Quaternion Method for the Kinematics Analysis of Parallel Metamorphic Mechanisms
Quaternion Method for the Kinematics Analysis of Parallel Metamorphic Mechanisms
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DOI：
10.1007/978-3-319-23327-7_23
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Zhonghai Zhang;Jian Sun-;Zhenhua Wang;Gongjing Yu;Duanling Li;Jinguo Liu
中科院分区：
文献类型：
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作者：
Zhonghai Zhang;Jian Sun-;Zhenhua Wang;Gongjing Yu;Duanling Li;Jinguo Liu
平行变胞机构是一种新型的变胞机构。其运动学分析是一个新的研究领域，也是一个难点问题。本文用动平台上的坐标原点描述它的位置，欧拉角描述它的方位，给出了动平台上任意点在固定坐标系中的位置的四元数表达式。提出了一种建立并联变胞机构运动学分析统一数学模型的方法。基于该统一的数学模型，可以对不同构型的并联变胞机构进行运动学正反分析。在对一种新型4-URU并联变胞机构进行运动学分析的基础上，进一步阐述了所提出的运动学分析方法，并提出了求解运动学方程的合成消去法。最后给出了一个数值算例，验证了该方法的正确性和有效性。
The parallel metamorphic mechanism is a novel metamorphic mechanism. Its kinematics analysis is not only a new research field, but also a difficult problem. In this paper, with the origin of coordinates on the moving platform describing its position and Euler angles describing its orientation, we present the quaternion expression of an arbitrary point’s location on the moving platform in the fixed coordinate system. Then a method to establish the unified mathematical model for kinematics analysis of the parallel metamorphic mechanism is presented. Based on this unified mathematical model, forward and inverse kinematics analysis of the parallel metamorphic mechanism in different configurations can be conducted. Using kinematics analysis of a novel 4-URU parallel metamorphic mechanism, the proposed kinematics analysis method is further elaborated, and the resultant elimination method is presented to solve the kinematics equations. Finally, a numerical example is given to verify that the proposed method is correct and effective.