AbstractCobots are devices which use computer‐oriented passive constraints to guide an end‐effector driven by a human. This synergistic union of human skill and robotic precision is desired in fields such as surgical robotics (our application area of interest) where the surgeon would prefer not to hand over control of a procedure to an autonomous robot. Typical cobot designs intrinsically allow at most one degree of freedom of motion, but there are some tasks (such as using a bone saw to cut a plane in knee replacement surgery) where allowing two or more degrees of freedom is desireable. While it is possible to use selective constraint alignment to increase the apparent degrees of freedom of a cobot, this requires more actuators than are strictly necessary for the task, as well as a force sensor to detect the user's intent. We, therefore, introduce here the concept of minimally constrained cobots for multiple degree of freedom (DOF) tasks such as planar cutting, and outline a general framework for controlling such devices. We illustrate our control algorithms by using a planar cart example and discuss how they might be applied to potential designs for three‐dimensional parallel cobots intended for surgical applications. © 2002 Wiley Periodicals, Inc.