The polode synthesis method

Abstract

The Polode Synthesis method makes use of inversion letting the end point of the coupler of a dyad move on the desired curve keeping the other end joint fixed. The resultant moving centrode and moving polodes yield information about where solutions can be found. The method can be applied towards path generation, timed path generation, function generation, motion generation and timed motion generation. If neither the corresponding centrode nor the polodes intersect then, in general, the resultant coupler curve has only 4 points common with the desired curve. If the polodes intersect then 6-point solutions are obtained etc. The method is applied to straight line mechanisms where the coupler curve is to deviate little from the straight line over the entire range. The same kind of curve is generated so that certain crank positions correspond to certain positions of the coupler point. The method is then applied to a circular arc. The generation of an approximate ellipse is shown for illustrative purposes and the resultant curve is almost identical to the ellipse. The new method approximates the entire curve rather than selecting a few precision points through which the resultant coupler curve is intended to pass. However, only part of the desired curve may be prescribed. The method can be applied to any combination of links and joints.