摘要
少自由度并联机构完整雅可比矩阵为6×6矩阵,包括运动子矩阵和约束子矩阵两部分,由于前者的代数特征不能反映出机构的约束特性,在对此类机构进行运动学分析和几何参数优化设计时,必须建立完整的6×6雅可比矩阵。鉴于此,基于对偶螺旋理论,以4自由度机构2RPS-2UPS为例,给出非全对称少自由度并联机构完整雅可比矩阵的推导方法。首先,根据螺旋理论推导约束支链中的运动螺旋系和反螺旋系,并利用互易积获得约束子矩阵。其次,锁定每个支链中的主动关节,根据螺旋理论计算约束支链和全运动支链中新增反螺旋系,并利用互易积建立运动子矩阵。将约束子矩阵和运动子矩阵联立建立机构完整雅可比矩阵。最后,分析雅可比矩阵的秩,得到2RPS-2UPS并联机构产生奇异位形的条件。
The complete Jacobian matrix of a lower-mobility parallel mechanism is a six by six matrix that consists of the actuation sub-matrix and the constraint sub-matrix. As the algebraic feature of the former one cannot account for the related constraint characteristics, modeling complete six by six Jacobian matrix becomes necessary in the kinematic analysis and optimal design of geometric parameters of this kind of parallel mechanisms. A method for deducing the complete Jacobian matrix of an incompletely symmetrical lower-mobility parallel mechanism is illustrated by taking 2RPS-2UPS as an example based on the theory of reciprocal screw. Firstly, the systems of twists and reciprocal screws of the constraint limbs are established based on the screw theory, then the constraint sub-matrix is obtained through the orthogonal product. Secondly, by locking active joints of each limb, the system of additional reciprocal screws of both constraint and unconstraint limbs is established, then the actuation sub-matrix is also obtained through the orthogonal product. By integrating these two sub-matrices properly, the complete Jacobian matrix of an incompletely symmetrical lower-mobility parallel mechanism can be finally set up. In the end, the singular conditions of 2RPS-2UPS parallel mechanism are analyzed by investigating the ranks of the Jacobian matrices.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2007年第6期37-40,共4页
Journal of Mechanical Engineering
基金
国家自然科学基金(50535010
50675151)
教育部高校博士点基金(20060056018)资助项目
关键词
并联机构
少自由度
非全对称雅可比矩阵
螺旋理论
Parallel mechanism Lower-mobility Incompletely symmetrical Jacobian matrix Screw theory
