Kinematic Analysis Of Mechanism Based On The Double Vector And The Double Matrix

For the general 6-DOF(Degree-of-freedom)serial manipulator,the problem that whether the inverse kinematic analysis can be solved by a unified method has always been the goal of the researchers in the filed of robotic mechanisms at home and abroad.In the master thesis,the double number is introduced to the modeling of the kinematic analysis of the robotic mechanisms,similar to the representation of the dual number in the three-dimensional spatial kinematic analysis.In terms to the relationship between the double quaternion and the dual quaternion for the spatial rigid-body displacement,the novel double matrix method in three-dimensional space is presented based on the dual matrix.Combined to the four-dimensional rotational matrix,the new algorithm for the inverse kinematics analysis of general 6-DOF serial manipulators is proposed based on the novel double matrix method.In the master thesis,first of all,the double matrix representation of the rigid-body displacement in three-dimensional space is derived,and the double matrix representation of the basic transformation matrix in three-dimensional space is given.The double matrix can transform the rotation and translation displacement in three-dimensional space to the rotation matrix in four-dimensional space.Secondly,the relationships of the four-dimensional rotation matrix,the double quaternion and the double matrix for the rigid-body displacement in the three-dimensional space are derived and the results show that they can be transformed by the linearly algebraic operation or the nonlinearly square root operation.And then,based on the new double matrix method,the kinematic equations for the inverse kinematic analysis of the general 6R serial manipulator are established.Finally,the variables of the kinematic equations are separated,and the univariate higher-order equation of the problem is derived by applying for the linear elimination and Sylvester resultant elimination.And thus,a new algorithm for the inverse kinematic analysis of the general 6R serial manipulator is established based on the double matrix theory.Based on the new algorithm,the inverse kinematic analysis of the general 6R serial manipulators are extended to the general 1P5R,4R1C,2P4R,3P3R and other 6-DOF serial manipulators with the special structure,and the adaptability of the new algorithm to the different configurations of 6-DOF serial manipulators are summarized.The results show that the double matrix method is generalized well for the inverse kinematic analysis of 6-DOF serial manipulators,and the introduction of the double matrix theory enriches the mathematical method to the modeling for the kinematic analysis of the robotic mechanisms.