Quantitative Performance Analysis of Haptic Devices with Parallelogram Subsystems

Parallel-architecture haptic devices offer significant advantages over serial-architecture counterparts in applications requiring high stiffness and high accuracy. To this end, many haptic devices have been created and deployed by modularly piecing together several serial-chain arms to form an in-parallel system. Furthermore, recent haptic devices design such as the Sensable’s PHANToM Premium line of haptic devices and Quanser’s High Definition Haptic Device (HD) placed the 2nd actuated joint (of a 2-DOF RR serial manipulator) at the base of the device that allowed the control of the 2nd joint through a parallelogram/fourbar structure. This design is favorable from the view point of reducing the overall weight that the first motor has to carry. However, such design choices can affect the overall system performance which depends both on the nature of the individual arms as well as their interactions. In this paper, we build on the rich theoretical background of constrained articulated mechanical systems to provide a systematic framework for formulation of system-level kinematic performance from individual-arm characteristics. Specifically, we discuss: (i) development of pertinent symbolic equations; (ii) generalization to arbitrary architectures; and (iii) combined symbolic/numeric analyses of performance, focusing on manipulability and stiffness. These aspects are illustrated using the example of Quanser High Definition Haptic Device (HD) – an in-parallel haptic device formed by coupling two 3-link PHANToM 1.5 type serial chain manipulators with appropriate passive joints.