An Exechon robot with offsets between the axes of the joints that connect the legs to the fixed platform is analyzed for the first time. Ideally these axes intersect constituting two universal and one spherical joints. The introduction of imperfections in these universal and spherical joints leads to more complex forward and inverse kinematics, which are solved in this paper. It is proved that the equations used for the kinematics of the ideal Exechon robot are no longer applicable when these offsets are added. The constraint system is also obtained, and it is found to be different to the one of the ideal case. Finally, the combination of offsets that lead to the largest deviation in the position of the parallel platform is determined.