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12-6臺(tái)體型Stewart冗余并聯(lián)機(jī)構(gòu)正向運(yùn)動(dòng)學(xué)研究
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國(guó)家自然科學(xué)基金項(xiàng)目(51405237)、江蘇省精密與微細(xì)制造技術(shù)重點(diǎn)實(shí)驗(yàn)室開放基金項(xiàng)目、南京林業(yè)大學(xué)高學(xué)歷人才基金項(xiàng)目(GXL2014045)和江蘇省高等學(xué)校大學(xué)生創(chuàng)新創(chuàng)業(yè)訓(xùn)練計(jì)劃項(xiàng)目(201710298012Z)


Forward Kinematics of General 12-6 Stewart Redundant Parallel Mechanism
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    摘要:

    針對(duì)六自由度并聯(lián)機(jī)構(gòu)的正向運(yùn)動(dòng)學(xué)無全解析解或全解析解推導(dǎo)困難、不便于程式化、存在多解選擇的現(xiàn)狀,提出一種含混合單開鏈支路的12-6臺(tái)體型Stewart冗余并聯(lián)機(jī)構(gòu),推導(dǎo)了適用于實(shí)時(shí)反饋控制的正向運(yùn)動(dòng)學(xué)全解析算法。通過單開鏈的方位特征集運(yùn)算及路線分解,對(duì)機(jī)構(gòu)的拓?fù)錁?gòu)型進(jìn)行了剖析,并解算了耦合度,為運(yùn)動(dòng)學(xué)方程的構(gòu)造及同構(gòu)處理指明了方向?;趧?dòng)平臺(tái)上4個(gè)共面特征點(diǎn)的拓?fù)潢P(guān)系,對(duì)15個(gè)二次相容方程進(jìn)行同構(gòu)運(yùn)算,推導(dǎo)了12個(gè)一次多項(xiàng)式,得到正向位姿方程的全解析解,具有形式簡(jiǎn)潔、對(duì)稱,且根能夠唯一確定的特點(diǎn)。根據(jù)速度基點(diǎn)法,建立特征點(diǎn)速度之間的矢量關(guān)系,解決了機(jī)構(gòu)的速度正解問題。結(jié)合桿長(zhǎng)協(xié)調(diào)方程及速度映射方程,并運(yùn)用Jacobian代數(shù)法解析出機(jī)構(gòu)的3組奇異曲面方程。實(shí)驗(yàn)結(jié)果表明,位姿正解的計(jì)算值與測(cè)量值完全一致,速度正解的最大相對(duì)誤差為0.08%,它們的效率指標(biāo)值分別為0.21和0.32,均滿足實(shí)時(shí)性要求。

    Abstract:

    Aiming at the present situation that forward kinematics of most 6-DOF (degrees of freedom) parallel mechanisms cannot be described with whole analytical solutions, and a very few of them can be described with whole analytical solutions but also with these difficulties, including calculation, programming, and sorting the suitable solution, a general 12-6 Stewart redundant parallel mechanism with hybrid single opened chains was presented, and a whole analytical decoupling algorithm of forward kinematics, which was needed by the closed-loop real-time feedback control system, was constructed. By calculating the position and orientation characteristics set and decomposing the routes of single opened chains, the topological configuration of new mechanism was analyzed, and then the coupling degrees was solved, which were useful to show clearly direction to construct and process the kinematics equations. Based on the topological relations between four coplanar feature points on the moving platform, the combination algorithms of 15 quadratic isomorphic compatible equations were designed, and then the whole analytical solution, which was succinct, symmetric and unique, of forward displacement equations was derived. Based on the method of base points, velocity relations between feature points were established, and then forward velocity equations were solved. Based on compatibility equations and velocity equations, the Jacobian matrix of mechanism was derived, and then three types of singular equations were also derived. Experimental results indicated that the calculated values of forward displacement equations were well consistent with the measured values, and calculation error of forward velocity equations was 0.08%, and the calculation/sampling time ratios of these two equations were 0.21 and 0.32, respectively, which met the real-time demand of control algorithms.

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尤晶晶,符周舟,吳洪濤,李成剛,周為.12-6臺(tái)體型Stewart冗余并聯(lián)機(jī)構(gòu)正向運(yùn)動(dòng)學(xué)研究[J].農(nóng)業(yè)機(jī)械學(xué)報(bào),2017,48(12):395-402. YOU Jingjing, FU Zhouzhou, WU Hongtao, LI Chenggang, ZHOU Wei. Forward Kinematics of General 12-6 Stewart Redundant Parallel Mechanism[J]. Transactions of the Chinese Society for Agricultural Machinery,2017,48(12):395-402.

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  • 收稿日期:2017-08-09
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  • 在線發(fā)布日期: 2017-12-10
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