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This paper introduces the mechanical structure and control technique of robot finger. The fingers has been developed as elements of the robot hand which has 20 joints and 16 degrees of freedom in order to express fingerspelling. The first joint is driven by the small DC servo motor and the second and the third joints are driven by shape memory alloy (SMA) wires. The hand system will consist of four parts of "hand mechanism", "drive device", "control unit" and "man machine interface". This paper introduces a finger control technique. In order to realize the cooperative smooth motion, the control system is designed based on an experimental result of system identification and the position trajectory reference is designed considering time delay on the pair of SMA in our finger. Finally, we report the simulation and experimental control results to evaluate the presented control law.