Screw theory provides geometrical insight into the mechanics of rigid bodies. Screw axis is defined as the line coinciding with the joint axis. Line transformations in the form of a screw operator are used to determine the joint axes of a seven degree of freedom manipulator, representing the human upper limb. Multiplication of a unit screw axis with the joint angular velocity provides the joint twist. Instantaneous motion of a joint is the summation of the twists of the preceding joints and the joint twist itself. Inverse kinematics, velocities and accelerations are calculated using the screw Jacobian for a non-redundant six degree of freedom manipulator. Netwon and Euler dynamic equations are then utilized to solve for the forward and inverse dynamic problems. Dynamics of the upper limb and the upper limb combined with an exoskeleton are only different due to the additional mass and inertia of the exoskeleton. Dynamic equations are crucial for controlling the exoskeleton in position and force.