Formulating Jacobian matrices for the dexterity analysis of parallel manipulators

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Dynamic formulation and performance evaluation of the redundant parallel manipulator (2009, methodology): “In order to avoid the unit inconsistency problem, some works [25–27] had been done based on the principle that the plane is determined by three noncollinear points.”
A generalized approach for computing the transmission index of parallel mechanisms (2014, methodology): “The methods available for doing so include: (1) a length-based method, in which all translational elements in the Jacobian are normalized with the help of a “characteristic/natural length” [2-8]; however, this method depends on the choice of the characteristic length, and – although a “best” charact”