Biomechanics of Function and Injury
Adam Gotlin, BS, MS
The human body consists of a system of bones, muscles, ligaments, tendons, cartilage, and other connective tissues that work together to move the body through space. This musculoskeletal system allows us to perform an expansive and diverse set of athletic tasks, from everyday walking to the complex twists and turns of a gymnastics routine. In this light, the human body is one of the most versatile, powerful, and robust mechanical machines that exists in nature. However, by participating in sport, professional and amateur athletes often push the human machine to the limits, which can unfortunately result in injury.
In short, an injury is damage to or failure of the human body that impairs normal function and movement. During sport, athletes attempt to manipulate themselves or other objects in their environment (such as a ball or even other people) to accomplish a particular goal. When functional limits are exceeded, failure occurs, and the body becomes injured.
The biomechanics of function and injury sits at the intersection of three primary academic disciplines: mechanics, material science, and biology. This chapter investigates how we can use an interdisciplinary approach to examine, analyze, and understand the mechanics of the human body in an effort to prevent and treat sports injuries. We present each core academic discipline of biomechanics from a high-level perspective. For more detailed text on the topics covered here, please consult the references at the end of this book on page 346. This chapter also serves as a foundation for subsequent chapters that will dive deeper into various injuries subdivided by region of the body.
FIGURE 1.1 The three disciplines of biomechanics of function and injury.
Let’s begin by briefly reviewing key concepts from the fields of mechanics, material science, and biology and quickly connect these concepts to bodily function and injury (see figure 1.1).
Mechanics and the Human Body
Mechanics is a broad field of study that investigates how physical objects bend, stretch, twist, push, pull, translate, and rotate. The terms body and object can be used somewhat interchangeably in the study of mechanics. For our purposes, both a body and an object represent a collection of matter in space, such as a ball, a bone, or the entire human body.
Mechanics has been central to major innovations throughout human history; it is the core discipline to understanding the function of essentially all machines, from airplanes, to cranes, to robots, and of course, the human body. In this section, we review mechanics through the lens of kinematics (how objects move) and forces (what moves objects).
We are going to reference and analyze various mechanical quantities related to biomechanics of form and function. Namely, we will review forces, moments, acceleration, velocity, and position, all of which are vector quantities. As such, let’s ensure our terminology is aligned and start by reviewing vectors. So, what is a vector anyway?
Simply defined, a vector is a quantity that has both magnitude and direction. For our purposes, it is also useful to include the point of application as an attribute of a vector. The three primary kinematic vectors we use in biomechanics are these:
- Position. The displacement of one object relative to some reference point
- Velocity. The time rate of change of the position of an object
- Acceleration. The time rate of change of the velocity of an object
Position is measured in units of length such as meters; velocity has dimensions of length over time, and acceleration has dimensions of length over time squared. If you are familiar with calculus, you will recognize that velocity is simply the derivative of position, and acceleration is the derivative of velocity, with respect to time. Table 1.1 contains common units used to describe the mechanical quantities discussed in this chapter.
Kinematics is the study of spatial geometry of movement with regard to an object’s position, velocity, acceleration, and orientation. At any given point in time, the limbs in our body are located at a certain position. Further, each limb will have its own velocity (which may have magnitude of zero) and acceleration. In order to play sports, athletes must accelerate their limbs to change their velocity and move themselves to different positions. In this case, where do accelerations come from? As Isaac Newton described in the 17th century, acceleration is the result of force (Newton 1687).
TABLE 1.1 Base Units for Key Mechanical Quantities
Meters per second (m/s)
Foot per second (ft/s)
Meters per second squared (m/s2)
Foot per second squared (ft/s2)
Pascal (Pa or N/m2)
Pounds per square inch (psi)
Forces accelerate mass. Mass, also called inertial mass, describes how much “stuff” a body of matter is made up of. Surprisingly, it really doesn’t get more scientific than that! Mass can also be thought of as a property that describes the extent to which a body of matter resists acceleration. The more massive an object, the less it will accelerate due to a given force. Our classical understanding of the relationship between mass and force was first brought to light by Isaac Newton and is summarized in three fundamental laws of motion known as Newton’s three laws.
For our purposes, a useful interpretation of Newton’s three laws of motion is as follows:
- An object’s velocity will remain constant unless acted upon by an external force.
- The relationship between force and mass is governed by the equation where , m, and represent force, mass, and acceleration, respectively.
- When one body exerts a force on a second body, the second body also exerts a reactive force of equal magnitude and opposite direction on the first body.
