A parameter optimization framework for determining the pseudo-rigid-body model of cantilever-beams |
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| Affiliation: | 1. School of Electro-Mechanical Engineering, Xidian University, Xi’an, Shaanxi 710071, China;2. Precision Systems Design Lab, Mechanical Engineering, University of Michigan, 2350 Hayward Street, Ann Arbor, MI 48109, China;3. State Key Laboratory for Manufacturing Systems Engineering and Shaanxi Key Lab of Intelligent Robots, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;1. Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA;2. Mechanical, Maritime and Materials Engineering, Delft University of Technology, Delft, The Netherlands;1. School of Electro-Mechanical Engineering, Xidian University, Xi''an, Shaanxi 710071, China;2. State Key Laboratory for Manufacturing Systems Engineering and Shaanxi Key Lab of Intelligent Robots, Xi''an Jiaotong University, Xi''an, Shaanxi 710049, China |
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| Abstract: | This paper focuses on developing a framework for determining the optimal pseudo-rigid-body (PRB) model of 2D cantilever beams. PRB models are commonly used in design and analysis of compliant mechanisms since they significantly reduce the number of degrees of freedom compared with the finite element approach. Although a number of PRB models are available in literature, there is not a unified method to determine the most suitable pseudo-rigid-body model for a specific application. In this work, we first study a modified Timoshenko beam equation which accommodates shear forces and axial deformation. The numerical solution to the Timoshenko beam equation provides a baseline for comparing various models. A novel concept of “PRB matrix” is proposed for representing topologies of all PRB models in a uniform way. The optimal set of kinematic parameters (characteristic lengths and spring constants) of PRB models are determined by minimizing the error of tip deflection and comparing with the solution of the Timoshenko beam equation. To validate this formulation, we compare the results with existing PRB models and obtained equivalent if not a more accurate set of PRB parameters. At last, a case study of a compliant slider mechanism is provided to demonstrate the accuracy of two PRB models in this particular application. |
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| Keywords: | Compliant mechanisms Pseudo-rigid-body model Parameter optimization Timoshenko beam theory |
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