  This paper proposes a new methodology for deriving a point-based
dimensionally homogeneous Jacobian, intended for performance evaluation and
optimization of parallel manipulators with mixed degrees of freedom. Optimal
manipulator often rely on performance indices obtained from the Jacobian
matrix. However, when manipulators exhibit mixed translational and rotational
freedoms, the conventional Jacobian's inconsistency of units lead to unbalanced
optimal result. Addressing this issue, a point-based dimensionally homogeneous
Jacobian has appeared as a prominent solution. However, existing point-based
approaches for formulating dimensionally homogeneous Jacobian are applicable to
a limited variety of parallel manipulators. Moreover, they are complicated and
less intuitive. This paper introduces an extended selection matrix that
combines component velocities from different points to describe the entire
motion of moving plate. This proposed approach enables us to formulate an
intuitive point-based, dimensionally homogeneous Jacobian, which can be applied
to a wide variety of constrained parallel manipulators. To prove the validity
of proposed method, a numerical example is provided utilizing a
four-degree-of-freedom parallel manipulator.
