In order to increase the driving force of the voice coil actuator while reducing its size and mass, the structural parameters of the coil and magnet in the actuator are optimized by combing Biot–Savart law with Lagrangian interpolation. A 30 mm × 30 mm × 42 mm robot based on a 3-RPS parallel mechanism driven by voice coil actuators is designed. The Lagrangian dynamic equation of the robot is established, and the mapping relationship between the driving force and the end pose is explored. The results of dynamic analysis are simulated and verified by the ADAMS software. The mapping relationship between the input current and the end pose is concluded by taking the driving force as the intermediate variable. The robot can bear a load of 10 g. The maximum axial displacement of the robot can reach 9 mm, and the maximum pitch angle and return angle can reach 40 and 35 degrees, respectively. The robot can accomplish forward movement through vibration, and the maximum average velocity can reach 4.1 mm/s.

In order to predict and evaluate the response time and displacement of a large-stroke, high-speed micro-LSPEA under different currents and springs, numerical and analytical methods are used to obtain the dynamic and steady-state performance indicators of the nonlinear system. Firstly, the analytic functions of the electromagnetic force and the magnetic field distribution were presented. The nonlinear vibration equation was obtained by dynamic modeling. The averaging method and the KBM method were employed to obtain analytical solutions of the undamped system. The equivalent linearization of the damped nonlinear system was performed to obtain the approximate analytical solutions of performance indicators. Finally, the displacement of the actuator equipped with different springs was measured experimentally. Meanwhile, the transient network was constructed by Simulink software to solve the nonlinear equation numerically. The displacement curves and performance indicators obtained by experiment, numerical and analytical methods are compared. The maximum errors of the peak time, overshoot and steady displacement through experiment and simulation are 8.4 ms, 4.36% and 0.59 mm, respectively. The solution result of the vibration equation considering stiffness nonlinearity can reflect the dynamic and steady-state performance of the LSPEA within a certain error, which is helpful for the solution of nonlinear systems caused by multi-physics coupling.