A Method to Formulate a Dimensionally Homogeneous Jacobian of Parallel Manipulators

This paper presents a general and systematic approach to formulate the dimensionally homogeneous Jacobian, which is an important issue for the dexterity evaluation and dimensional synthesis of f-degrees-of-freedom (DOF) (f ≤ 6) parallel manipulators having mixed rotational and translational movement capabilities. By the utilization of f independent coordinates to describe the specified motion types of the platform, the f × f dimensionally homogeneous Jacobian is derived directly from the generalized Jacobian, provided that the manipulator has only one type of actuator. The condition number of the new Jacobian is then employed to evaluate the dexterity of two typical 3-DOF parallel manipulators as an illustration of the effectiveness of this approach.