Controlling the apparent inertia of passive human-interactive robots

We have been exploring the use of passive robotic mechanisms for the display of virtual surfaces. Cobots are one way of producing virtual surfaces using a passive mechanism. Unlike powered robots, the nonlinear dynamics of the passive mechanism (e.g., an arm) can be felt by the user as a spatially varying apparent inertia. This effect occurs in many passive designs, including but not limited to cobots. We explain the variable apparent inertia as the projection of the spatially-varying inertia matrix onto the direction of motion, and discuss several ways to control the apparent inertia. We explore apparent inertia in detail for the unicycle two link arm, a cobot we have developed for experiments in single-arm motor control studies and rehabilitation. Special paths ("iso-mass contours") are found for this mechanism along which the apparent inertia is constant.