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Haptic interface devices are machines that are controlled by the human arm contact forces. These devices are necessary elements of virtual reality machines. These devices may be programmed to give the human arm the sensation of forces associated with various arbitrary maneuvers. As examples, these devices can give the human the sensation that he/she is maneuvering a mass, or pushing onto a spring or a damper. In general, these devices may be programmed for any trajectory-dependent force. To illustrate and verify the analysis of these machines, a two-degree-of-freedom electrically-powered haptic interface device was designed and built at the Human Engineering Laboratory (HEL) of the University of California-Berkeley.< >