The direct kinematics analysis is the foundation of implementation of realworld application of parallel manipulators. For most parallel manipulators thedirect kinematics is challenging. In this paper, for the first time a fast andefficient Homotopy Continuation Method, called the Ostrowski Homotopycontinuation method has been implemented to solve the direct and inversekinematics problem of the parallel manipulators. This method has advantage overconventional numerical iteration methods, which is not rely on the initialvalues and is more efficient than other continuation method and it can find allsolutions of equations without divergence just by changing auxiliary Homotopyfunction. Numerical example and simulation was done to solve the directkinematic problem of the 3-UPU parallel manipulator that leads to 16 realsolutions. Results obviously reveal the fastness and effectiveness of thismethod than the conventional Homotopy continuation methods such as NewtonHomotopy. The results shows that the Ostrowski-Homotopy reduces computationtime up to 80-97 % with more accuracy in solutions in comparison with theNewton Homotopy.
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