This paper introduced the application of a more efficient mathematical representation of the kinematics of avatars, or digital human beings, in telecollaborative virtual reality environments (VRE). The human head, torso and arms were modeled as a redundant eight-degree-of-freedom kinematics structure using an excellent alternative tool to transformation matrices, called dual quaternions. This approach achieves an extremely fast and accurate iterative algorithm that converges to one possible solution of this inverse kinematics problem. The method was implemented and tested in a CAVE Automatic Virtual Environment to demonstrate its performance in real time.