基于四元数的台体型5SPS-1CCS并联机器人位置正解分析

FORWARD DISPLACEMENT ANALYSIS OF GENERALIZED 5SPS-1CCS PARALLEL ROBOT MECHANISM BASED ON QUATERNION

提出一种台体型5SPS-1CCS并联机器人机构,并对其位置正解进行分析。首先基于四元数建立并联机构位置正解的数学模型,然后应用Mourrain簇理论对模型解的个数进行理论分析,得出该并联机构位置正解上限为80,并应用同伦连续法进行数值演算,给出该机构全部80组位置正解,证明该机构位置正解上限是可以达到的。求解过程中,将四元数运算转化为矩阵运算,将数学模型中的4个二次方程转化为双线性方程,降低方程组的Bezout数,从而减少跟踪路径数目,提高计算效率。最后给出数字实例,分析结果表明计算方法简洁,具有一般性,适合其他并联机构的位置正解分析,为此类机构的尺度设计、路径规划和控制提供了理论依据。

The generalized 5SPS-1CCS parallel robot mechanism and its forward displacement analysis are presented. The mathematic model of the parallel mechanism is created based on quaternion. It is proved theoretically that the forward displacement problem of the generalized 5SPS-1CCS parallel platform has at most 80 nonsingular solutions using Mourrain variety. All 80 nonsingular solutions of the forward displacement problem are obtained using homotopy continuation method. The procedure of quaternion manipulation is transformed into that of matrix manipulation and 4 quadric equations are reduced into bi-linear equations in the procedure of the calculation. The efficiency and feasibility are improved through the method proposed above. The result is verified by a numerical example. The analysis results prove that the proposed algorithm is simple and can be used to forward displacement analysis of other generalized parallel mechanisms. The research builds the theory basis for dimensional design, trajectory planning and control of this type of manipulator.