Analytical Solution of the Forward Position Analysis of Parallel Manipulators That Generate 3-RS Structures

In this work the forward position analysis (FPA) of 3-RS structures (R, S, P and C = revolute, spherical, prismatic and cylindrical, respectively) is carried out applying recursively the Sylvester dialytic elimination method. The analytical solution provided in this contribution yields 16 possible poses of the moving platform given the limb lengths of the manipulator and it is applicable to a wide class of parallel manipulators, e.g., the 3-RP*S mechanism, 3-CP*S mechanism, 6–3 Gough–Stewart platforms and 3-RR*S mechanism. A case study is included which consists of solving the FPA of a 3–3 Gough–Stewart platform, also known as an octahedrical mechanism.

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