Dimensional synthesis and dynamic manipulability of a planar two-degree-of-freedom parallel manipulator

This article deals with the dimensional synthesis and dynamic manipulability of a planar two-degree-of-freedom (DOF) parallel manipulator. The dimensional synthesis based on the workspace and velocity output ratio is presented. The dynamic formulation is derived by using the virtual work principle. Taking into account that the accelerating capabilities at a given point along all directions are more isotropic, the condition number of inertia matrix in the dynamic equation is presented as an index to evaluate the dynamic manipulability of a manipulator. Furthermore, two global performance indices, which consider the mean value and standard deviation of the condition number of inertia matrix, are proposed, respectively. The dynamic manipulability of the parallel manipulator is more isotropic in the centre than at the peripheries of the workspace. The parallel manipulator is incorporated into a four-DOF hybrid machine tool, which also includes a two-DOF worktable.