Dynamic response of robotic systems is affected by deformation of their flexible components, velocity and mass of the systems, as well as by the presence of clearance or impact between the components. Since accurate simulations of such robotic systems are increasingly important, the modelling and dynamical behaviour of an extensible mechanism with a rigid crank and a flexible link is investigated in this paper. The equations of motion of the extensible flexible link, constrained to a circular, Cartesian, elliptical, Cassinian, Lame or pear-shaped quartic path, are presented. A dynamical analysis is carried out in order to compare the dynamical response of the flexible link vs. a rigid link under the combined effect of different parameters such as flexibility and clearance. The simulation result shows clear trajectories divergence due to the impact effect of the flexible link on the rigid crank.