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From various papers we know trigonometric equations and their solutions — called prototype equations hereafter− which successfully can be employed to compute closed form solutions of inverse robot kinematics. In this paper we show, that the prototype equations known up to now are not sufficient to compute the inverse solution of some arms. In addition we propose new prototype equations whose solutions are equivalent to the solutions of polynomials of degree two and four and show how these new prototypes can be employed successfully to some arms. The last part of the paper gives an insight to the implementation of some of these prototypes in our Symbolic Kinematics Inversion Program SKIP.