Study On Performance Characteristics Of A Class Of Double Parallel Coupled Mechanisms

Due to the influence of component interference and motion singularity,the workspace of traditional parallel mechanisms is generally small,which limits the application scope of parallel mechanisms to a certain extent.By matching the coupling branching chains to increase the output space of parallel mechanisms,the research team synthesized and obtained a number of new coupled parallel mechanisms,namely double parallel coupling mechanisms.In this paper,some performance characteristics of this new type of largeworkspace double parallel coupling mechanism and 4-RRR//RRR+R hybrid spherical humanoid shoulder joint mechanism with redundant branched chain based on a spherical double parallel coupling mechanism are studied.The mathematical principle of rotation and movement superposition of double parallel coupling mechanism is deduced,and the degree of freedom of double parallel coupling mechanism with two rotations is indirectly proved.The closed-form forward and backward solutions of symmetrical spherical two-rotating double parallel coupling mechanism are solved and verified numerically.The closed-form inverse solutions of symmetrical doublerotating parallel mechanism with two spherical centers are derived.Taking a 3-RRRRR//RRRRR mechanism as an example,the forward and backward kinematics solutions of a kind of two-turn-one-shift double parallel coupling mechanism is analyzed.Based on the forward and inverse kinematics solutions,the velocity,acceleration and Jacobi of the symmetrical spherical double parallel coupling mechanism are derived.Kinematics simulation is carried out based on Adams,and the velocity curve and acceleration curve of the dynamic platform measured by simulation are compared with the theoretical calculation results of MATLAB,which proves the correctness of the derived results of kinematics theory.Based on the Jacobian matrix of kinematics,the singularity of the symmetrical spherical double parallel coupling mechanism is analyzed,and the singularity space is plotted.The attitude and position workspace of the mechanism are plotted based on the relationship of component interference.Based on the forward and inverse kinematics solutions of symmetrical spherical double parallel coupling mechanism,the forward and inverse kinematics solutions of 4-RRR//RRR+R spherical hybrid humanoid shoulder joint is derived.The effective workspace of humanoid shoulder joint is drawn based on the inverse kinematics solutions,and the installation posture parameters of humanoid shoulder joint are determined.The dynamic performance of 4-RRR//RRR+R spherical hybrid shoulder joint is analyzed by Lagrange energy method,and the theoretical model of mechanism dynamics is established.Dynamics simulation is carried out using Adams simulation software.The simulation results are compared with the theoretical calculation results,which proves the correctness of the theoretical calculation of dynamics.A general implicit solution method for asymmetric spherical double parallel coupling mechanism is presented.Two new configurations of double parallel complex coupling mechanism are proposed.Taking one of them as an example,a general method for position solution of double parallel complex coupling mechanism is given.