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Numerical direct kinematic analysis of fully parallel linearly actuated platform type manipulators

This article presents a new numerical approach for solving the direct kinematics problem of fully parallel, linearly actuated platform manipulators. The solution procedure consists of two stages. The first stage transforms the direct kinematics problem into an equivalent nonlinear programming program, and a robust search algorithm is developed to bring the moving platform from arbitrary initial approximation to a feasible configuration that is near to the true solution. The second stage uses the Newton-Raphson iterative method to converge the solution to the desired accuracy. This approach is numerically stable and computationally efficient. In addition, by randomly perturbing the initial approximations, it can be implemented successively to find multiple solutions to the direct kinematics problem. Two numerical examples are presented to demonstrate the stability and efficiency of this approach. © 2002 Wiley Periodicals, Inc.