Controllable underactuated manipulators were successfully developed based on the nonlinear control theoretic approach. The nonholonomic gear is designed to create nonlinear structure on the robot manipulator. The nonholonomic gear is a special type of velocity transmission consisting of a ball and wheels, and provides the kinematic nonholonomic constraint. The gear can be employed not only to build underactuated manipulators but also to be used in many other applications as a continuously variable transmission having a nonlinear gear ratio of trigonometric functions.