The singularity loci of two triangular parallel manipulators
The singularity loci of two triangular parallel manipulators
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DOI：
10.1109/icar.1997.620224
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发表时间：
1997-07
期刊：
影响因子：
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通讯作者：
Curtis L. Collins;J. M. Mccarthy
中科院分区：
文献类型：
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作者：
Curtis L. Collins;J. M. Mccarthy
研究了具有三角形基座和顶平台结构、2-2-2和3-2-1作动器构型的空间并联机器人的雅可比矩阵。雅可比矩阵是用对偶四元数坐标表示的。得到的雅可比矩阵行列式的零轨迹就是我们所说的奇异轨迹。结果是对偶四元数坐标中的一个八阶多项式。2-2-2作动器布置的固定方向的奇异位置轨迹是一个立方曲面。3-2-1作动器布置的奇异位置轨迹也是一个立方曲面，可分解为三个平面。
We study the Jacobian of spatial parallel manipulators that have triangular base and top platform architectures with 2-2-2 and 3-2-1 actuator configurations. The Jacobian matrix is formulated using dual quaternion coordinates. The zero locus of the determinant of the resulting Jacobian is what we refer to as the singularity loci. The result is an eighth order polynomial in the dual quaternion coordinates. The loci of singular positions for a fixed orientation for the 2-2-2 actuator arrangement is a cubic surface. The loci of singular positions for the 3-2-1 actuator arrangement is also a cubic surface, which factors into three planes.