﻿ Biomechanics - AAOS Comprehensive Orthopaedic Review ﻿

## AAOS Comprehensive Orthopaedic Review

### Chapter 2. Biomechanics

I. Introduction

A. Biomechanics combines the fundamentals of multiple fields to predict the effects of energy and forces on biologic systems.

1. The static and/or dynamic behavior of a body is characterized in response to internal and external factors.

2. Principles of biomechanics can be used to help understand normal forces and motions, altered situations such as responses to injury or surgery, and design considerations of orthopaedic implants and equipment.

B. Definitions and basic concepts

1. Rigid body—Maintains the relative position of any two particles inside it when subjected to external loads. All objects deform to some degree in response to their environment, but for rigid bodies, these deformations are so small compared to the size of the body that they can be ignored. For example, the small deformations that occur in bone under standard conditions are ignored, and bone is considered to be a rigid body.

2. Deformable body—Unlike a rigid body, a deformable body undergoes significant changes when subjected to external loads. For example, intervertebral disks are considered to be deformable bodies. Deformable body mechanics describes internal force density (stress) and the related deformation (strain). These terms are described in detail in the chapter on biomaterials.

3. Force—The physical quantity that changes the state of rest or state of uniform motion of a body and/or deforms its shape.

a. Forces exist as a result of interaction and are not necessarily associated with motion; for example, a person sitting on a chair exerts a force on the chair but the chair does not move.

b. Force is a vector quantity, which has both magnitude and direction. The International System of Units (SI) unit for force is the newton (N), with 1 N being the force required to give a 1-kg mass an acceleration of 1 m/s2.

4. Resultant force—If more than one force is applied to a body, the resultant force will be the vector sum of all the forces.

a. A force vector can be represented graphically by an arrow, where the orientation of the arrow indicates the line of action of the force vector, the base of the arrow represents the point of application of the force, the head of the arrow identifies the direction along which the force is acting, and the length of the arrow is proportional to the magnitude of the force it represents.

b. Graphic and trigonometric methods can be used to add forces (

Figure 1).

5. Mass—Represents the amount of matter physical objects contain. The SI unit of mass is the kilogram (kg).

6. Velocity—The rate of positional or angular change of an object's position with time. The SI unit for velocity is meters per second (m/s) for linear velocity and radians per second (rad/s) for angular velocity.

[Figure 1. The forces applied on the patella by the quadriceps () and patellar tendon () and the resultant force ().]

[

Table 1. Joint Reaction and Muscle Forces for Various Activities]

7. Acceleration—The rate at which the velocity of an object changes with time. Like velocity, acceleration can be either linear or angular. The SI units for linear acceleration and angular acceleration are m/s2 and rad/s2, respectively.

8. Moment—A measure of the ability of a force to generate rotational motion.

a. The axis the object rotates about is called the instantaneous axis of rotation (IAR).

b. The shortest distance between the IAR and the point of load application is called the moment arm.

c. The magnitude of the moment generated by a force is the magnitude of the force times its moment arm. The SI unit for moment is the newton-meter (N·m).

9. Torque—A rotational moment.

10. Mechanical equilibrium—A system is in mechanical equilibrium when the sums of the forces and moments are zero.

a. A body in mechanical equilibrium is undergoing neither linear nor rotational acceleration; however, it could be translating or rotating at a constant velocity.

b. Static equilibrium describes the special case of mechanical equilibrium of an object that is at rest.

11. Free body diagrams—Drawings used to show the location and direction of all known forces and moments acting upon an object in a given situation. They are useful to identify and evaluate the unknown forces and moments acting on individual parts of a system in equilibrium.

12. Degrees of freedom (DOF)—The number of parameters that it takes to uniquely specify the position and movement of a body.

a. For a body moving in three-dimensional space, there are six DOF, three translational and three rotational.

b. For a body moving in two dimensions, there are three DOF (eg, two translational and one rotational).

c. Clinical examples

i. A hinge joint such as the elbow has one DOF; the geometric constraints of the joint permit only one rotational motion about its axis of rotation.

ii. A ball-and-socket joint such as the hip has three rotational DOF.

13. In biomechanics, the three-dimensional motion of a body segment is generally expressed using a Cartesian coordinate system (xy, and z axes).

a. Sagittal (divides the body into right and left sides)

b. Coronal (divides the body into anterior and posterior parts)

c. Transverse (divides the body into upper and lower parts)

II. Kinematics and Kinetics

A. Kinematics describes the motion of objects without regard to how that motion is brought about.

1. In general, kinematics is concerned with the geometric and time-dependent aspects of motion without considering the forces or moments responsible for the motion.

2. Kinematics principally involves the relationships among position, velocity, and acceleration.

3. Knowledge of joint kinematics helps in understanding an articulation. As an example, this is important for the design of prosthetic implants to restore function and to understand joint wear, stability, and degeneration.

