七支链Stewart并联机构位置正解的半解析算法
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摘要
设计了3种七支链并联机构,并提出了数值迭代与解析方法相结合的正运动学求解思路。引入辅助支链,推导出支链协调方程,再运用数值迭代方法由协调方程反求辅助支链的长度,并研究了数值迭代法初值偏差与迭代效率的关系。在求得辅助支链和实际支链长度的基础上提出一种全解析算法,通过消去高次项得到四组多元一次方程组,由四组多元一次方程组推导出动平台位姿唯一的解析表达式。通过虚拟试验对该半解析算法进行了验证,结果证明此算法具有准确、高效的特点。
It introduces three kinds of seven-branches parallel mechanism, describes a method for forward kinematics solution, which combines analytical method and numerical method. Adding auxiliary branches, it derives coordination equations. Based on numerical iterative methods, it obtains the length of branches. Aiming at the initial value selection, it analyzes the relationship between initial value and iterative efficiency. Combining the length of actual branches with auxiliary branches, it proposes an analytical method, eliminates high order terms, obtains four groups of multiple equations. Virtual tests prove that this semi-analytical algorithm is precise and effective.
It introduces three kinds of seven-branches parallel mechanism, describes a method for forward kinematics solution, which combines analytical method and numerical method. Adding auxiliary branches, it derives coordination equations. Based on numerical iterative methods, it obtains the length of branches. Aiming at the initial value selection, it analyzes the relationship between initial value and iterative efficiency. Combining the length of actual branches with auxiliary branches, it proposes an analytical method, eliminates high order terms, obtains four groups of multiple equations. Virtual tests prove that this semi-analytical algorithm is precise and effective.
引文
[1] 杜鹃,吴洪涛,张云剑.共形空间中的少自由度空间并联机构正解[J].机械设计与制造,2015(6):1-8.
[2] 曹磊,马春生,李瑞琴,等.3-PUPU并联机构的运动学分析与仿真[J].包装工程,2018,39(3):118-123.
[3] 宋孟军,张明路.仿生移动机器人并联机构运动学正解的鱼群算法求解[J].中国机械工程,2012,23(9):1029-1036.
[4] 方喜峰,赵若愚,吴洪涛,等.6-UPS交叉杆型并联机床的运动学正解算法[J].机械工程学报,2012,48(13):56-60.
[5] 程世利,吴洪涛,姚裕,等.6-SPS并联机构运动学正解的一种解析化方法[J].机械工程学报,2010,46(9):26-31.
[6] 刘安心,杨延力.求一般6-SPS并联机器人机构的全部位置正解[J].机械科学与技术,1996,15(4):543-546.
[7] ZHOU W Y,CHEN W Y,LIU H D,et al.A new forward kinematic algorithm for a general Stewart platform[J].Mechanism and Machine Theory,2015,87:177-190.
[8] WAMPLER C W.Forward displacement analysis of general six-in-parallel SPS platform manipulatore using some coordinates[J].Mechanism and Machine Theory,1996,31(3):331-337.
[9] HUSTY M L.An algorithm for solving the direct kinematics of general Stewart-Gough platforms[J].Mechanism and Machine Theory,1996,31(4):365-379.
[10] 王启明,苏建,张益瑞,等.一种冗余6-DOF并联机构的结构特征与运动学分析[J].机械工程学报,2017,53(18):121-130.
[11] 尤晶晶,符周舟,吴洪涛,等.12-6台体型Stewart冗余并联机构正向运动学研究[J].农业机械学报,2017,48(12):395-402.
[2] 曹磊,马春生,李瑞琴,等.3-PUPU并联机构的运动学分析与仿真[J].包装工程,2018,39(3):118-123.
[3] 宋孟军,张明路.仿生移动机器人并联机构运动学正解的鱼群算法求解[J].中国机械工程,2012,23(9):1029-1036.
[4] 方喜峰,赵若愚,吴洪涛,等.6-UPS交叉杆型并联机床的运动学正解算法[J].机械工程学报,2012,48(13):56-60.
[5] 程世利,吴洪涛,姚裕,等.6-SPS并联机构运动学正解的一种解析化方法[J].机械工程学报,2010,46(9):26-31.
[6] 刘安心,杨延力.求一般6-SPS并联机器人机构的全部位置正解[J].机械科学与技术,1996,15(4):543-546.
[7] ZHOU W Y,CHEN W Y,LIU H D,et al.A new forward kinematic algorithm for a general Stewart platform[J].Mechanism and Machine Theory,2015,87:177-190.
[8] WAMPLER C W.Forward displacement analysis of general six-in-parallel SPS platform manipulatore using some coordinates[J].Mechanism and Machine Theory,1996,31(3):331-337.
[9] HUSTY M L.An algorithm for solving the direct kinematics of general Stewart-Gough platforms[J].Mechanism and Machine Theory,1996,31(4):365-379.
[10] 王启明,苏建,张益瑞,等.一种冗余6-DOF并联机构的结构特征与运动学分析[J].机械工程学报,2017,53(18):121-130.
[11] 尤晶晶,符周舟,吴洪涛,等.12-6台体型Stewart冗余并联机构正向运动学研究[J].农业机械学报,2017,48(12):395-402.