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Based on flexible pneumatic actuator FPA, two new kinds of pneumatic rigid-flexible joints are proposed. Three bending joints and one side-sway joints are used for designing two kinds of 4-DOF robot fingers. When inflating the FPA of each joint of 4-DOF fingers with different compressed air pressure, the fingers can simulate human fingers and realize bending movement and side-sway movement. Then the 20-DOF robot multi-fingered dexterous hand composed five fingers and a palm is designed which is named ZJUT Hand. Driving directly by FPA is ZJUT Hand's most notable characteristic. Because of this, ZJUT Hand has many advantages such as good adaptability, simple structure, small size and little energy loss and so on. At last, simulation experiments are carried to verify the grasping ability of ZJUT Hand. Simulation experimental results show that ZJUT Hand can complete power grasp and precision grasp for objects with different size and shape.