This paper presents an investigation of the effectiveness of different inverse kinematics strategies in a context of physical human-robot interaction in which passive articulated shells are mounted on the links of a serial robot for manual guidance. The concept of passive link shells is first recalled. Then, inverse kinematics strategies that are designed to plan the trajectory of the robot according to the motion sensed at the link shells are presented and formulated. The different approaches presented all aim at interpreting the motion of the shells and provide an intuitive interaction to the human user. Damped Jacobian based methods are introduced in order to alleviate singularities. A serial 5-dof robot used in previous work is briefly introduced and is used as a test case for the proposed inverse kinematics schemes. The robot includes two link shells for interaction. Simulation results based on the different inverse kinematic strategies are then presented and compared. Finally, general observations and recommendations are discussed.