Synthesis And Optimization Of Some Kinds Of Lower-mobility Redundant Actuation Parallel Mechanisms

Parallel mechanisms have the advantages of higher accuracy, stiffness, and bearing capacity compared to serial mechanisms. Especially the lower-mobility parallel mechanisms have broad application prospect in many aspects. However, parallel mechanisms also have the drawbacks of small workspace and there are singular positions in the workspace, which limit their application. The mechanisms that have redundant actuation can reduce or even avoid the drawbacks of the normal parallel mechanism and keep the merits of the normal parallel mechanism at the same time. But the present research on redundant actuation parallel mechanism is mainly about a single parallel mechanism and lack the systematic synthesis on redundant actuation parallel mechanism. So, the paper takes the redundant actuation parallel mechanism as the research object and studied the method of constructing new redundant actuation parallel mechanisms and optimized some new mechanisms.A method based on klein mapping and can be used to determine the dependence of the line vectors is proposed in the paper. By applying projective geometry to the research of the singularity of the parallel mechanism, and the computational formula and the space geometry relationship of the line vectors and couples when they are linear dependent were gotten, and a method which can be used to determine the linear dependence of the mixture of line vectors and couples was gotten. The inner singularity of some lower-mobility parallel mechanisms were analysed using this method. The method provides theoretical reference to the singularity research of parallel mechanism and it is also the theoretical reference of the optimization of the parallel mechanism.Based on screw theory, a new method of constructing redundant actuation parallel mechanism was proposed. The type of redundant actuation branched chains were synthesized, and the installation position, the number of the branched chains were analysed theoretically. The six new kinds of 3R, 2T1 R, 3R1 T, 2R2 T, 3R2 T, 3T2 R redundant actuation branched chain parallel mechanisms were synthesized. These synthesized new mechanisms can reduce the unexpected motion, such as the singularity positions of these mechanisms have been avoided effectively and the performance index such as driving force, stiffness and dexterity have been improved.A kind of mechanisms which have unconstraint branched chains were synthesized, including all the nine kinds of freedom types of parallel mechanism. By combination of different redundant branched chains and adding different number of branched chains, lots of redundant actuation parallel mechanisms were gotten, such as 3-UPU/SPS, 3-UPU/UPU, 3-UPU/UPS, 4-SPS/RZPZUXY, 3-RPUR/SPS, et al. These mechanisms can avoid all the inner singularity positions.Using the mechanism synthesis method of constructed full rank Jacobi matrix, the common formula of the force matrix and torque matrix of the mechanism when the actuation screw has any angle with the fixed platform was gotten. The formula can compute the smallest singular value of the dexterity and stiffness of the redundant branched chain parallel mechanism that have any input angle. By this method, the combination of redundant actuation branched chains that have the best dexterity and stiffness can be gotten. And the method provides theoretical reference to the performance optimization of redundant actuation parallel mechanism.Using Ansys software to simulate the synthesized redundant actuation parallel mechanism, and using Matlab software to calculate the condition number of the force and torque matrix of the redundant actuation branched chain, the dexterity relationship of size between different branched chains were gotten. By theoretical and simulation research, some new redundant actuation parallel mechanisms which have better dexterity and stiffness were synthesized in the paper, and these mechanisms can avoid all the singular positions.