Search

Abstract In order to improve the low output accuracy caused by the elastic deformations of the branch chains, a finite element-based dynamic accuracy analysis method for parallel mechanisms is proposed in this paper. First, taking a 5-prismatic-spherical-spherical (PSS)/universal-prismatic-universal (UPU) parallel mechanism as an example, the error model is established by a closed vector chain method, while its influence on the dynamic accuracy of the parallel mechanism is analyzed through numerical simulation. According to the structural and error characteristics of the parallel mechanism, a vector calibration algorithm is proposed to reduce the position and pose errors along the whole motion trajectory. Then, considering the elastic deformation of the rod, the rigid-flexible coupling dynamic equations of each component are established by combining the finite element method with the Lagrange method. The elastodynamic model of the whole machine is obtained based on the constraint condition of each moving part, and the correctness of the model is verified by simulation. Moreover, the effect of component flexibility on the dimensionless root mean square error of the displacement, velocity and acceleration of the moving platform is investigated by using a Newmark method, and the mapping relationship of these dimensionless root mean square errors to dynamic accuracy is further studied. The research work provides a theoretical basis for the design of the parameter size of the prototype.

Abstract Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult to find a better desired trajectory. In this paper, a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) is proposed. Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves. Then, an INSGA-II, by introducing three genetic operators: ranking group selection (RGS), direction-based crossover (DBX) and adaptive precision-controllable mutation (APCM), is developed to optimize travelling time and torque fluctuation. Inverted generational distance, hypervolume and optimizer overhead are selected to evaluate the convergence, diversity and computational effort of algorithms. The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory. Taking a serial-parallel hybrid manipulator as instance, the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method. The effectiveness and practicability of the proposed method are verified by simulation results. This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Abstract To study the characteristics of the 5-prismatic–spherical–spherical (PSS)/universal–prismatic–universal (UPU) parallel mechanism with elastically active branched chains, the dynamics modeling and solutions of the parallel mechanism were investigated. First, the active branched chains and screw sliders were considered as spatial beam elements and plane beam element models, respectively, and the dynamic equations of each element model were derived using the Lagrange method. Second, the equations of the 5-PSS/UPU parallel mechanism were obtained according to the kinematic coupling relationship between the active branched chains and moving platform. Finally, based on the parallel mechanism dynamic equations, the natural frequency distribution of the 5-PSS/UPU parallel mechanism in the working space and elastic displacement of the moving platform were obtained. The results show that the natural frequency of the 5-PSS/UPU parallel mechanism under a given motion situation is greater than its operating frequency. The maximum position error is − 0.096 mm in direction Y, and the maximum orientation error is − 0.29° around the X-axis. The study provides important information for analyzing the dynamic performance, dynamic optimization design, and dynamic control of the 5-PSS/UPU parallel mechanism with elastically active branched chains.