This study establishes unified kinematics of Schönflies parallel manipulators (PMs) considering the constraint matrix. Based on vectorial algebra, the kinematics of 4-RRRRR PM is solved using the geometric relation between the links, which solves the PM problem that the vector method could not solve using several kinematic pairs and links. First, the overall Jacobian and Hessian matrices of the Schönflies PM are derived. Then, a complex 4-RRRRR PM was selected and the inverse displacement analysis is performed using a new strategy. The 6 × 6 Jacobian and 6 × 6 × 6 Hessian matrices of the mechanism are deduced. Finally, the kinematics is derived and the results are used to demonstrate the proposed method.
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