5R平面机构在不同装配、工作模式下的工作空间

Workspace of 5R Planar Mechanism in Different Assembly and Work Modes

目的研究5R并联机构工作空间在不同装配模式和工作模式下的工作空间,对与5R平面机构类似的机构工作空间分析、路径规划等问题提供理论支持。方法对约束方程求导,得到运动学奇异矩阵。建立工作空间边界约束方程,根据装配模式和工作模式的定义,建立不等式约束方程。使用Cylindrical Decomposition对约束方程进行求解。结果得到了5R并联机构工作空间在不同装配模式和工作模式下工作空间的图像,装配模式"+-"对应的工作空间的并集为机构的可达工作空间,根据装配模式和工作模式的组合,可得到8种不同的工作空间。结论 Cylindrical Decomposition在解决工作空间问题方面有着一定的应用价值,使用Mathematica对不等式组进行求解得到的结果较直观,容易理解。

The work aims to study the workspace of 5R parallel mechanism in different assembly and working modes, and provide theoretical support for the workspace analysis and path planning of the mechanism similar to 5R planar mechanism. The singular matrix of kinematics was obtained by deriving the constraint equation. The workspace boundary constraint equations were established and the constraint inequations were built based on the definition of assembly and working modes. The workspace image of 5R parallel mechanism in different assembly and working modes was obtained. The union of the workspaces corresponding to assembly mode ＂＋-＂ was the reachable workspace. According to the combination of assembly and working modes, eight different workspaces could be obtained. Cylindrical Decomposition in solving the problem of workspace has certain application value. The set of inequalities are solved with Mathematica, and the results are intuitive and easy to understand.