Newton’s first law simply states that an object needs a force to change its velocity. If the object is not moving (velocity has a magnitude of 0 m/s), then it will continue to remain motionless until acted upon by a force. Objects in this state describe a static system. For example, a person who is standing very steadily might be considered static. Though forces exist in a static system, all of the forces cancel each other out; the net force on the system is 0 N. Thus, no acceleration exists and the body remains motionless. If on the contrary an object is moving (say, a hockey puck traveling at a velocity of 2 m/s toward a goal), the object will remain in motion indefinitely unless acted upon by an external force (like hitting the wall, another player’s stick, or the frictional force from the ice on the puck). Most injuries occur in dynamic situations where net forces are nonzero.
FIGURE 1.2 A basketball player applies a contact force to a ball. The resultant acceleration of the ball due to the contact force points in the same direction as the applied force.
Newton’s second law introduces the equation which is often the first equation taught in a high school physics class, and for good reason. In the equation, the represents the force acting on the body, whereas m represents mass of the body, which is multiplied by , the body’s acceleration. This equation mathematically describes how all forces in the universe interact with matter. (There are certain regimes, such as quantum mechanics, where the laws of break down. However, this regime is not relevant to sports injury biomechanics.) Whether that force comes from magnets, gravity, or a push from someone’s hand, the governing equation at play is . The arrow symbols on top of the and may look unfamiliar to some readers. In biomechanics, it is convention to use arrows to indicate that the given quantity is a vector (has magnitude and direction). Mass, on the other hand, is a scalar, a quantity with magnitude but no corresponding direction. Consequently, the direction of the net force applied to a mass corresponds to the same exact direction as the resultant acceleration of that mass. For example, in figure 1.2 we see a basketball player exerting a force on a ball to make a pass. If the basketball player exerts a force of 100 N in the horizontal-right direction on a 5-kg ball, the ball will accelerate at 20 m/s in the horizontal-right direction for as long as the force is applied (100 = 5 × 20).
Finally, Newton’s third law states that forces come in pairs of equal-and-opposites. In rugby, when a fullback pushes a ball carrier to make a tackle, the ball carrier will exert an equal force in the opposite direction from the fullback’s contact. Whether the play results in a completed tackle depends on how massive each player is and the players’ initial velocities before the tackle.
Common Forces in Human Mechanics
Now that we have a more complete understanding of forces and how they relate to mass and motion, let’s highlight some of the sources of force we often see in human locomotion and sports injuries. The most common forces we encounter and will consider here are external forces from gravity and contact, along with internal forces from muscle, bone, tendons, ligaments, and joint tissue. Forces are also vector quantities, and a complete biomechanical analysis should consider each force’s magnitude, direction, and location of application on the human body. We will use figure 1.3 to guide our introduction to forces.
FIGURE 1.3 A side view of a weightlifter holding a dumbbell stationary. Force vectors acting on the forearms are shown with arrows starting at the point of application. The dumbbell pushes on the athlete’s hand while the weight of the arm pulls the arm down. To counteract this downward force, the muscle pulls the arm upward. Since the force vector of the muscle also pulls the lower arm into the elbow joint, the joint provides a reaction force. The net force on the system (i.e., a motionless arm) is 0 N.
Gravity is the force that brings everything together, literally. Mass tends to attract other mass. We call the force of attraction between two masses the gravitational force. Gravity is a distance force; no contact is necessary for the force to exist. When we analyze sports injuries, gravity from the massive Earth results in a force that pulls other bodies of matter closer to the center of Earth. In fact, the very concept of the direction “vertically downward” is defined by the direction of gravity force vector. Gravity is omnipresent, and thus is a crucial force to include in any mechanical analysis of the human body.
In biomechanics, a massive object’s weight is equivalent to the force of gravity due to the object’s attraction to Earth. In figure 1.3, we represent the weight of the arm as a vertically downward (toward Earth) force vector located at the center of mass of the arm. The center of mass is a point located at the average position of all the matter in a body. (Technically, each cell in the arm has its own gravity vector; however, it is conventional and mechanically equivalent to replace all the tiny weight vectors from each cell with one cumulative weight vector located at the arm’s center of mass.) Similarly, the dumbbell has a gravitational force that pushes the dumbbell down into the athlete’s hand. So then, why doesn’t the dumbbell simply fall through the athlete’s hand toward the ground? The answer: contact.
