Workspace-constrained optimal design of three-degrees-of-freedom parallel manipulators with minimum parasitic motions by integrating interval analysis, region mapping and differential evolution

Abstract

Three-degrees-of-freedom (3-DOF) parallel manipulators have many advantages such as simple structure, fewer actuators, and lower maintenance cost. However, parasitic motions may degrade the positioning accuracy of the platforms. In order to design 3-DOF parallel manipulators which can fulfil specified workspace requirements and exhibit minimum parasitic motions, the design problem is formulated into a minimax problem with workspace constraints. Then, an interval-based method is exploited to determine the feasible solution set which is derived as a union of many scattered parameter intervals (boxes). Then, a new approach based on region mapping and a powerful optimizer (namely differential evolution) is proposed to solve the optimization problem over scattered search regions. Benchmark tests show the superiority of the proposed approach. Then, the approach and interval analysis are used to solve a real-world design problem involving a 3-DOF manipulator. Numerical results demonstrate the effectiveness and advantages of the proposed design method.

Keywords:

• 3-DOF parallel manipulators
• interval analysis
• region mapping
• differential evolution
• optimization over scattered regions

Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant numbers 61304215, 61175112), the National Science Fund for Distinguished Young Scholars (grant number 60925011), and the Projects of Major International (Regional) Joint Research Program NSFC (grant number 61120106010).