# Cervical-Occipital Assembly Movements of the Upper Cervical Assembly

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## Traveling Axes of Rotation

The quantitative approach just illustrated utilizes the concept of travelling frames of reference. It is a natural approach for gimbal-like joints, because each movement is most readily and logically expressed as a movement about a particular axis, but the orientation of that axis is a function of movements about other axes.

There are advantages to using an approach, which utilizes traveling frames of reference. Perhaps the greatest advantage is that the order of the calculations is reversible. Flexion of the elbow is always fundamentally the same movement, whether the shoulder is in neutral position, flexed, abducted, or rotated. When using traveling axes, changing the order of a series of movements about different joints does not change the final outcome. Flexing the elbow and then the shoulder leads to the same final position as first flexing the shoulder and then the elbow. The details of the calculation are quite different, but the final result is the same.

Because of the geometry of a gimbal-like joint, it may be treated as a collection of separate joints or joint elements. The first element is the vertical or support element, the element that holds the other elements. In the neck, it would be the cervical spine up to the axis. The other elements are the atlanto-axial joint and the atlanto-occipital joint.

## Calculation of the Orientation of Frames of References

Framed vectors are arrays of three type of vectors. The location vector, , is the placement of the object relative to the origin of a coordinate system {i, j, k}. The extension vector, , is an attribute of the structure of the object, in this case its height. The frame of reference, , is a set of three vectors, {r, s, t}, that specify the orientation of the object.