Abstract
The parallel mechanisms having mixed degrees-of-freedom (DoFs) of one translation and two rotations have been used in manufacturing the extra large structural aircraft components with complex geometries. This statement can be demonstrated practically by very successful applications of the Sprint Z3 head to aircraft industry. However, to evaluate the kinematic performance of these parallel mechanisms is a challenging issue because serious problems may occur due to dimensional inconsistencies of the Jacobian matrix. By taking a 3-PRS parallel mechanism as an example, this paper presents an approach to formulate a set of local dimensionless kinematic performance indices on the basis of the overall Jacobian developed by screw theory. The merits of these indices are that they can be represented by the instantaneous virtual power transmission ratios within one limb and amongst limbs, leading to the global ones represented by their mean values and standard deviations throughout the entire workspace. In-depth discussion is made via the example to illustrate the validity of these brand new indices. The outcome may provide with the designers a powerful tool for the kinematic performance evaluation and optimal design of the parallel mechanisms having combined DoFs in terms of translations and rotations.
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