Biomechanics of Torque, Levers, and Angular Motion

Torque and the Moment Arm

Torque is the turning effect produced by a force, also known as a moment. It is directly proportional to the magnitude of the force as well as the distance between the line of action of the force and the axis of rotation. In the motion of a restrained system, torque occurs when force is applied away from the axis and the line of action does not pass through the axis. Common examples include muscles, doors, wrenches, and hammers.

The moment arm is the shortest distance between the axis of rotation and the line of action. It is always perpendicular to the force's line of action and the axis of rotation.

Classification of Lever Systems

A lever consists of three primary components:

• Axis of rotation (fulcrum)
• Motive forces (muscles)
• Resistive forces (weight of limbs)

Levers are classified according to the relative positions of the axis, motive force, and resistive force:

First-Class Lever

The axis is located between the motive force and the resistive force (MAR). Examples include elbow extension and cervical extension.

Second-Class Lever

The resistance is in the middle (ARM). In this arrangement, a torque advantage exists for the motive force, though it is not as versatile. Examples include push-ups and the action of the plantar flexors.

Third-Class Lever

The motive force is in the middle (AMR). Most human joints act as third-class levers where the muscle provides the motive force. This system provides an advantage in Range of Motion (ROM) and speed of movement but a disadvantage in force. Examples include the bicep and elbow joint.

Calculating Mechanical Advantage

Mechanical Advantage (MA) is calculated as the ratio of the motive lever to the resistive lever. If MA > 1, a mechanical advantage exists, such as during a push-up.

Principles of Angular Motion

Angular motion refers to rotation about a point. it occurs when a force acts at a distance from a fixed point. Key terms include:

• Angular displacement: The difference between the initial and final positions of a rotating object.
• Angular speed: The angular distance traveled per unit of time.
• Angular velocity: The rate of change of angular displacement.

Linear and Angular Kinematics

The motion of any point on a rotating body can be explained in linear terms. To determine this, one must know the axis of rotation and the radius. An increase in the radius of rotation results in an increase in linear displacement.

For example, the radius (r) of a long club is greater than the radius of a short club. Because the radius is larger, the distance (d) covered over a given angle is increased. Increasing distance over the same time (t) results in an increase in velocity. The linear velocity of a rotating object is always tangential to the path of motion.

Understanding Acceleration

Tangential acceleration represents the change in linear velocity. Conversely, radial acceleration is directed toward the center along a curved path. It represents a change in direction; even if linear speed remains constant, the direction of the object is constantly changing as it travels.