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This paper proposes a new methodology for deriving a point-baseddimensionally homogeneous Jacobian, intended for performance evaluation andoptimization of parallel manipulators with mixed degrees of freedom. Optimalmanipulator often rely on performance indices obtained from the Jacobianmatrix. However, when manipulators exhibit mixed translational and rotationalfreedoms, the conventional Jacobian's inconsistency of units lead to unbalancedoptimal result. Addressing this issue, a point-based dimensionally homogeneousJacobian has appeared as a prominent solution. However, existing point-basedapproaches for formulating dimensionally homogeneous Jacobian are applicable toa limited variety of parallel manipulators. Moreover, they are complicated andless intuitive. This paper introduces an extended selection matrix thatcombines component velocities from different points to describe the entiremotion of moving plate. This proposed approach enables us to formulate anintuitive point-based, dimensionally homogeneous Jacobian, which can be appliedto a wide variety of constrained parallel manipulators. To prove the validityof proposed method, a numerical example is provided utilizing afour-degree-of-freedom parallel manipulator.

Dimensionally Homogeneous Jacobian using Extended Selection Matrix for Performance Evaluation and Optimization of Parallel Manipulators