Forward displacement analysis of one kind of general 5–5 parallel manipulators

Presented is the forward displacement analysis of a general 5–5 parallel manipulator, in which the spherical joints on the base and top platforms are not restricted to be in planes. Two new approaches, which are vector elimination and calculating remainder for polynomials, are used. Moreover some new vector formulae are given at the end of paper. By changing structure, the 5–5 parallel manipulator can be equivalent to a special form of 4–4 parallel manipulator. The original equations are reduced to two univariate polynomial equations by using vector elimination. The true roots are the greatest common divisor (gcd) for these two equations. The gcd which has 24th degree polynomial is obtained by calculating remainder for two polynomials. A program for the forward displacement analysis has been made. The numerical examples have been studied. All solutions have been verified by inverse position analysis.