Research On A Planar 2-DOF Redundant Parallel Mechanism

Parallel mechanisms have found broad applications in industry for compact structure, well accuracy, high stiffness and larger payload. However, most of these mechanisms have deficiencies, such as small workspace, singularities etc. In order to eliminate singularities, redundancy is introduced to the parallel mechanisms. Firstly, the kinematic analysis is made on a planar 2-DOF(degree-of-freedom) redundant parallel mechanism, which includes inverse kinematics, forward kinematics and Jacobian matrix. Based on the kinematic analysis, a simulation on trajectory programming and an experiment on kinematic control are followed. Secondly, the mathematical relationship between the structural parameters of a planar 2-DOF(degree-of-freedom) redundant parallel mechanism and non-redundant parallel mechanism and the configurations of their workspaces is derived in terms of the non-dimensional geometric parameters. And the workspace spectrograms for the two parallel mechanisms are drawn respectively. A contrastive analysis of the spectrograms is followed which shows the effect of singularities on workspaces. On the basis of Jacobian matrix, three types of singularities of the two parallel mechanisms are discussed respectively. Further the equations of singular curves are derived and the singular curve spectrograms are drawn in terms of some nondimensional structural parameters. By a contrastive analysis of the spectrograms, the availability of redundancy on eliminating singularities of the parallel mechanisms is shown. The researching results provide valuable references for the singularity-free path planning. Thirdly, accuracies, dexterities and stiffnesses of the two mechanisms are studied. The effect of singularity and redundancy on mechanism performance is analyzed in detail. And the spectrograms of accuracy index, dexterity index and stiffness index for the two mechanisms are plotted. This spectrograms provide valuable references for the design of the two manipulators. At last the dynamic models of the two mechanisms are established by D'Almbert principle and virtual work principle, which lay a foundation for torque control.