Forward displacement analysis of a quadratic 4-DOF 3T1R parallel manipulator: The Quadrupteron

A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) and the Type II singularity analysis of a quadratic 4-DOF 3T1R (SCARA) parallel manipulator: the Quadrupteron. It will be proved that there exists a one-to-one correspondence between the two formulas, each producing one solution to the FDA, and the two singularity-free regions. Therefore, a unique solution to the FDA can be obtained in a straightforward way for such a parallel manipulator if the singularity-free region in which it works is specified. The Type II singularity analysis in the joint space will also be investigated in order to identify the conditions on the inputs to keep the Quadrupteron working in the same singularity-free region in its Cartesian workspace. © 2010 Springer Science+Business Media B.V.