Geometry of Movement  «Prev  Next»

General Aspects of Physiological Movement

Introduction to the Geometry of Physiological Movement

A study of the various joints at which movement takes place in keyboard playing, will enable us to tell what type of movement is possible when the movement is restricted to a single joint. Conversely, given the path of the movement , we can learn wheth er or not it is the result of motion in one joint or in several joints.
Rotation in the shoulder-socket will use the humerus as a radius. The elbow will describe an ellipse or a circle. Such a motion is used in winding a windlass[1]. In this type of movement in which joint-motion is restricted to the shoulder-socket, the elbow cannot describe a straight line.
With the humerus it describes a cone of
  1. A study of the various joints at which movement takes place in piano playing will enable us to tell what type of movement is possible when the movement is restricted to a single joint.
  2. Given the path of the movement, we can learn whether or not it is the result of 1) motion in one joint or 2) in several joints.
  3. Rotation in the shoulder will use the humerus as a radius.
  4. In this type of movement in which joint-motion is restricted to the shoulder, the elbow cannot describe a straight line.
  5. The elbow will describe an elipse.
Shape generated by an elipse
Shape generated by an elipse

Geometric shape generated by the elbow

See Figure 6 below.
  1. The elbow describes with the humerus a cone of movement, the pitch of which varies considerably, and the base of which is a spherical surface.
  2. The elbow cannot move in a straight line since the humerus acts as a moving radius of fixed length.
  3. The elbow must describe paths along the surface of the sphere generated by the multiplanar[2] movements of the humerus.
  4. By restricting the movement to one plane, the humerus as a whole may describe a segment of this plane.
  5. The elbow will describe one of an unlimited number of arcs across the base of the cone in Figure 6.
  6. The direction of this arc in relation to its plane may be a straight line, but the movement of the elbow itself must be an arc of a sphere of which the humerus is the radius.
  7. As long as the shoulder is stationary the elbow cannot move in a straight line.
  8. The motions of the elbow are necessarily curvilinear but may take place in any direction along the spherical movement shown in Figure 6.
  9. When the humerus itself rotates around its longitudinal axis, the path described by any point fixed to the humerus will be the arc of a circle, the radius of which is the perpendicular distance of the point from the axis of rotation.
  10. Straight line movement from simple rotation cannot occur.
  11. In spite of the wide range of movements possible through the hull and socket joint at the shoulder, all movements of distal[3] parts are curvilinear.
  12. The ball and socket joint of the shoulder is not capable of rectilinear[4] motion.
  13. Movement around the elbow joint takes place in the arc of a circle, the short radius of which is the length of the forearm.
  14. With the hand extended the radius is increased by the length of the hand.
  15. Movement round the elbow joint is curvilinear.
Figure 6
In the figure above.
  1. S represents the shoulder,
  2. h represents the humerus, and
  3. e represents the elbow.

[1] windlass: a type of winch used especially on ships to hoist anchors and haul on mooring lines and, especially formerly, to lower buckets into and hoist them up from wells.
[2] multiplanar: of or pertaining to multiple planes.
[3] distal: (adjective used in anatomy); situated away from the center of the body or from the point of attachment. "the distal end of the tibia"
[4] rectilinear: adjective: consisting of, or moving in a straight line or lines. (i.e.) "a rectilinear waveform". In photography, of or relating to a straight line or lines.