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2UPR-RPU過約束并聯(lián)機(jī)構(gòu)剛度性能評價(jià)
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國家自然科學(xué)基金項(xiàng)目(51705465)和浙江省基礎(chǔ)公益研究計(jì)劃項(xiàng)目(LGG19E050029、LGG19E050018)


Stiffness Performance Evaluation of 2UPR-RPU Over-constrained Parallel Mechanism
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    摘要:

    運(yùn)用螺旋理論和應(yīng)變能方法研究了具有2R1T三自由度的2UPR-RPU過約束并聯(lián)機(jī)構(gòu)的靜彈性剛度性能,模型考慮了桿件和關(guān)節(jié)的柔度。首先,基于螺旋理論得到分支的約束螺旋系;其次,基于材料力學(xué)得到分支中桿件的應(yīng)變能,通過映射分支約束螺旋系到鉸空間得到關(guān)節(jié)的應(yīng)變能,通過匯總桿件、關(guān)節(jié)的應(yīng)變能和卡氏定理得到與約束螺旋系對應(yīng)的分支緊湊剛度矩陣;最后,通過虛功原理得到機(jī)構(gòu)的總體剛度矩陣。采用有限元商業(yè)軟件建立了有限元模型,并與理論模型進(jìn)行對比,驗(yàn)證了理論模型的正確性。定義彈性元件存儲(chǔ)的應(yīng)變能與總應(yīng)變能之比作為應(yīng)變能因子指標(biāo),給出了應(yīng)變能因子指標(biāo)在規(guī)則工作空間的四維切片分布圖,從應(yīng)變能的角度定量評價(jià)了各彈性元件對機(jī)構(gòu)剛度性能的影響程度,給出了不同載荷作用下的全局應(yīng)變能因子指標(biāo)。本研究為定位對機(jī)構(gòu)剛度性能影響最大的彈性元件提供了新的思路。

    Abstract:

    The elastostatic stiffness modeling of a 2UPR-RPU parallel manipulator with 2R1T three degrees of freedom was studied based on the screw theory and strain energy, considering the compliance of the bars and joints. Firstly, the limb constraint wrenches was formulated based on the screw theory. Secondly, the strain energy of bar was formulated by material mechanics, and joint by mapping the constraint wrenches to the joint space, and concentrated limb stiffness matrix corresponding to the constraint wrenches was thus obtained by summarizing the strain energy of bars and joints in the limb, and combining with the Castigliano second theorem. Finally, the overall stiffness matrix was assembled based on the virtual work principle. The theoretical result was verified by commercial ANSYS software. The strain energy factor index was defined as the strain energy of the elastic component account for total strain energy for illustrating the influence of each elastic component on the stiffness performance of the mechanism. A fourdimensional image of slice distribution was presented, the influence of each elastic element on the stiffness performance of the 2UPR-RPU parallel mechanism was quantitatively evaluated from the perspective of strain energy. Finally, the global strain energy factor indices of the mechanism under different external wrenches were presented to find the elastic component with the maximum compliance. The proposed modeling provided a new ideas for improving the stiffness performance of the mechanism more effectively.

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楊超,葉偉,張克濤,黃風(fēng)立,張偉中.2UPR-RPU過約束并聯(lián)機(jī)構(gòu)剛度性能評價(jià)[J].農(nóng)業(yè)機(jī)械學(xué)報(bào),2020,51(2):392-401. YANG Chao, YE Wei, ZHANG Ketao, HUANG Fengli, ZHANG Weizhong. Stiffness Performance Evaluation of 2UPR-RPU Over-constrained Parallel Mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery,2020,51(2):392-401.

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  • 收稿日期:2019-07-01
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  • 在線發(fā)布日期: 2020-02-10
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