Structural Analysis of the 3-PRS Mechanism of a Serial-Parallel Machine Tool

串並聯式工具機之3-PRS機構結構分析

蕭庭郎(Ting-Nung Shiau) ； 蔡宜政(Yi-Jeng Tsai) ； 楊定家(Ting-Chia Yan) ； 蔡孟勳(Meng-Shiun Tsai)

《中國機械工程學刊》 29卷2期 (2008/04) Pp. 99-109

https://doi.org/10.29979/JCSME.200804.0002

摘要

本篇論文探討具有接頭剛性之3-PRS串並聯式機構之結構分析，首先應用牛頓法推導機構之運動方程式，再以Runge-Kutta數值積分方法求解非線性之系統響應，並且利用線性化的技巧來求得系統自然頻率及其對應的模態。結果顯示自然頻率隨著滑行對位置改變，並利用自然頻率對應之模態形狀來解釋其變化的趨勢。此外，探討系統設計變數對於自然頻率的影響，根據結果顯示，進給位置、接頭剛性及連桿的長度與密度影響最大。

並列摘要

This paper presents the structural analysis of a 3-PRS series-parallel mechanism with consideration of joint stiffness. The Newtonian approach is applied to derive the equations of motion of the 3-PRS mechanism. The Runge-Kutta method is applied to solve the nonlinear response of the system. Then linearization is utilized to determine the natural frequencies and the associated mode shapes. The results show that the natural frequencies vary as the sliders positions change, and the cause of the frequencies shift is explained by analyzing their associated mode shapes. The parameters influencing the natural frequencies are discussed based on simulation results. The parameters of the sliders' location, the stiffness of joints, the length of links and the density of the links are critical to the shifting of natural frequencies, and their effects are analyzed.

並列關鍵字

serial-parallel machine tool ； natural frequency ； joint stiffness ； structural analysis