A Geometric Newton-Raphson Method for Gough-Stewart Platforms

DOI: 10.1007/978-3-642-01947-0_23


A geometric version of the well known Newton-Raphson methods is introduced. This root finding method is adapted to find the
zero of a function defined on the group of rigid body displacements. At each step of the algorithm a rigid displacement is
found that approximates the solution. The method is applied to the forward kinematics problem of the Gough-Stewart platform.

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    ABSTRACT: In this paper, structurally-novel manipulator called “hybrid manipulator” is proposed. The hybrid manipulator is defined as a serial connection of a binary manipulator and a (Gough-Stewart type) parallel manipulator. Both structures are known as high rigidity and stability for static loads. The binary manipulator has wide workspace, however, its workspace is discrete. On the other hand, the parallel manipulator has high accuracy for continuous positioning, however, its workspace is narrow. Therefore, the proposed structure has advantages of both the binary manipulator and the parallel manipulator. An inverse kinematics algorithm of hybrid manipulator is also proposed. The proposed algorithm consists of ellipsoidal approximation of the workspace and recursive process. The proposed algorithm can realize fast solution of the inverse kinematics problem. The proposed algorithm is verified through numerical experiments.
    No preview · Article · Jan 2014 · IEEJ Transactions on Electronics Information and Systems