Global Stiffness Optimization of Parallel Robots Using Kinetostatic Performance Indices

Abstract

Global Stiffness design and optimization of parallel mechanisms can be a difficult and timeconsuming exercise in parallel robot design, especially when the variables are multifarious and the objective functions are too complex. To address this issue, optimization techniques based on kinetostatic model and genetic algorithms are investigated as the effective criteria. First, a 5-DOF parallel mechanism with a passive constraining leg and five identical legs with prismatic actuators for machine tool is proposed, and its corresponding inverse kinematics, Jacobian matrices and global velocity equation are derived. Second, with the kinetostatic model, the mean value and the standard deviation of the trace of the global compliance distribution are proposed as these two kinetostatic performance indices. Finally, the effectiveness of this optimization design methodology for global stiffness indices is validated with simulation. Compared with traditional serial manipulators, a parallel robot manipulator offers different potential benefits, including high rigidity, high accuracy, and high loading capacities. The parallel robot manipulator is used for applications where the demand on workspace and manoeuvrability is relatively low, while the dynamic loading is severe, and high speed and precision motions are primarily required. These applications include parallel kinematic machines (PKMs), aircraft flight simulators, telescope positioning, position tracker, and medical devices (Zhang & Gosselin, 2000; Dunlop & Jones, 1999; Carretero & Podhorodeski, 2000; Staicu et al., 2006; Zhang & Wang, 2000; Liu et al., 2005). Past research and development efforts with parallel robot manipulators have shown the ever-increasing demand on the robot’s rigidity which is directly related to the system stiffness. In order to increase the production, a parallel manipulator which is capable of high speed operations with optimal rigidity is necessary. Recently, researchers have been trying to utilize these advantages to develop parallel robot based multi-axis machining tools and precision assembly tools. Since most machining operations only require a maximum of five axes, new configurations with less than six axes would be more appropriate (Bi et al., 2005). A 5-DOF parallel mechanism with a passive constraining leg and five identical legs with prismatic actuators for machine tool is proposed in this work. Kinetostatic analysis is essential for PKMs. A great deal of work so far has been 6