The 3-D Arm Model




The 3-D arm model used so far is rather simple:

  • conical cross section for upper and lower arm
  • rotational axis along main axis of cones
  • hand is model solely as a hand-tip position along forearm axis
    • (conical arm model here)

    There are seven (7) parameters which need to be measured on the subject to create the model:
  • l12, l23, l34 : the lengths of the upper arm, forearm, and hand
  • B12, B21, B23, B32 : the cross-sectional radii of the cones near the shoulder, elbow, and wrist
  • (d12, d21, d23, d32 are also chosen so that the conical elements don't overlap when "rendered" - each distance is typically 3 cm)



    • To model the degrees of freedom and describe the arm pose, we use a cascaded spherical coordinate system:

    (spherical coordinate system here)

    Phi1 and Psi1 describe the orientation of the upper arm with respect to the shouler coordinate frame O1.
    Phi2 and Psi2 describe the orientation of the forearm with respect to the elbow coordinate frame O2.
    O2 is fixed with respect to the upper arm axis, in the sense that it's X axis is along the upper arm axis, and it's Y axis is always parallel to the ground plane and perpendicular to the upper arm axis.
    Note that this coordinate system is not anatomically correct; we assign only two (2) degrees of freedom to the shoulder and two (2) to the elbow. However, for our simple conical model, this system is indistinguishable from the true distribution of degrees of freedom.