A mechanical system comprising: a linkage assembly having a first number of degrees of freedom, wherein the linkage assembly includes a plurality of links, pairs of the plurality of links being mechanically coupled together by a corresponding one of a plurality of joints; a plurality of actuators coupled to the linkage assembly, each actuator configured to actuate a respective joint of the plurality of joints and being operable to control a corresponding one of the first number of degrees of freedom of the linkage assembly; and a processor coupled to the actuators, the processor being operable to generate movement commands for actuating at least one of the actuators based on information identifying a desired motion of the linkage assembly, the movement commands being generated by operations including: applying the information identifying the desired motion to a kinematic model having a second number of degrees of freedom greater than the first number of degrees of freedom, the second number of degrees of freedom including at least one phantom degree of freedom not existing in the linkage assembly, the application of the information including: a kinematic calculation of a joint space velocity for each of the second number of degrees of freedom in accordance with the desired motion; and generating the movement commands from the joint space velocities by discarding the joint space velocity calculated for the at least one phantom degree of freedom. a linkage assembly having a first number of degrees of freedom, wherein the linkage assembly includes a plurality of links, pairs of the plurality of links being mechanically coupled together by a corresponding one of a plurality of joints; a plurality of actuators coupled to the linkage assembly, each actuator configured to actuate a respective joint of the plurality of joints and being operable to control a corresponding one of the first number of degrees of freedom of the linkage assembly; and a processor coupled to the actuators, the processor being operable to generate movement commands for actuating at least one of the actuators based on information identifying a desired motion of the linkage assembly, the movement commands being generated by operations including: applying the information identifying the desired motion to a kinematic model having a second number of degrees of freedom greater than the first number of degrees of freedom, the second number of degrees of freedom including at least one phantom degree of freedom not existing in the linkage assembly, the application of the information including: a kinematic calculation of a joint space velocity for each of the second number of degrees of freedom in accordance with the desired motion; and generating the movement commands from the joint space velocities by discarding the joint space velocity calculated for the at least one phantom degree of freedom. a kinematic calculation of a joint space velocity for each of the second number of degrees of freedom in accordance with the desired motion; and generating the movement commands from the joint space velocities by discarding the joint space velocity calculated for the at least one phantom degree of freedom.