No 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.

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.

In this paper, the main purpose is to study existence of the global attractor for the weakly damped wave equation with gradient type nonlinearity. To this end, we first verify the existence and uniqueness of global weak solution by the Galerkin method and compulsively variational method. Furthermore, we obtained the global strong solution under some mild assumptions on f. Secondly, we utilize the $$\omega$$ ω -limit compactness to show the semigroup generated by the equation has a compact, connected and invariant attractor.

The paper deals with the workspace-based optimization of a novel humanoid robotic arm. The eight-degree-of-freedom hybrid manipulator that conforms to the kinematics characteristics of the human arm is briefly introduced. According to the structural features of this mechanism and the requirements of tasks in the complex environment, the workspace is divided into three parts, the orientation space of the humanoid shoulder joint, the position space of the humanoid elbow joint, and the active orientation space of the end-moving platform. Moreover, a multi-parameter planar model is proposed for the optimization problem with multidimensional parameters and highly nonlinear constraints. Based on the visualized optimization result, the coupling effect of each parameter on the corresponding workspace is clearly presented. Considering the compactness and the processing and assembling technology of this mechanism, a set of structural parameters satisfying the workspace-based optimization objective is obtained. Simulation results show that the corresponding workspace of the three parts has increased significantly by the factor of 1.45, 1.68, and 1.3, respectively.