the mass of each segment (in% of body weight); on the left - locations of the centers of mass of the segments (in % of the segment length) - see table. 1 (according to V. M. Zatsiorsky, A. S. Aruin, V. N. Seluyanov)

V. N. Seluyanov established that the masses of body segments can be determined using the following equation:

Where m X - the mass of one of the body segments (kg), for example, the foot, lower leg, thigh, etc.;m— total body weight (kg);H— body length (cm);B 0, B 1, B 2— coefficients of the regression equation, they are different for different segments(Table 1).

Note. The coefficient values ​​are rounded and are correct for an adult male.

In order to understand how to use Table 1 and other similar tables, let’s calculate, for example, the mass of the hand of a person whose body weight is 60 kg and whose body length is 170 cm.

Table 1

Equation coefficients for calculating the mass of body segments by mass (T) and body length(s)

Segments	Equation coefficients
	B 0	IN 1	AT 2
Foot Shin Hip Brush Forearm Shoulder Head Upper body Mid torso Lower torso	—0,83 —1,59 —2,65 —0,12 0,32 0,25 1,30 8,21 7,18 —7,50	0,008 0,036 0,146 0,004 0,014 0,030 0,017 0,186 0,223 0,098	0,007 0,012 0,014 0,002 —0,001 —0,003 0,014 —0,058 —0,066 0,049

Brush weight = - 0.12 + 0.004x60+0.002x170 = 0.46 kg. Knowing what the masses and moments of inertia of the body links are and where their centers of mass are located, you can solve many important practical problems. Including:

- determine the quantity movements, equal to the product of body mass and its linear speed(m·v);

— determine kinetic moment, equal to the product of the moment of inertia of the body and the angular velocity(J w ); it should be taken into account that the values ​​of the moment of inertia relative to different axes are not the same;

- assess whether it is easy or difficult to control the speed of a body or an individual link;

— determine the degree of body stability, etc.

From this formula it is clear that during rotational motion about the same axis, the inertia of the human body depends not only on mass, but also on posture. Let's give an example.

In Fig. Figure 8 shows a figure skater performing a spin. In Fig. 8, A the athlete rotates quickly and makes about 10 revolutions per second. In the pose shown in Fig. 8, B, the rotation slows down sharply and then stops. This happens because, by moving her arms to the sides, the skater makes her body more inert: although the mass ( m ) remains the same, the radius of gyration (R in ) and therefore the moment of inertia.

Rice. 8. Slowing down rotation when changing pose:A -smaller; B - a large value of the radius of inertia and moment of inertia, which is proportional to the square of the radius of inertia (I=m R in)

Another illustration of what has been said can be a comic problem: what is heavier (more precisely, more inert)—a kilogram of iron or a kilogram of cotton wool? During forward motion, their inertia is the same. When moving in a circular motion, it is more difficult to move the cotton. Its material points are further away from the axis of rotation, and therefore the moment of inertia is much greater.

BODY LINKS AS LEVERS AND PENDULUMS

Biomechanical links are a kind of levers and pendulums.

As you know, levers are of the first kind (when forces are applied on opposite sides of the fulcrum) and of the second kind. An example of a second-class lever is shown in Fig. 9, A: gravitational force(F 1)and the opposing force of muscle traction(F 2) applied on one side of the fulcrum, located in this case at the elbow joint. There are a majority of such levers in the human body. But there are also levers of the first kind, for example the head (Fig. 9, B) and the pelvis in the main stance.

Exercise: find the lever of the first kind in fig. 9, A.

The lever is in equilibrium if the moments of the opposing forces are equal (see Fig. 9, A):

F 2 — traction force of the biceps brachii muscle;l 2 —a short lever arm equal to the distance from the tendon attachment to the axis of rotation; α is the angle between the direction of the force and the perpendicular to the longitudinal axis of the forearm.

The lever device of the motor apparatus gives a person the opportunity to perform long throws, strong blows etc. But nothing in the world comes for free. We gain in speed and power of movement at the cost of increasing the strength of muscle contraction. For example, in order to move a load weighing 1 kg (i.e. with a gravity force of 10 N) by bending the arm at the elbow joint as shown in Fig. 9, L, the biceps brachii muscle should develop a force of 100-200 N.

