Improved Centerpoint Curve Generation Techniques for Four-Precision Position Synthesis Using the Complex Number Approach

A method for predetermining the properties of a centerpoint curve of the Burmester curve pair which will result from an arbitrary set of four precision positions is introduced. The method is based on the discovery that the shape of any Burmester curve is dependent on the Grashof type of the associated compatibility linkage. Three improvements over the existing theory result. First, the exact range of the independent parameter which will generate solution dyads may be determined, eliminating the need to search for solutions on a trial-and-error basis. Second, the composition of the centerpoint curve may be predicted in advance, enabling improved plotting techniques. Third, the points comprising the centerpoint curve can be generated in their natural sequential order. These techniques may be readily programmed for automatic computation.