A Study On Some Issues For Kinimatics Of Planar And Spatial Mechanism

The kinematics of planer and spatial mechanism are one of the main topics and difficult problems in the robotics. This dissertation presents the research work on the basic kinematic chain (Barranov Truss) and on the redundant degree of freedom, 7R robot. Some new ideas are presented include method of set up the mathematic model of the mechanisms, new theory and deduction process etc. Then using some novel methods, some new conclusions are proposed. The new algorithm is applied to the practical problems. The main contents and contributions can be summarized as follows:(l)According to the different topological structure of every kind of nine-link Barranov truss, adopt different algebraic elimination method to solve the position analysis of all kinds of nine-link Barranov trusses.Where, the position analysis of the 25th nine-link Barranov truss is completed by using Sylvester resultant method alone. According to the relationship of the vectors, the degree of unknowns in the resultant is decreased to obtain the 46 degree univariate polynomial closed-form equation without extra roots.The position analysis of the 30th, 31st, 32nd and 25th nine-link Barranov truss are completed by adopting Dixon's resultant method together with Sylvester resultant method in two steps. Three constraint equations are used to construct the Dixon resultant, which is a 6×6 matrix and contains two variables to be eliminated. Calculating the determinant of the Dixon's matrix,...