The analysis of multibody systems requires an exact description of the kinematics of the joints involved. In the present work the master–slave approach is employed and endowed with the possibility of including several more complex types of joints. We present the formulation for joints where some relation between the different released degrees of freedom exists such as the screw joint, the rack-and-pinion joint or the cam joint. These joints are implemented in conjunction with geometrically exact beams and an energy-momentum conserving time-stepping algorithm