Biomechanics is an interdisciplinary field that uses the principles of mechanics to improve the human body through design, development, and analysis of equipment, systems, and therapies. This biomechanical knowledge can help in understanding the loading of the musculoskeletal system and its mechanical responses, which can be used to determine normal function, predict changes, and propose interventions. More specifically, basic biomechanics explores forces and moments required for movement and balance of the human body by muscle recruitment and the consequence of internal forces on loading of soft tissues. This chapter explores biomechanics in terms of four different topics: statics, dynamics, mechanics of materials, and applications. Additionally, examples of these concepts are provided throughout the chapter to illustrate how they can be directly applied to sports medicine.
Basic Concepts
Units of Measure
Understanding the basic units of measure for biomechanics is important in describing the dimensional or spatial analyses. Three primary dimensions exist (length, time, and mass) from which secondary dimensions have subsequently been derived ( Table 2-1 ). Metric unit measurements are commonly used in the field of biomechanics to describe such dimensions and will also be used in this chapter. One measurement not described in Table 2-1 is that used for angular descriptions. The unit for angles is typically defined in terms of radians or degrees.
| Dimensions | SI Unit |
|---|---|
| Primary | |
| Length | Meter (m) |
| Time | Second (s) |
| Mass | Kilogram (kg) |
| Secondary Dimensions | |
| Area | m 2 |
| Volume | m 3 |
| Velocity | m/s |
| Acceleration | m/s 2 |
| Force | Newton (N) = kg • m/s 2 |
| Pressure/stress | Pascal (Pa) = N/m 2 |
| Moment/torque | N • m |
| Work/energy | Joule (J) = N • m |
| Power | J/s |
Scalars and Vectors
Most of the physical quantities encountered in mechanics are either scalars or vectors. Scalar quantities describe only the magnitude of an element and are used for concepts such as time, length, speed, mass, temperature, volume, work, power, and energy. In contrast, both a magnitude and a direction are associated with vector quantities. Examples of vector quantities are displacement, force, moment, velocity, and acceleration. The magnitude of an object’s velocity is identical to its speed, but the velocity vector also contains information about the direction of motion. Graphically, a vector is represented as an arrow, with the orientation of the arrow indicating its line of action or direction. For example, the force of gravity is a vector quantity that can be represented by a downward arrow at an object’s center of mass. Typically, vectors are represented in a Cartesian coordinate system.
Coordinate Systems
A coordinate system is a frame of reference for a structure or system. Coordinate systems are spatial tools that are useful in describing body position and orientation and the directionality of all vector quantities. To apply mechanical principles to a system, all vector quantities must be expressed with respect to the same coordinate system. Several types of coordinate systems are available, but the most commonly used in sports medicine research is the Cartesian coordinate system. This system can be either two- or three-dimensional. All axes are perpendicular to one another (a condition known as orthogonality) and have both positive and negative components. A vector quantity contains a component in each dimension corresponding to the magnitude associated with each axis. In a two-dimensional system, the horizontal and vertical axes are typically labeled “x” and “y,” respectively. In a three-dimensional system, the “z” axis is added. This axis lies perpendicular to both the x and y axes, with its positive side determined by the right-hand rule. This rule states that if you align the index finger of your right hand with positive x axis and the middle finger with the positive y axis, then your thumb will be pointing in the positive direction of the z axis. Similarly, the right-hand rule can be used to determine the positive and negative directions of angles and moments about a specified axis. While the thumb of your right hand is aligned with the rotational axis, your fingers will curl in the positive direction of rotation. These rules are very important in establishing the correct spatial quantities of a system within a designated coordinate system.
Anatomic Coordinate System
An anatomic coordinate system is a Cartesian coordinate system with each axis representing anatomic directions such as superior-inferior, medial-lateral, and anterior-posterior. The corresponding rotations about these axes are represented by internal-external rotation, flexion-extension, and abduction-adduction, respectively. Researchers and clinicians use the anatomic coordinate system whenever possible, because it is the most clinically relevant for diagnosis and treatment.
Degrees of Freedom
Degrees of freedom are the total number of independent movements needed to completely describe the position and orientation of a body in a given coordinate system. The musculoskeletal system has numerous degrees of freedom through which countless movements are accomplished. These movements can be performed in three-dimensional space through a set of translations and rotations and are typically described in an anatomic coordinate system. For example, the glenohumeral joint has a total of six degrees of freedom: three translations (superior-inferior, medial-lateral, and anterior-posterior) and three rotations (internal-external, abduction-adduction, and flexion-extension). However, depending on the analysis, the glenohumeral joint can be assumed to be a ball-and-socket joint, thus reducing the number of degrees of freedom to three rotations by constraining the translations. Similarly, the elbow only allows for one degree of freedom when it is considered a simple hinge joint.
Degrees of freedom are important to consider when numerically describing body motion and position. Joint motion may be constrained by the shape of the articular surfaces or by stabilizing ligaments, reducing the degrees of freedom and simplifying the description. However, some joints, such as the knee and ankle, also allow for small amounts of translation that are important to consider when interpreting a clinical examination. With an anterior cruciate ligament (ACL) injury, the knee will have an increased level of anterior translation, thereby altering the anterior degree of freedom. Using reduced degrees of freedom is strategic when modeling or characterizing joints of the body. For example, when a person picks up an object from the floor and subsequently returns to an erect posture, each vertebra moves in three-dimensional space to achieve the desired posture, representing a large number of degrees of freedom. To evaluate lower back injuries using modeling techniques, the degrees of freedom can be significantly reduced by only considering the L5–S1 joint and assuming that the motion occurs only in the sagittal plane, resulting in a two-dimensional analysis. Similarly, when assessing the tibiofemoral joint during a kicking motion, it could be assumed that the tibia only moves in two dimensions within the sagittal plane ( Fig. 2-1, A ). These reductive assumptions often overestimate the translations, rotations, forces, and moments required to perform the motion.
Newton’s Laws
Three basic rules of physics—Newton’s laws of motion—are used to describe the relationship between the forces applied to the body and the consequences of those forces on human motion ( Table 2-2 ).
Newton’s First Law (Inertia)
Newton’s first law states that an object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction (velocity) unless acted upon by an unbalanced force. This law is also commonly referred to as the law of inertia . Therefore a nonzero resultant force must act on a rigid body to change its velocity. For example, headrests are placed in cars to prevent whiplash injuries during rear-end collisions by stopping the motion of the head, which illustrates decreasing linear velocity and acceleration by application of an unbalanced force. Furthermore, if the resultant moments and forces are zero, then the body will also have no rotational or linear acceleration.
Newton’s Second Law (Acceleration)
Newton’s second law pertains to the behavior of objects for which all forces are not balanced. Therefore the resultant force is not equal to zero, and acceleration in the direction of the applied force will occur. The magnitude of the acceleration is proportional to the magnitude of the resultant forces or moments applied to the body. Thus, in essence, the first law is a special case of the second law:
Σ F = m ⋅ a : Σ M = I ⋅ α ,
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