Joint constraints
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Joint constraints are rotational constraints on the joint of a bone system, used in an inverse kinematics chain. Joint constraints can be implemented in a number of ways, but the most common method is to limit rotation about the X, Y and Z axis independently. An elbow, for instance, could be represented by limiting rotation on Y and Z axis to 0 degress of freedom, and constraining the X-axis rotation to 130 degrees of freedom.
To simulate joint constrains more accurately, one could use dot-products and an independent axis to repulse the child bones orientation from the unreachable axis. Or could limit the orientation of the child bone to a border of vectors tangent to the surface of the joint, repulsing the child bone away from the border, useful in the precise restriction of shoulder movement.