# 054: Degrees of Freedom

Nov 27, 2021

The location of a given point in space can be described by three pieces of information contained in its coordinate location, which are commonly described by the letters X, Y, and Z.

According to the convention adopted by the International Society of Biomechanics, the X-axis corresponds with the principal horizontal direction of movement, the Z-axis is orthogonal (at a right-angle) to the X-axis in the horizontal plane (approximately medial-lateral to the subject), and the Y-axis is a right-perpendicular to the horizontal X-Z plane, pointing upwards vertically.

It is important to note that many applications in the field of three-dimensional biomechanics use global coordinate systems that differ from the ISB convention.

To fully describe a rigid body in space, six pieces of information are needed: the location of its centre of mass (determined by the X, Y, Z values) and the three angles that represent its orientation.

The number of independent pieces of information (called parameters) that uniquely define the location of a point or body is known as the object's degrees of freedom (DOF).

Therefore, a point particle has three DOF, and a rigid body has six DOF.

The complete description of motion involves three-dimensional, spatial movement, but in many cases, human movement can be described using primarily one specific plane.

For example, walking involves moving the segments of the arms and legs within the sagittal plane (defined by the X and Y-axes), while movements in the frontal and transverse planes display less ranges of motion; thus, much of the detailed analysis of walking dynamics can be determined just by examining the sagittal plane.

Walking (gait) analysis is a relatively simple procedure (owing to the reduction in DOF from three [X, Y, Z] to two [X, Y] to describe the position of a point) and provides a good starting point for students to understand movements that are mainly uniplanar.

The DOF of human joints is determined by the number of axes about which the articulation can rotate (all joint motions are rotational in nature).

For example, the glenohumeral joint at the shoulder can rotate around three axes: mediolateral (flexion-extension), anteroposterior (adduction-abduction), and transverse (medial-lateral rotation), thus it has three DOF.

In other words, the number of axes of rotation corresponds to the number of DOF at a joint.

Another way to think about DOF is that they are the number of directions in which the joint can move.

A hinge joint like the elbow moves about one axis, therefore it has one DOF, and so it can only move in one direction (flexion-extension).

In the biomechanics literature, the sum of DOF (i.e., the number of directions in which a joint or series of joints can move) is referred to as the "mobility of the system."

This is probably the origin of the phenomenon of using the word "mobility" to refer to ranges of motion since ROM is measured in degrees and a joint with sufficient ROM is said to have the necessary freedom of movement.

Keep in mind, however, that DOF cannot be increased or decreased except in cases of immobilisation.

For example, unless the movement of your elbow is completely restricted, say, it has been encased in a hard cast following fracture or dislocation such that it cannot move at all, then being able to move the joint by just 1° (of an arc) means the joint still has 1 DOF.

If the elbow is completely immobile, then it is accurate to say the joint has lost its DOF; once the cast is removed and the joint is able to display motion again, regardless of how much motion exists, it has regained its DOF.

This detail has significance when discussing flexibility because it is becoming increasingly common for trainers and therapists to make the declaration that DOF can be increased with training.

Such a statement is false.

It is accurate to say that we can increase a joint's excursion through its DOF, which would be measured by ROM.

This ability to move a joint through its DOF is, of course, the motor quality we call "flexibility."

DOF is just a value that represents the number of movement options available to a joint but it is not a trainable quality.