A virtual exercise machine

The dynamics and design of multiple-degree-of-freedom robotic systems built as general purpose exercise machines for the human arm are discussed. These machines may be programmed to give the human arm the sensation of forces associated with various arbitrary maneuvers. As examples, these machines can give the human the sensation that he or she is maneuvering a mass or pushing onto a spring or a damper. In general, the machines may be programmed for any trajectory-dependent forces. To illustrate and verify the analysis of these machines, a two-degree-of-freedom electrically powered exercise machine was designed and built