In a virtual environment for small groups of interacting participants, it is important that the physical motion of each participant be replicated by synthetic human forms in real time. Sensors on a user's body are used to drive an inverse kinematics algorithm. Such iterative algorithms for solving the general inverse kinematics problem are too slow for a real-time interactive environment. In this paper we present analytic, constant time methods to solve the inverse kinematics problem and drive an avatar figure. Our sensor configuration has only eight sensors per participant, so the sensor data is augmented with information about natural body postures. The algorithm is fast, and the resulting avatar motion approximates the actions of the participant quite well. This new analytic solution resolves a problem with an earlier iterative algorithm that had a tendency to position knees and elbows of the avatar in awkward and unnatural positions.