Passive robots and haptic displays based on nonholonomic elements

We describe a new architecture for passive robots and haptic displays, which we call a programmable constraint machine (PCM). An n-dof PCM can, under computer control, exhibit constraints (smooth, impenetrable virtual surfaces of dimensionality < n), or it can allow free n-dof motion. At the heart of the PCM is a nonholonomic element, which is used as a continuously variable transmission (CVT). A rolling wheel, for instance, can be used as a CVT. A prototype 2-dof Cartesian PCM has been built, using a single rolling wheel, We sketch PCMs of higher dimensionality. A rolling wheel may be thought of as a translational CVT, coupling the x and y velocities of its center by a transmission ratio which is the tangent of its steering angle, Its utility in a Cartesian PCM motivates interest in a rotational analog for revolute architectures. We develop a novel rotational CVT which couples two angular velocities by an adjustable ratio.