The “exchange” of force for speed is more pronounced, the greater the ratio of the lever arms. Let us illustrate this important point with an example from rowing (Fig. 10). All points of the oar-body moving around an axis have the samesame angular velocity

But their linear speeds are not the same. Linear speed(v)the higher, the larger the radius of rotation (r):

Therefore, to increase speed, you need to increase the radius of rotation. But then you will have to increase the force applied to the oar by the same amount. That is why it is more difficult to row with a long oar than a short one, throwing a heavy object over a long distance is more difficult than over a short distance, etc. Archimedes, who led the defense of Syracuse from the Romans and invented lever devices for throwing stones, knew about this.

A person's arms and legs can make oscillatory movements. This makes our limbs look like pendulums. The least energy expenditure for moving the limbs occurs when the frequency of movements is 20-30% greater than the frequency of natural vibrations of the arm or leg:

where (g= 9.8 m/s 2 ; l - the length of the pendulum, equal to the distance from the point of suspension to the center of mass of the arm or leg.

This 20-30% is explained by the fact that the leg is not a single-link cylinder, but consists of three segments (thigh, lower leg and foot). Please note: the natural frequency of oscillations does not depend on the mass of the swinging body, but decreases as the length of the pendulum increases.

By making the frequency of steps or strokes when walking, running, swimming, etc. resonant (i.e., close to the natural frequency of vibration of the arm or leg), it is possible to minimize energy costs.

It has been noted that with the most economical combination of frequency and length of steps or strokes, a person demonstrates significantly increased physical performance. It is useful to take this into account not only when training athletes, but also when conducting physical education classes in schools and health groups.

An inquisitive reader may ask: what explains the high efficiency of movements performed at a resonant frequency? This happens because the oscillatory movements of the upper and lower extremities are accompanied by recuperation mechanical energy (from lat. recuperatio - receipt again or reuse). The simplest form of recovery is the transition of potential energy into kinetic energy, then back into potential energy, etc. (Fig. 11). At a resonant frequency of movements, such transformations are carried out with minimal energy losses. This means that metabolic energy, once created in muscle cells and converted into mechanical energy, is used repeatedly - both in this cycle of movements and in subsequent ones. And if so, then the need for an influx of metabolic energy decreases.

Rice. eleven. One of the options for energy recovery during cyclic movements: the potential energy of the body (solid line) transforms into kinetic energy (dotted line), which is again converted into potential and contributes to the transition of the gymnast’s body to the upper position; the numbers on the graph correspond to the athlete's numbered poses

Thanks to energy recovery, performing cyclic movements at a pace close to the resonant frequency of the limbs is an effective way to conserve and accumulate energy. Resonant vibrations contribute to the concentration of energy, and in the world of inanimate nature they are sometimes unsafe. For example, there are known cases of a bridge being destroyed when a military unit was walking across it, clearly taking steps. Therefore, you are supposed to walk out of step on the bridge.

MECHANICAL PROPERTIES OF BONES AND JOINTS

Mechanical properties of bones determined by their various functions; In addition to motor, they perform protective and support functions.

The bones of the skull, chest and pelvis protect the internal organs. The supporting function of bones is performed by the bones of the limbs and spine.

The bones of the legs and arms are oblong and tubular. The tubular structure of bones provides resistance to significant loads and at the same time reduces their mass by 2-2.5 times and significantly reduces moments of inertia.

There are four types of mechanical effects on bone: tension, compression, bending and torsion.

With a tensile longitudinal force, the bone can withstand a stress of 150 N/mm 2 . This is 30 times more than the pressure that destroys a brick. It has been established that the tensile strength of bone is higher than that of oak and almost equal to that of cast iron.

When compressed, bone strength is even greater. Thus, the most massive bone, the tibia, can withstand the weight of 27 people. The maximum compression force is 16,000–18,000 N.

When bending, human bones also withstand significant loads. For example, a force of 12,000 N (1.2 t) is not enough to break a femur. This type of deformation is widely found in Everyday life, and in sports practice. For example, segments of the upper limb are deformed into bending when maintaining the “cross” position while hanging on the rings.

When we move, bones not only stretch, compress, and bend, but also twist. For example, when a person walks, the moments of torsional forces can reach 15 Nm. This value is several times less than the tensile strength of bones. Indeed, to destroy, for example, the tibia, the moment of twisting force must reach 30–140 Nm (Information about the magnitude of forces and moments of forces leading to bone deformation is approximate, and the figures are apparently underestimated, since they were obtained mainly from cadaveric material. But they also indicate a multiple safety margin of the human skeleton. In some countries, intravital determination of bone strength is practiced. Such research is well paid, but leads to injury or death of the testers and is therefore inhumane).

