Introducing mass parameters to Pseudo–Rigid–Body models for precisely predicting dynamics of compliant mechanisms. (August 2018) - She, Yu; Meng, Deshan; Su, Hai-Jun; Song, Siyang; Wang, Junmin
Highlights: Analytical expressions of the natural frequencies of the continuum model are developed according to vibration analysis. Theoretical expressions of the natural frequencies of the parameterized Pseudo–Rigid–Body (PRB) models are derived via Lagrange Dynamics. Non-dimensional mass property parameters are introduced to the classical PRB models and then optimized. Dynamics of the optimized PRB model are evaluated via comparing with that of the finite method analysis (FEA). Effects on the dynamics accuracy from design parameters and input parameters are explored from both the time domain and frequency domain. Graphical abstract: Abstract: In this paper, we introduce non-dimensional mass property parameters to the classical PRB model for accurately predicting the dynamics of the compliant mechanisms. Given extensive work on PRB models accurately modeling the statics and kinematics of compliant mechanisms, few works have investigated on their accuracy in predicting dynamics. Here we study the fundamental natural frequency of two typical mechanisms: fixed-root and pinned-root compliant parallel-guiding mechanisms (CPGM). First, analytical expressions of the natural frequencies of the continuum models are derived according to the vibration mechanics. Second, theoretical expressions of the natural frequencies of the parameterized PRB model are obtained from their dynamics equations. Third, the mass property parameters are optimized to minimize the error between the continuum models and the parameterized PRB model. We conclude that the optimized PRB models can well predict the dynamics especially the low input signal frequency or mass of beams are not negligible. These new PRB models can significantly improve computational efficiency in dynamics simulation of compliant mechanisms.