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含柔性動平臺并聯(lián)機(jī)器人動力學(xué)建模方法研究
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國家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2017YFB1303502),、天津市重點(diǎn)研發(fā)計(jì)劃科技支撐重點(diǎn)項(xiàng)目(20YFZCGX01050)和天津市企業(yè)科技特派員項(xiàng)目(22YDTPJC00460)


Dynamic Modeling Method of Parallel Robot with Flexible Moving Platform
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    摘要:

    針對含柔性動平臺的空間并聯(lián)機(jī)器人剛?cè)狁詈蠁栴},,基于Bézier三角形與絕對節(jié)點(diǎn)坐標(biāo)法提出一種高階柔性三角形厚板單元模型和連續(xù)性約束條件,,基于該模型分析動平臺變形狀態(tài)及其對系統(tǒng)動力學(xué)特性的影響,。利用自然坐標(biāo)法與絕對節(jié)點(diǎn)坐標(biāo)法建立剛?cè)狁詈舷到y(tǒng)動力學(xué)模型,通過引入板單元第4個面積坐標(biāo)的二階梯度來描述厚度方向上的變形并解決泊松閉鎖問題,,結(jié)合廣義α法與牛頓迭代法求解動力學(xué)方程,,并對系統(tǒng)靜力學(xué)模型和動力學(xué)模型進(jìn)行仿真分析。結(jié)果表明,,動平臺在運(yùn)動過程中產(chǎn)生的周期性凹陷變形對機(jī)器人空間位姿的影響與機(jī)構(gòu)布局方式,、質(zhì)量分布和負(fù)載作用方式完全一致,系統(tǒng)剛性構(gòu)件與柔性動平臺的運(yùn)動耦合方式符合多體動力學(xué)模型的非線性規(guī)律,;運(yùn)動軌跡誤差低于1.2×10-12mm,,動力學(xué)方程和約束方程迭代誤差均小于設(shè)定閾值10-6和10-14,求解精度能滿足工程應(yīng)用要求,;基于不同參數(shù)開展仿真對比分析,,驗(yàn)證了所述方法的有效性和通用性,。

    Abstract:

    In order to solve the coupling problem of a spatial rigidflexible parallel robot with flexible moving platform, a high-order flexible triangular thick plate element and its continuity constraints were proposed based on the Bézier triangle and absolute nodal coordinate formulation (ANCF). The deformation of the platform was divided by the element and its effects on dynamics were analyzed. The robotic dynamics was established by natural coordinate formulation (NCF) and ANCF. The second-order gradients of the fourth area coordinate were introduced to describe the element deformation in thickness. Besides, the Poisson locking problem was solved accordingly. The Lagrange dynamics equations were solved via the generalized α method and the Newton’s method. The statics and dynamics models of the system were simulated. The results showed that the periodic concave deformation of the moving platform had an impact on the spatial posture of the robot which was exactly consistent with the mechanism layout, mass and load distribution. The coupling mode between the rigid components and flexible moving platform conformed to the nonlinear characteristics of multibody dynamics. The trajectory error was less than 1.2×10-12mm. The errors of dynamics and constraint equations were less than the preset thresholds of 10-6and 10-14, which met the requirements of engineering applications. Meanwhile, the validity and versatility of the method were verified by comparative analysis based on different system parameters.

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劉涼,汪博深,馮建峰,趙新華.含柔性動平臺并聯(lián)機(jī)器人動力學(xué)建模方法研究[J].農(nóng)業(yè)機(jī)械學(xué)報(bào),2023,54(12):417-430. LIU Liang, WANG Boshen, FENG Jianfeng, ZHAO Xinhua. Dynamic Modeling Method of Parallel Robot with Flexible Moving Platform[J]. Transactions of the Chinese Society for Agricultural Machinery,2023,54(12):417-430.

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  • 收稿日期:2023-04-15
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  • 在線發(fā)布日期: 2023-05-18
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