A contact force occurs when the surface of the bodies associated with force are collocated (i.e., in contact) (Mitiguy 2017). Contact forces are extremely common in sports because athletes, walls, projectiles, and the ground are constantly pushing against one another. Like all other forces, contact forces are in strict compliance with Newton’s three laws of motion. At the point of contact, each body pushes on the other with equal and opposite forces. The resultant motion of those bodies will obey .
In figure 1.3, the contact force between the hand and the dumbbell prevents the dumbbell from passing through the hand. Given that the dumbbell is being held steadily, we apply Newton’s third law and conclude that the force the hand exerts on the dumbbell must exactly counteract the weight of the dumbbell. A seemingly trivial result is that the hand exerts an upward contact force on the dumbbell of equal magnitude to the weight of the dumbbell. A more subtle subsequent consequence is that the same contact force results in a reaction force from the dumbbell on the hand in the downward direction. The weightlifter feels the dumbbell in his hand because he is pushing the dumbbell upward. The resultant force in the system is 0 N. When a muscle contracts to hold a weight steady (i.e., without acceleration), this is termed an isometric contraction.
Ground Reaction Force
The ground reaction force is a special type of contact force that exists between a person and the ground. This force is central to sports injury biomechanics because ground contact is almost always involved in both traumatic and overuse injuries. When the ground exerts a contact force on an athlete’s extremity (most often the foot), the force propagates through the joints of the lower and upper extremities. When combined with other contact forces discussed earlier, the musculoskeletal system can be placed in a compromising state in which the muscles, tendons, and bone reach points of failure. In this sense, forces are the culprits of athletic injury.
The ground reaction force is the force generated by the ground, on the body, that opposes the equal-and-opposite force applied by the body, on the ground. In order to walk, run, or simply move through space, we have to first push against the ground in the direction opposite where we want to travel. The ground then pushes back, producing a net force in the desired direction. If you look closely at people while they walk, you will notice that their foot pushes against the ground in the direction opposite the direction they are trying to move in. During the late stance of walking, the foot pushes down into the ground and posteriorly (backward). The ground reaction force produced by this action points upward and in the anterior (forward) direction, which results in the body rising and moving forward. This interaction is explained in more detail in the running case study later in this chapter.
Internal forces are forces that are produced from within the human body. The most pronounced internal force generated by athletes is the active muscle force. A muscle force is generated when the brain sends a signal to a muscle to contract. When a muscle contracts, it tries to shorten by pulling its two ends closer together, as shown in figure 1.3. Muscle attaches to bone directly or, more commonly, through connective tissue called tendons. Muscles and tendon together make up a musculotendon unit. Notice, contraction causes the muscle to generate a force at both attachment points, pulling the bones together along the line of action of the muscle. It is also interesting to note that muscles can only pull on bones; they never push. When the muscles pull bones about a joint closer together, it is called flexion. In order to move bones away from each other, there must be muscles working on the opposite side of the joint. Extension occurs when these opposing muscles move bones away from one another. Moving bones about a joint closer or farther refers to the angle between the bones at the joint. When the angle made by the joint decreases, the bones are said to move closer together, and the joint is in flexion. Extension straightens the joint by increasing the angle. Together, the pair of muscles that can flex and extend the same joint make an antagonist pair. At the elbow joint, as shown in figure 1.3, the biceps muscles flex the arm while the antagonist triceps muscles (not shown) extend the arm. Bones are rigid bodies that move when muscles contract.
Ligaments and Tendons
The other major set of internal forces comprises passive forces produced by tendons, ligaments, and even muscle. Passive forces are generated when connective tissue is stretched. Like a rubber band being pulled beyond its rest length, connective tissue acts like a spring and resists stretching by producing a passive tensile force. Similar to the active muscle force, tensile forces tend to pull the attachment points of a connective tissue closer together. Tendons, which connect muscles to bone, can become stretched when the muscle is activated or when the full musculotendon unit is pulled beyond its natural length (e.g., while an athlete stretches in a warm-up). Ligaments connect bone to other bone, and stretch when other forces attempt to pull those bone segments apart. Passive forces in connective tissue are crucial for stability around joints, and failure of connective tissue by being overstretched, or stretched too quickly, is a leading cause of sports injury.
