Optimization design using a global and comprehensive performance index and angular constraints in a type of parallel manipulator

The kinematic optimization of a type of parallel manipulator is addressed. Based on the kinematic analysis, the pressure angles within a limb and among the limbs are introduced, which have definite physical and geometrical meanings. In particular, a type of new pressure angle among the limbs (referred to as the second type of pressure angle among the limbs) is defined and considered to be one of the pressure angle constraints to ensure the kinematic performance. In the kinematic optimization phase, a global and comprehensive performance index, which combines the conditioning number of Jacobian matrix and pressure angles with the volume of workspace, is formulated as an objective function for minimization. One optimal kinematic design example that determines the dimensional parameters is provided to clarify the availability of the proposed approach. The analytical results indicate that good kinematic and dynamic performance can be guaranteed with the suggested design approach. Furthermore, the mutual effect between the dexterity and new pressure angle is analyzed. The effects of the pressure angle constraints on the minimum and maximum conditioning numbers and global dynamic performance indices through the entire workspace are discussed. The proposed research provides a method for the kinematic optimization design of parallel manipulators.