Table 2

The magnitude of the force acting on the head of the femur
(by X. A. Janson, 1975, revised)

Type of motor activity	Magnitude of force (according to type of motor activityrelation to body gravity)
seat	0,08
Standing on two legs	0,25
Standing on one leg	2,00
Walking on a flat surface	1,66
Ascent and descent on an inclined surface	2,08
Fast walk	3,58

The permissible mechanical loads are especially high for athletes, because regular training leads to working hypertrophy of the bones. It is known that weightlifters thicken the bones of the legs and spine, football players thicken the outer part of the metatarsal bone, tennis players thicken the bones of the forearm, etc.

Mechanical properties of joints depend on their structure. The articular surface is moistened by synovial fluid, which, as in a capsule, is stored by the joint capsule. Synovial fluid reduces the coefficient of friction in the joint by approximately 20 times. The nature of the action of the “squeezable” lubricant is striking, which, when the load on the joint decreases, is absorbed by the spongy formations of the joint, and when the load increases, it is squeezed out to wet the surface of the joint and reduce the coefficient of friction.

Indeed, the magnitude of the forces acting on the articular surfaces is enormous and depends on the type of activity and its intensity (Table 2).

Note. The forces acting on the knee joint are even higher; with a body weight of 90 kg they reach: when walking 7000 N, when running 20000 N.

The strength of joints, like the strength of bones, is not unlimited. Thus, the pressure in the articular cartilage should not exceed 350 N/cm 2 . At higher pressures, lubrication of the articular cartilage ceases and the risk of mechanical abrasion increases. This should be taken into account especially when conducting hiking trips (when a person carries a heavy load) and when organizing recreational activities for middle-aged and elderly people. After all, it is known that with age, lubrication of the joint capsule becomes less abundant.

BIOMECHANICS OF MUSCLES

Skeletal muscles are the main source of mechanical energy in the human body. They can be compared to an engine. What is the operating principle of such a “living engine” based on? What activates a muscle and what properties does it exhibit? How do muscles interact with each other? Finally, what are the best modes of muscle function? You will find answers to these questions in this section.

Biomechanical properties of muscles

These include contractility, as well as elasticity, rigidity, strength and relaxation.

Contractility is the ability of a muscle to contract when excited. As a result of contraction, the muscle shortens and a traction force occurs.

To talk about the mechanical properties of a muscle, we will use a model (Fig. 12), in which connective tissue formations (parallel elastic component) have a mechanical analogue in the form of a spring(1). Connective tissue formations include: the membrane of muscle fibers and their bundles, sarcolemma and fascia.

When a muscle contracts, transverse actin-myosin bridges are formed, the number of which determines the force of muscle contraction. Actin-myosin bridges of the contractile component are depicted on the model in the form of a cylinder in which the piston moves(2).

An analogue of a sequential elastic component is a spring(3), connected in series with the cylinder. It models the tendon and those myofibrils (contractile filaments that make up the muscle) that are not currently involved in contraction.

According to Hooke's law for a muscle, its elongation nonlinearly depends on the magnitude of the tensile force (Fig. 13). This curve (called “strength - length”) is one of the characteristic relationships that describe the patterns of muscle contraction. Another characteristic “force-velocity” relationship is named after the famous English physiologist Hill’s curve who studied it (Fig. 14) (This is how we call this important dependence today. In fact, A. Hill studied only overcoming movements (the right side of the graph in Fig. 14). The relationship between force and speed during yielding movements was first studied by Abbot. ).

Strength muscle is assessed by the magnitude of the tensile force at which the muscle ruptures. The limiting value of the tensile force is determined by the Hill curve (see Fig. 14). Force at which muscle rupture occurs (in terms of 1 mm 2 its cross section), ranges from 0.1 to 0.3 N/mm 2 . For comparison: the tensile strength of the tendon is about 50 N/mm 2 , and fascia is about 14 N/mm 2 . The question arises: why does a tendon sometimes tear, but the muscle remains intact? Apparently, this can happen with very fast movements: the muscle has time to absorb shock, but the tendon does not.

