Kinematics of a class of hybrid robotic mechanisms with parallel and series modules

The position and velocity kinematics for a class of 6 d.o.f. hybrid robotic mechanisms is studied. The specific class of hybrid manipulators features a 3 d.o.f. in-series actuated module mounted on a moving platform of another 3 d.o.f. in-parallel actuated manipulator. In both position and velocity case, constraint compatibility conditions necessary for the 3 d.o.f. in-parallel actuated module have been identified first. Then the constraint equations have further been used to “decouple” the variables between serial and parallel modules. Two examples (one for position and one for velocity kinematics) are shown to verify the feasibility of the proposed methods. It is demonstrated that closed form solutions can be reached in the position case under some assumptions, whereas one can always obtain closed form solution in the velocity case