Joint Contact Forces
The human machine is made up of hundreds of bone segments that are in contact with one another at joints. Joint contact forces are reaction forces resulting from external and internal forces acting across the joint. These pivotal internal forces exist to ensure body segments move as expected. For example, in figure 1.3, the elbow joint acts as a pivot point for the forearm (radius and ulna bones) to rotate about the upper arm (humerus bone). Similar to our analysis of the dumbbell and the hand, forces must be present at the contact surface between the forearm and upper arm to enforce that the radius and ulna do not travel through the humerus bones during motion. We see that the muscle force vector on the forearm produced by the biceps muscle group flexes the forearm up toward the humerus along the direction of the force vector. To prevent the forearm from translating in this direction, contact forces are produced at the joint where the upper and lower arm meet. Joint contact forces are typically applied on a cartilage surface, or sometimes directly to bone, near the joint center.
Other Internal Forces
Beyond tendons, ligaments, and passive and active muscle forces, there are plenty of other internal forces that play roles in the biomechanics of movement. Articular cartilage provides a cushion between bones at a joint and bears the load for many of the joint reaction forces discussed earlier. Even skin, the vascular system, and other soft tissue technically provide resistance and generate internal forces. Nevertheless, most models of the human body (e.g., mathematical representations used for analysis) focus on muscles, bones, ligaments, and tendons. These structures produce the majority of internal forces and are the source of athletic injuries.
While the majority of this section has focused on forces, the more precise role of muscles in the body is to rotate limbs about a joint center. Though muscles act to pull bones and other soft tissue toward one another (i.e., translation through flexion or extension), muscle functionally moves body segments throughout space by rotating limbs about a joint. Rotation of one limb about another can be defined as an angular displacement, or a change in relative orientation of the two limbs. In the simple two-dimensional configuration of the elbow joint in figure 1.3, we can think of the orientation of the forearm as a line pointing from the elbow to the hand, whereas the orientation of the upper arm is a line pointing from the elbow to the shoulder. In this case, the forearm is making a 90-degree angle to the upper arm. If the weightlifter further flexed his bicep, the forearm and dumbbell would rotate about the elbow and decrease the angle between the upper arm and forearm. On the other hand, extension (performed by the triceps) would increase the angle formed at the joint. The joint center of the elbow is called the pivot point, and the line passing through the pivot point that the forearm rotates about is called the axis of rotation.
The elbow provides a pivot point for the forearm to rotate about the upper arm. Since this rotation is largely done in one plane, the elbow is considered a hinge joint. The hip joint, on the other hand, is a ball-and-socket joint that allows for multiple axes of rotations. Understanding the structure and function of a joint will help in understanding the types of motions that are safe (or dangerous) for athletes to perform.
The tendency of a force to rotate an object about a point is the moment of force (the rotary component of a force is also called torque). Moments about a joint produce angular acceleration about the point of rotation. The magnitude of the moment produced by a force about a point is proportional to the magnitude of the force multiplied by the moment arm. A moment arm is the minimum distance between the line of action of the force and the pivot point. To better illustrate these terms and highlight the importance of the moment arm, let’s analyze two different postures in figure 1.4. The gravity vector located at the center of the mass of the head is pointing downward in both figure 1.4a and 1.4b. However, the moment arm about the pivot point (the C5 vertebra) is much larger in 1.4b. Therefore, the moment produced by the weight of the head in 1.4b is much larger. To keep the head stationary, muscles in the back of the neck must work harder to provide a moment in the clockwise direction to counteract the counterclockwise moments caused by the weight of the head.
FIGURE 1.4 By placing the head in a compromising position, humans can substantially increase the torque experienced at the neck. In posture a, the moment arm of the weight of the head, d1, is quite small. In posture b, the moment arm, d2, is significantly increased. In each position, muscles and tendons pull at the back of the head to prevent the neck from rotating about the C5 vertebra (an arbitrary pivot point chosen for analysis). Greater musculotendon forces are required in posture b in order to generate a clockwise moment sufficient enough to keep the head steady.
Humans carefully coordinate active muscle forces to rotate limbs about one another. In doing so, athletes balance internal and external forces to produce desired motions to accomplish athletic tasks, such as jumping, throwing, or running.
In human biomechanics, stability can be defined as “the ability of a joint to maintain an appropriate functional position throughout its range of motion” (Burstein and Wright 1994, 63). Injury often results from the lack of stability; and further, injured tissue often leads to additional instability. Stable mechanical systems are ones that tend to apply forces that restore normal functional positions, as opposed to forces that pull that system apart. To better understand this concept, let’s refer to figure 1.5. Here we see two stable mechanical systems and two unstable ones. The top row shows a ball resting in a valley (stable) and one resting on top of a hill (unstable). If the ball were to become slightly displaced in the valley, the force of gravity would tend to guide the ball back to its original position; the system is stable. On the other hand, a minor displacement of the ball at the top of the hill will send the ball crashing down the hill. These same concepts can be applied to the human knee. In both scenarios pictured, the femur rests on top of the tibial plateau at the knee joint. In the stable case, minor rotations or displacements of the femur will tend to be corrected by internal restoring forces applied by the cruciate and collateral ligaments. But imagine if those ligaments did not exist (or maybe they were torn or ruptured due to an athletic injury), the knee would become much less stable. A slight displacement of the femur could put the whole system off-balance, which would be disastrous for an athlete.
