Interactions and Optimizations Analysis between Stiffness and Workspace of 3-UPU Robotic Mechanism

Abstract

The interactions between stiffness and workspace performances are studied. The stiffness in x, y and z directions as well as the workspace of a 3-UPU mechanism are studied and optimized. The stiffness of the robotic system in every single moveable direction is measured and analyzed, and it is observed that in the case where one tries to make the x and y translational stiffness larger, the z directional stiffness will be reduced, i.e. the x and y translational stiffness contradicts with the one in z direction. Subsequently, the objective functions for the summation of the x and y translational stiffness and z directional stiffness are established and they are being optimized simultaneously. However, we later found that these two objectives are not in the same scale; a normalization of the objectives is thus taken into consideration. Meanwhile, the robotic system’s workspace is studied and optimized. Through comparing the stiffness landscape and the workspace volume landscape, it is also observed that the z translational stiffness shows the same changing tendency with the workspace volume’s changing tendency while the x and y translational stiffness shows the opposite changing tendency compared to the workspace volume’s. Via employing the Pareto front theory and differential evolution, the summation of the x and y translational stiffness and the volume of the workspace are being simultaneously optimized. Finally, the mechanism is employed to synthesize an exercise-walking machine for stroke patients.

Designation and Multiobjective Optimization of a New Six‐DOF Haptic Device Based on Genetic Algorithm

“…Many literatures focus on the intelligent optimization algorithm. Zhang et al used the differential evolution algorithm to optimize the stiffness and reachable workspace of 3-UPU in literature [13]. Cui and others optimized the workspace and dexterity of 3-ups-s based on Isight in literature [14].…”

Kinematics Analysis of 3UPU_UP Coupling Parallel Platform in the Marine Environment

“…The joint of the UPU limb is R x R b P 1 R c R d , where the c-axis is parallel to the b-axis and the y-axis. The d-axis is not parallel to the x-axis, forming a 3-DOF translational parallel platform [9], [10]. For case II, if the moving platform needs to meet 3-DOF rotation, it means that the constraint forces generated by the three UPU limbs are linearly independent.…”

Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods

“…An in-depth analysis of PKMs addressing different subjects can be found in the literature. They include aspects such as the workspace [4,5], kinematics [6,7], dynamics [8,9], elastostatics [10], motion/force transmissibility [11], robot control [12], optimal robot reconfiguration [13], robot calibration [14], and so on. Furthermore, there is exhaustive literature dealing with optimization approaches for parallel robot trajectory planning [15][16][17].…”