Abstract
A Taylor series approach is used to derive a general procedure for determining an nth-order local parametric approximation to the displacement functions. It is proven that the developed approach will provide local displacement functions in the neighborhood of any regular position as well as in the neighborhood of any singular position for which a certain nonsquare augmented matrix has full rank. The computational procedure requires only the solution of systems of (nonsingular) linear equations and is illustrated for the examples of the crank-slider, RRCPRP and RCRCR linkages. The importance of the proposed approach is that it enables determination of the local behavior of the displacement functions to: (i) provide a higher-order numerical predictor for extending the displacement functions and (ii) provide the nth order instantaneous kinematics of the system in the space of motion parameters. The method can be applied to any system of N equations in N + 1 unknowns.
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