摘要
提出了台体型4SPS-2CCS广义并联机构,并对该机构的位置正解进行分析.基于四元数建立位置正解的数学模型,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160;同时应用同伦连续法进行数值计算,给出该机构全部160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,将四元数作为变量代替欧拉角旋转变换矩阵,降低方程组的Bezout数,从而减少跟踪路径数目,提高计算效率;采用四元数的矩阵运算,方便计算机程序实现.最后给出数字实例进行验证.
A 4SPS-2CCS generalized Stewart platform is put forward and its forward displacement is analyzed. Based on quaternion, the model of the forward displacement solutions is built up. In order to obtain the number of solutions of this kind mechanism, Mourrain variety is used, The results show that the number of the forward displacement solutions of the parallel mechanism has at most 160. In addition, all the 160 solutions have been obtained by using homotopy continuation method. The example shows that the upper bound of 160 solutions can be reached in the general case. In stead of using Euler angle rotation matrix, the use of quaternion can reduce the Bezout number of the equations and the calculation time to increase the efficiency, and make the computer program easy to write. The result is verified by a numerical example,
出处
《北京邮电大学学报》
EI
CAS
CSCD
北大核心
2007年第3期15-18,31,共5页
Journal of Beijing University of Posts and Telecommunications
基金
国家"973计划"项目(2004CB31800)
国家自然科学基金项目(50475161)
高等学校博士点基金项目(20050013006)
北京市自然科学基金项目(3053017)
教育部科技研究重点项目(104043)
关键词
位置正解分析
并联机构
同伦连续法
四元数
forward displacement analysis
parallel mechanism
homotopy continuation method
quaternion
