A Study On Some Issues For Robotics Mechanism

This dissertation presents the research work on the the basic kinematics chain (Barranov Truss) and Stewart mechanism. The mathematic model, algorithmic theory and solving process are studied, some new conclusions are proposed. Also metamorphic parallel mechanisms are studied and new designs have been given, their mobility varieties are demonstrated during the topological change by using reciprocal screws. The main contents and contributions can be summarized as follows:1,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 28th kind of non-planar nine-link Barranov truss is completed by using Sylvester resultant method alone to obtain the 46 degree univariate polynomial closed-form equation without extra roots.The position analysis of the 26th kind of nine-link Barranov truss is finished by using only the Sylvester resultant method. Four constraint equations are used to construct a Sylvester resultant by three steps and a 44 order univariate polynomial equation is obtained. Then Euclidean algorithm is used to solve other 3 variables, but the process shows that there are 4 extraneous roots in the 44 degree univariate polynomial equation. The reason of extraneous roots is analyzed and the improved method is given. After that a 40 degree univariate polynomial equation can be obtained.The position analysis of the 29th kind of non-planar 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 6x6 matrix and contains two variables to be eliminated. Calculating the determinant of the Dixon's matrix, a new equation is obtained. This equation together with the original forth equation, which contains 2 variables, can be used to construct the Sylvester resultant. During using Sylvester resultant, the different degree of univariate polynomial equation is obtained because the different variable is eliminated, which leads to extraneous roots. The reason of extraneous roots is analyzed and the improved method is given. After that a 50 degree univariate polynomial equation can be obtained.2,To obtain the closed-form solutions of the forward kinematics of the Stewart mechanism robot, the Groebner-Sylevester hybrid approach is presented. By using Calay's formula, the closed-form equations of the forward kinematics of Stewart mechanism robot are built, which are reduced to six polynomial equations in three unknown. The reduced Groebner basis under degree lexicographic ordering for the closed-form equations is obtained by using computer algebra. Selecting 20 Groebner basis from 51 ones, a 20×20 Sylvester's matrix can be constructed, which is relatively small in size. A 40th degree univariate equation is obtained from the determinate of the matrix. The results show that the proposed algorithm is simple and requires less computation time. The process shows that there are many different resultants, which will lead to the same univariate equation. The same results can be obtained by using the continuation method. The analysis results prove that the proposed algorithm is exact and simple.3,Based on studying and improving the traditional Hook's joint, this thesis introduces a new design of a three-DOF rT joint. The new rT joint not only has two rotation axes that intersect at right angle, but also has another rotational degree of freedom which can be used to modify the assembly of other joints. This can change the mobility of the parallel mechanisms that assembled with the new rT joints and leads to a new metamorphic parallel mechanisms 3P(rT)CR.The 3P(rT)CR parallel mechanism can change its topology by turning the new rT joints in all limbs into different configurations which reconfigures the constraints within the limbs by introducing local mobility. This qualifies the 3P(rT)CR to have variable mobility from 3 through to 6 and reciprocal screw theory is used to analyze the mobility change.Base on the analysis of the rT joint and its geometrical constrait, the condition needed to change the joint into different configurations has been given, workspace and other property change are also need to be considered for the whole mechanism to work in different topology. By analyzing the constraint forces on the moving platform, the way to choose pure rotational axes for the mechanism has been studied.