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Measurement accuracy of the angular stiffness of flexible joint is directly related to the control accuracy and sensitivity of gyro, but the traditional measurement methods have many problems. According to the principle of angular stiffness measurement of flexible joint, two static measurement methods of angular stiffness are proposed based on different loading ways, namely mechanical loading angular stiffness measurement and piezoelectric loading angular stiffness measurement. The mechanical loading angular stiffness measurement system is built by using a motor driven indexing feeding tilting table, the measure experiment if the angular stiffness of flexible joint is conducted, and the angular stiffness of flexible joint is measured. For the excessive fluctuation problem of the measure result in mechanical load test, a piezoelectric loading structure is designed and a measurement method employing piezoelectric actuator is proposed for angular stiffness measurement of flexible joint. Based on ANSYS Workbench, the displacement output of the piezoelectric loading structure is analyzed by simulations. The simulation results illustrate that the displacement output meets the requirement of static loading angular stiffness measurement of flexible joint, and the theoretical feasibility of piezoelectric loading angular stiffness measurement method is validated.