基于螺旋理论的多模式移动3-RSR并联机构奇异性分析
Singularity analysis of multi-mode mobile 3-RSR parallel mechanism based on screw theory
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摘要: 针对3-RSR并联机构在运动过程中的奇异位形，提出了一种基于螺旋理论、几何代数法和空间线性几何理论的新方法，对3-RSR并联机构的全姿态多运动模式进行奇异性分析.该方法首先运用螺旋理论求出3-RSR并联机构的完整雅克比矩阵，然后通过代数法和几何作图法表示出机构各分支的反螺旋，再结合空间线性几何理论分析反螺旋相关性，得出固定模式下机构的奇异性图解，由此对全姿态多运动模式进行奇异性分析.结果表明，该方法能够更加简洁、直观地表示出3-RSR并联机构在两种运动模式下的奇异位形，且不需要大量计算，也适用于其他多模式移动并联机构的奇异位形求解.Abstract: Aiming at the singular configuration of 3-RSR parallel mechanism in the process of motion, a new method based on the theory of screw, geometric algebra and space linear geometry theory was proposed to analyze the singularity of 3-RSR parallel mechanism in the full-attitude and multi-motion mode.The method first used screw theory to find the 3-RSR complete Jacobin matrix of parallel mechanism, and then represented the anti-screw of each branch of the mechanism by algebraic method and geometric mapping method.The singularity diagram of the mechanism in the fixed mode was obtained to make the singularity analysis of the full-attitude and multi-motion mode, combining with the space linear geometry theory to analyz the anti-screw correlation. The results showed that this method could more concisely and intuitively represent the singular configuration of 3-RSR parallel mechanism in two motion modes, and it did not need a lot of calculation. It was also suitable for solving the singular configuration of other multi-mode mobile parallel mechanisms.
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Key words:
- parallel mechanism /
- multi-mode mobile /
- screw theory /
- space linear geometry theory /
- singularity
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