Kinematic synthesis of analytical laws of the actuator displacement of a manipulator with the parallel-sequential structure and additional coupling

The paper considers an algorithm for kinematic synthesis of analytical laws of the program actuator displacement of the hybrid manipulators with the excessive number of degrees of freedom implementing displacement of the working element characteristic point along a given trajectory. The proposed method is based on the point quadratic approximation of the sought law by a polynomial on a set of points of the actuator successive positions. The set of points of the actuator successive positions is found by solving optimization problem of the manipulator output link positioning. The proposed method is realized using the example of displacing the output link of a parallel-series manipulator with the additional connection along a circle. Analytical laws of the hybrid manipulator actuators displacement are obtained. Cases of the trajectory approximation by polynomials of the fifth and seventh degrees are studied taking into account the specified boundary conditions. Maximum deviations of the approximating polynomials from the original values ??are obtained. The paper provides recommendations for selecting the polynomial degree to increase the results accuracy and ensure the displacement along the selected trajectory.
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