A new representation of the knots and links is introduced, called 'spoke diagrams', which consist of disjoint circles in the plane (Seifert-circles), connected in the plane without crossings by so called spokes.
For these spoke diagrams are deduced the changes by Reidemeister moves. Since they are dependent on orientation, we get for the R-move 2 always 2 cases: (+R2a), and (+R2b). Similarly we get also 2 cases for R-move 3.
After demonstration of different examples it is proved, that the arbitrary consecutive application of (+R2b) between always 2 circles at an arbitrary given spoke diagram always leads to a centred diagram (thus replacing the Vogel-algorithm). The transfer of this simple method into a treatment of the customary diagrams is not possible, because in these cannot be distinguished, whether the 2 ropes of the Reidemeister move R2 belong to 2 different (Seifert-) circles or to only 1.
The advantageous use of the centred spoke diagrams at the recurrence relation AX(+) + BX(-) + CX(0) + D = 0 for purpose of determining knot-invariant polynomials is demonstrated. For its finite recursion process is given a proof by the so called twin spokes theorem, which is proved before.
As appendix are given centred spoke diagrams of the prime- knots and links until 8 spokes, represented by a simple numerical code according to the algebraic word of their view as closed braids, which is specifically suited for computerizing.