This paper proposed a circular flexible spherical joint to reduce the processing difficulty and manufacturing cost, and design a six-dimensional force sensor based on it. This paper analyzes the influence of the structural parameters of the flexible spherical joints on the accuracy of the six-dimensional force sensor by comparing the force mapping matrix of flexible spherical and ideal spherical joints. As the force mapping matrix is related to the stiffness matrix, the stiffness matrix of a six-dimensional force sensor based on a circular flexible spherical joint and the force mapping matrix of the generalized external force acting on the sensor was derived. Finally, a set of optimal parameters was selected to create a prototype and was verified through finite elements and experiments. The results show that the six-dimensional force sensor with a circular flexible spherical joint has good accuracy and provides some guidance for the design and analysis of the sensor.

As robot haptic provider, six-dimensional force sensors are an indispensable component of industrial intelligence. To address the disadvantages of the existing six-dimensional force sensor, a novel circular flexible spherical joint is proposed, its stiffness model is derived by numerical analysis method and microelement, and the stiffness model of the circular flexible spherical joint is verified by finite element simulation. A parallel six-dimensional force sensor is designed based on a circular flexible spherical joint, and a mathematical model of the sensor was established. Based on the genetic algorithm, the structural optimization design of the circular flexible spherical joint was performed, and the structural parameters of the circular flexible spherical joints are obtained by analyzing isotropy. Finally, according to the optimization results, a sensor was developed and calibration experiments were carried out. The experimental results show that the maximum error of the sensor is 1.85%, which verifies the effectiveness of the mathematical model of the sensor, which has high measurement accuracy and can accurately measure the six-dimensional external force and moment applied to the sensor.

In order to solve the external periodic disturbance and unknown dynamics influence in the passive rehabilitation process of a rope-driven lower limb rehabilitation robot, a control method with periodic repeated learning was designed. In this control method, the closed-loop dynamics are divided into a periodic disturbance term, an unknown dynamics term, and a basic term, and the shape function is designed by using the Stone–Weirstrass theorem. In the process of periodic operation, the estimated value of the shape function coefficient is repeatedly learned to obtain the periodic disturbance term approximation and to realize the compensation in advance. Through the design of the impedance learning rate, the unknown dynamic term is periodically learned, and the unknown dynamics approximation is obtained. By combining the two approximations with the basic terms which can be solved directly, the external periodic disturbance is compensated for in advance and the control precision is improved. The control algorithm was verified by simulation, and the error fluctuation of the system gradually decreases and reaches the ideal value within several cycles. The performance of the control system is stable, and the problem of limb impedance caused by different patients is well solved.