Dynamic dexterity evaluation of a 3-DOF 3-PUU parallel manipulator based on generalized inertia matrix

Abstract

Dynamic performance evaluation that takes into account the inertial properties is an important issue for both the behavior analysis and dimensional synthesis of parallel kinematic manipulators (PKMs). Firstly, by virtue of the principle of virtual work, the complete inverse dynamic model of a 3-prismatic-universal-universal (PUU) parallel manipulator is formulated, which does not neglect the inertial and gravitational properties of the struts. The condition number of generalized inertia matrix can evaluate the mapping from joint accelerations to realizable joint torques. This paper utilizes the condition number of generalized inertia matrix as the index to evaluate the dynamic dexterity property of a 3-PUU PKM which possesses three translational degrees of freedom. For a given set of geometrical and inertia parameters, numerical simulations indicate that the global dynamic dexterity performance of this type of 3-PUU PKM is consistent with the local dynamic dexterity on a specific z-plane, it has the best dynamic dexterity at the center of task workspace and decreases from the center to the edge of task workspace.