3-PRRU并联机构的解析雅可比矩阵

Screw-Based Analytic Formulation of Jacobian Matrix of 3-PRRU Parallel Mechanism

并联机构的雅可比矩阵将驱动关节的速度映射为动平台的线速度和角速度,是并联机构性能分析和设计的重要工具。为建立3-PRRU并联机构的完整雅可比矩阵,首先运用螺旋理论分析各分支,通过求出各分支的反螺旋系建立约束雅可比矩阵,该矩阵为3×6阶长方阵;然后锁定并联机构的驱动副后再求出各分支螺旋系的反螺旋系,可求出3×6阶驱动雅可比矩阵;最后综合这两个矩阵得到3-PRRU并联机的6×6阶雅可比矩阵。该矩阵可反映出机构的所有奇异。

The jacobian matrix of parallel manipulator maps the velocities of actuations into the angular and linear velocities of the moving platform.It＇s an important tool for performance analysis and design of parallel manipulator.In order to establish the complete jacobian matrix of 3-PRRU parallel manipulator,each single limb kinematic chain was firstly analyzed by screw theory.Jacobian of constraints is obtained through reciprocal basis screw of each single chain,which is a 3×6 non-square matrix.Then,jacobian of actuations is obtained through the second reciprocal basis screw of each single chain where the actuation is locked,which is a 3×6 non-square matrix.Finally,the 6×6 matrix of 3-PRRU parallel manipulator can be established on the basis of the two matrixes.The 6×6 Jacobian matrix provides information about singularities of 3-PRRU parallel manipulator.