B. Kinetics involves analysis of the effects of the forces or moments that are responsible for the motion.

C. Kinematics and kinetics involve categorizing motion into translational components, rotational components, or both.

III. Joint Mechanics

A. Each joint provides various degrees of mobility and stability based on specific structural considerations (Table 1). These are acted on by internal and external loads.

B. Mechanics of the elbow joint—

Figure 2 shows a free body diagram in the x-y plane (two-dimensional problem) for the forearm at 90° of flexion and holding a weight in the hand.

1. The forces acting on the forearm are the total weight of the forearm (Wf), the weight of the object in the hand (Wo), the magnitude of the force exerted by the biceps on the forearm (Fmuscle), and the magnitude of the joint reaction force at the elbow (Fjoint).

2. Point O is the IAR of the elbow joint, P is the point of attachment of the biceps on the radius, Q represents the center of gravity of the forearm, and R lies on the vertical line passing through the center of gravity of the weight held in the hand.

3. The distances from these points to the center of rotation (moment arms) are shown in the figure and are assumed to be known from the anatomy. The direction of the muscle force is also known; in this problem, it is assumed to be vertical.

4. Considering the rotational equilibrium of the forearm about O,

[Figure 2. Free body diagram for an arm holding a weight in the hand.]

5. Because the forearm is in translational equilibrium, the sum of the forces is zero:

6. Breaking down the vector into the components along the Cartesian axes,

 Σ Fx = 0 → FXjoint = 0

(There is no joint reaction force along the x axis.)

 Σ Fy = 0 → FYjoint = Fjoint = Fmuscle - (Wf + Wo).

7. The above equations can be solved for the muscle force and the joint reaction force for given geometric parameters and weights. By assuming that Wf = 25 N, Wo = 100 N, P = 5 cm, q = 12 cm, and r = 40 cm, the muscle force and joint reaction force can be calculated as follows:

 Fmuscle = (1/0.05)[(0.12 × 25) + (0.4 × 100)] = 860 N Fjoint = (860 - 25) - 100 = 735 N.

[

Figure 3. Forces acting across the hip joint during single-limb stance.]

C. Mechanics of the hip joint—Figures 3 and

4 show the forces acting across the hip joint during single-limb stance (2-dimensional problem). During walking and running, all the body weight is momentarily on one leg.

1. The forces acting on the leg carrying the total body weight during such a single-leg stance are shown in Figure 3, where M is the magnitude of the resultant force exerted by the hip abductor muscles, assumed vertical; J is the magnitude of the joint reaction force applied by the pelvis on the femur, again assumed vertical; and W is the partial body weight (body weight minus weight of the right leg).

[Figure 4. The free body diagram for the problem defined in Figure 3.]

2. The free body diagram of the body without the supported leg is shown in Figure 4, where O is the point where the hip abductor muscles attach to the femur; B is a point along the IAR of the hip joint; and A is the center of gravity of the body without the supported leg.

3. The distances between O and B and between A and B are specified as b and a, respectively.

4. To find the magnitude of the force M exerted by the hip abductor muscles, the condition of the rotational equilibrium of the leg about B can be applied. (Assumption: Clockwise moments are positive.)

 (W · a) - (M · b) = 0M = (W · a)/b

For W = 600 N, b = 50 mm, and a = 100 mm,

 M = (600 · 100)/(50)M = 1200 N

5. To calculate the joint reaction force J, consider force equilibrium along the y axis. (Assumption: Forces acting downward are negative.)

 Σ Fy = 0J - M - W = 0J = M + W= 1200 + 600J = 1800 N

Top Testing Facts

1. Mechanical equilibrium is when the sums of all forces and moments are zero.

2. Free body diagrams show the locations and directions of all forces and moments acting on a body.

3. Kinematics describes the motion of objects without regard to how that motion is brought about.

4. Kinetics involves analysis of the effects of forces and/or moments that are responsible for motion.

5. Each joint has specific load interactions because of the particular characteristics of the joint and the muscle actions that cross the joint.

Bibliography

Ashton-Miller JA, Schultz AB: Basic orthopaedic biomechanics, in Mow VC, Hayes WC (eds): Biomechanics of the Human Spine, ed 2. Philadelphia, PA, Lippincott-Raven, 1997, pp 353-385.

Lu LL, Kaufman KR, Yaszemski MJ: Biomechanics, in Einhorn TA, O'Keefe RJ, Buckwalter JA (eds): Orthopaedic Basic Science: Foundations of Clinical Practice, ed 3. Rosemont, IL, American Academy of Orthopaedic Surgeons, 2007, pp 49-64.

Panjabi MM, White AA (eds): Biomechanics in the Musculoskeletal System. New York, NY, Churchill Livingstone, 2001.

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