The Stewart-Gough Platform of General Geometry can have 40 Real Postures

For a general Stewart-Gough platform, two rigid bodies connected by six rods attached via spherical joints, it is known that the maximum number of assembly modes can be at most 40 (counting complex modes as well). However, it was not known yet if there exist examples of Stewart-Gough platforms which actually possess 40 real (the only realizable) assembly modes or postures. This article presents a numerical method which systematically changes the parameters of a given Stewart-Gough platform with the goal to increase the number of real postures and ultimately to obtain an example which possesses 40 real postures. The proposed method is exemplified by way of one particular example of a Stewart-Gough platform for which we obtained 40 real postures.