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To improve high motion accuracy and efficiency in the high-speed operation of a 4-DOF (4 degrees of freedom) redundant parallel robot, this paper introduces a trajectory planning of the parallel robot in joint space based on the twelve-phase sine jerk motion profile. The 12-phase sine jerk motion profile utilizes the characteristics of a sine function. Furthermore, the penalty function is used to optimize the trajectory energy consumption under the constraint condition. The simulation and experimental results show that the energy consumption of joint space is slightly higher than that of the three-phase sine jerk motion profile, but the overall operation is more accurate and stable. Specifically, the sudden change of force and velocity in each joint is eliminated, which is the cause of mechanism oscillation. Moreover, the force of each joint is more average. The results indicate that each movement is closer to the maximum allowable limit and the running efficiency is higher.

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In the process of turning a maglev motorized spindle, there are problems such as system model time-varying, cross-coupling of control parameters, difficult measurement of system state variables, and nonlinear characteristics of active magnetic bearings, which lead to the inevitable cutting chatter phenomenon, difficult control algorithm design, and then the reduction of workpiece surface quality and accuracy, affecting machining efficiency and tool life. In this paper, the “multimodal-distributed parameter” model is extended to the “magnetic bearing-rotor-workpiece” variable mass turning process. An adaptive backstepping fast dynamic terminal sliding mode control is designed to address the model’s time-varying parameters and cross-coupling issues. In view of the difficulty in measuring the vibration displacement at the cutting point, the displacement field reconstruction method was introduced to reconstruct the vibration displacement field online and provide effective feedback for the previously designed control strategy. Finally, the proposed controller is applied to adjust and control the turning process of a maglev motorized spindle and compared with other advanced controllers. The simulation results show that the proposed control method has a better control effect than other control methods in the presence of unmodeled dynamics, uncertainties, and external disturbances.

A method is developed for kinematic and dynamic analysis of a spatial mechanisms that has one or more links with a passive degree of freedom. The Sphere-Sphere (SS) link, the most commonly known link having a passive degree of freedom, is investigated to develop in detail displacement, velocity, and acceleration matrices for complete kinematics. The dynamic analysis of the RSSR mechanism is presented as an example, using the developed kinematic method for SS links and Euler’s equations of motion.

As regards the impact and chattering of 4-DOF redundant parallel robots that occur under high-speed variable load operating conditions, this study proposed a novel control algorithm based on torque feedforward and fuzzy computational torque feedback hybrid control, which considered both the joint friction torque and the disturbance torque caused by the variable load. First of all, a modified dynamic model under variable load was established as follows: converting terminal load change to terminal centroid coordinate change, then mapping to the calculation of terminal energy, and lastly, establishing a dynamic model for each branch chain under variable load based on the Lagrange equation. Subsequently, torque feedforward was used to compensate for the friction torque and the disturbance torque caused by the variable load. Feedforward torques include friction torque and nonlinear disturbance torque under variable load. The friction torque is obtained by parameter identification based on the Stribeck friction model, while the nonlinear disturbance torque is obtained by real-time calculation based on the modified dynamic model under variable load. Finally, dynamic control of the robot under variable load was realized in combination with the fuzzy computational torque feedback control. The experimental and simulation results show that the motion accuracy of the fuzzy calculation torque feedback and torque feedforward control of the three drive joints of the robot under variable loads is 49.87%, 70.48%, and 50.37% lower than that of the fuzzy calculation torque feedback. Compared with pure torque feedback control, the speed stability of the three driving joints under fuzzy calculation torque feedback and torque feedforward control is 23.35%, 17.66%, and 25.04% higher, respectively.