Relaxation - a property of a muscle manifested in a gradual decrease in traction force at a constant lengthmuscles. Relaxation manifests itself, for example, when jumping and jumping up, if a person pauses during a deep squat. The longer the pause, the lower the repulsion force and the jumping height.

Modes of contraction and types of muscle work

Muscles attached by tendons to bones function in isometric and anisometric modes (see Fig. 14).

In the isometric (holding) mode, the length of the muscle does not change (from the Greek “iso” - equal, “meter” - length). For example, in the isometric contraction mode, the muscles of a person who has pulled himself up and holds his body in this position work. Similar examples: “Azaryan cross” on the rings, holding the barbell, etc.

On the Hill curve, the isometric mode corresponds to the magnitude of the static force(F 0),at which the speed of muscle contraction is zero.

It has been noted that the static strength exhibited by an athlete in the isometric mode depends on the mode of previous work. If the muscle functioned in a inferior mode, thenF 0more than in the case when overcoming work was performed. That is why, for example, the “Azaryan cross” is easier to perform if the athlete comes into it from the top position, rather than from the bottom.

During anisometric contraction, the muscle shortens or lengthens. The muscles of a runner, swimmer, cyclist, etc. function in anisometric mode.

The anisometric mode has two varieties. In overcoming mode, the muscle shortens as a result of contraction. And in the yielding mode, the muscle is stretched by an external force. For example, the calf muscle of a sprinter functions in a yielding mode when the leg interacts with the support in the depreciation phase, and in an overcoming mode in the push-off phase.

The right side of the Hill curve (see Fig. 14) displays the patterns of overcoming work, in which an increase in the speed of muscle contraction causes a decrease in traction force. And in the inferior mode, the opposite picture is observed: an increase in the speed of muscle stretching is accompanied by an increase in traction force. This is the cause of numerous injuries in athletes (for example, ruptured Achilles tendons in sprinters and long jumpers).

Rice. 15. The power of muscle contraction depending on the strength and speed exerted; the shaded rectangle corresponds to the maximum power

Group interaction of muscles

There are two cases of group interaction of muscles: synergism and antagonism.

Synergistic musclesmove body parts in one direction. For example, in bending the arm at the elbow joint, the biceps brachii, brachialis and brachioradialis muscles, etc. are involved. The result of the synergistic interaction of the muscles is an increase in the resulting force of action. But the significance of muscle synergism does not end there. In the presence of an injury, as well as in the case of local fatigue of a muscle, its synergists ensure the performance of a motor action.

Antagonist muscles(as opposed to synergistic muscles) have multidirectional effects. So, if one of them does overcoming work, then the other does inferior work. The existence of antagonist muscles ensures: 1) high precision of motor actions; 2) reduction of injuries.

Power and efficiency of muscle contraction

As the speed of muscle contraction increases, the traction force of the muscle operating in the overcoming mode decreases according to the hyperbolic law (see. rice. 14). It is known that mechanical power is equal to the product of force and speed. There are strengths and speeds at which the power of muscle contraction is greatest (Fig. 15). This mode occurs when both force and speed are approximately 30% of their maximum possible values.

In the game "Who Wants to Be a Millionaire?" today, October 7, 2017, the twelfth question for players of the first part of the game turned out to be difficult. The question concerned a model of the human body - a visual aid for future doctors. The correct answer is highlighted in blue and in bold font.

What is the name of the model of the human body - a visual aid for future doctors?

I found this visual aid for obstetricians. Below is an excerpt from a help site about this visual aid.

PHANTOM OBSTETRIC, visual tutorial for teaching obstetrics, ch. arr. the course and mechanism of labor and obstetric operations. In its simplest form, F. a. consists of a bony female pelvis and a skeletonized head of a full-term fetus. Usually, however, under F. a. imply a pelvis built into something resembling the lower half of a woman’s torso with the upper halves of the thighs, and a “doll” depicting a full-term fetus. F. a. these are prepared from a wide variety of materials, from wood to a specially processed corpse; the same goes for “dolls”. For the first time he began to use F. a. for teaching at the end of the 17th century. Swedish obstetrician Horn, describing it in his textbook. This same textbook was the first educational book on obstetrics in Russian (“Midwife”, M., 1764).

Therefore, it is obvious that the correct answer to the question is in last place in the list of answer options, this is a phantom.

• ghost
• zombie
• phantom