The spatial Burmester problem is studied in this work, focusing on the synthesis of CCCC and RCCC linkages for rigid-body guidance, where R stands for revolute, C for cylindrical pair. The synthesis equations for CC and RC dyads are formulated using dual algebra. The formulation is developed in such a way that it leads to a robust solution, based on a semigraphical approach, which produces all the real solutions to the problem of CC-dyad synthesis for five given poses. This eases the equation-solving process by filtering out the complex solutions, while allowing for the handling of the special cases of none or infinitely many solutions. The synthesis procedure is illustrated with examples for four and five given poses.