Abstract: A trajectory guidance apparatus can guide motion with passive actuators with at least two degrees of freedom. The trajectory guidance apparatus has a linkage that is mounted to a reference and an interaction part that is to be manipulated by a master, such as a human, gravity g, water flow, a spring, or other force generator. The linkage has at least two force elements adapted to move the interaction part so that the interaction part is guided and can be moved along a prescribed path at a prescribed velocity relative to the reference. A controllable passive coupling connects the force elements and is adapted to impart passive forces against each force element of the linkage. The passive forces are derived substantially solely from a quantity of energy that is imparted to the interaction part by the master, not from other sources.