压电驱动式台体型并联机构的位置正解研究

Forward Displacement Analysis of Piezoelectric-drive General Parallel Mechanism

针对目前六自由度微动并联机构的位置正解无解析解或解析解求解难问题,提出了一种由压电陶瓷驱动12-SPS台体拓扑构型的并联机构,并构建了一种能完全解耦的位置正解模型。通过引入12个关于动平台上4个特征点坐标的中间变量,并根据支链长度和特征点尺度的约束关系,推导出15个二次相容方程,进而建立了输入、输出集合的映射。通过同构方程的合并运算,将正向运动学方程转换成12个线性相容方程。基于方程组系数矩阵的奇异性,讨论了一般及3种特殊情况下中间参量的计算流程,对应于唯一确定的位置正解。实验结果表明,该全解析算法具有效率高,精度高,无增根和失根等优点。

According to the problem that the forward displacement of the current six-degree-of-freedom micromotion parallel mechanism has no analytical solution or the analytical solution is difficult to solve,a new piezoelectric-drive 12-SPS general parallel mechanism is presented,and the fully decoupled mathematical model of forward kinematics is established.By introducing 12 intermediate variables of 4 feature point coordinates on the moving platform and calculating scales of chains and feature points,15 quadratic compatible equations are derived.Hereby,the mapping relations between input and output items are obtained.Based on the combination algorithm of isomorphic equations,the forward kinematics equations are converted into 12 linear compatible equations.Based on the matrix singularity,the calculation procedures of intermediate variables under various conditions and 3 kinds of special conditions are discussed,and the final solution is uniquely determined.The experimental result shows that the analytical algorithm has the advantages of high efficiency,high precision,no extraneous root and lost root.