FIGURE 1.5 (a) Stable systems with proper restoring forces tend to converge to the resting position, and (b) unstable systems without restoring forces will diverge with minor perturbations.
Human joints are provided stability through passive elements, such as the cruciate and collateral ligaments in figure 1.5, but also through dynamic neuromuscular control. Muscles that cross the joint can activate in an attempt to hold the joint in a favorable position. Further, cocontraction of opposing muscle groups (such as the hamstring and quadriceps group) can greatly enhance stability by pulling bones on opposite sides of the joint closer together. As you might have noticed, a major downside of using cocontraction for stability is that it tends to increase joint contact forces.
Material Properties of Human Tissue
The human machine is a complex system composed of diverse materials and elements. The primary structure consists of bones (hard tissue) connected by tendons, ligaments, and fascia (connective tissue) interwoven with nerves, blood, and muscle (soft tissue). Each material has its own set of properties that dictate how it responds to a particular load. For our purposes, a load is a set of external forces acting on a surface or body. Material properties also dictate the breaking points of body tissue, when injury often occurs. This section will help advance understanding of how and why tissue in the body fails by reviewing key concepts of material science and relating them back to the forces experienced during sport and other activities.
A Closer Look at the Mechanics of Running
Normal running on a flat surface serves as a great case study to summarize the mechanics concepts discussed in this chapter. The act of running is a continuous repetition of strides. The length of a stride is defined as the distance from initial heel contact of one foot (e.g., the right foot) to the subsequent heel contact of the same foot (i.e., the right foot again) along the line of progression. A step is roughly half a stride (i.e., heel contact of right foot to heel contact of left foot). Figure 1.6 summarizes the phases of the gait cycle and the key mechanical principles present in each phase. In this figure, the stride cycle begins at right-foot heel contact.
FIGURE 1.6 One stride of running gait, starting with right-foot heel strike. The gait cycle consists of phases that define the type of motion and muscle activation patterns used to accomplish the necessary tasks to complete one cycle.
The first phase of the gait cycle is the stance phase. The right foot is in contact with the ground throughout the first stance phase. During early stance, the body is braking from the previous step. Quadriceps muscles contract to extend the knee, causing the lower leg to rotate into the ground to resist forward motion. The ground reacts to this contact force with a reaction force that decelerates the runner (i.e., an acceleration that reduces the magnitude of velocity). Further, the athlete is falling into the ground during early stance; the ground reaction force also has an upward vertical component to prevent the body from going through the ground. In the latter part of stance phase, the foot transitions from heel to toe, and the muscles in the calf, notably the gastrocnemius and soleus, activate to propel the body forward. This time, these muscles cause the foot to push against the ground in the backward direction, resulting in a forward ground reaction force that propels the body forward into flight.
For a moment, both feet are off the ground and the body is completely in flight. The right leg begins to swing around the hips toward the front of the body to prepare for the next step. After a short period of flight, the left leg makes contact with the ground (this completes one step). Naturally, the right foot produces zero ground reaction force during its swing phase while the left foot undergoes the deceleration–acceleration coordination cycle described earlier. Meanwhile, hip flexors in the right leg, such as the iliopsoas and sartorius, contract to produce a moment on the lower leg about the torso that rotates the right leg forward. Toward the end of the swing phase, there is another brief flight phase in which both the right and left foot are off the ground. The running gait cycle concludes when the right foot makes contact with the ground again.
As we can see, the mechanics involved in running, one of the most fundamental mechanical motions, is not simple, to say the least. Further complexities can be introduced into our running analysis by considering the deformation of different body parts, stiffness of the ground (and stiffness of sneakers), medial-lateral (side-to-side) movement of the body, and so on. Nevertheless, we are able to make a simplified model of this complex biomechanical system to understand the major forces and moments involved in running.
Often, the body has no issue generating the necessary forces and moments to complete the running motion. Unfortunately, this is not always the case. As we will see in the next section, the material elements in the human body can take only so much before they ultimately fail.