**1. Introduction**

The radial cam and translated roller follower mechanism can be found in windshield wiper of the car in which the oscillating motion of the wiper is controlled by the rotary motion of the cam. This kind of cam has been selected based on the irregular profile in which it has two noses and two flanks. At high speeds of the cam, the follower will jump off the cam and introduce chaotic motion at the locations of the tip of the noses. The application of the proposed mechanism is in controlling the opening and closing of valves in internal combustion engine. Nonlinear dynamics phenomenon has happened in the presence of the follower guide's clearance. The mathematical model of transient impact, separation, and contact is described by Yang et al. using an oblique impact in cam-follower system [1]. They explained that at low speed for the

cam and without the use of coefficient of restitution, the cam, and the follower are in permanent contact. Due to the nonlinear dynamics phenomenon, the largest Lyapunov exponent, the power spectrum of Fast Fourier Transform (FFT), Poincare' map are discussed by Yousuf to investigate the detachment between the cam and the follower. The response of the follower is calculated at different coefficients of restitution, different cam speeds, and different follower Guides' clearaances [2]. By taking into consideration the coefficient of restitution, Sundar et al. analyzed the model of nonlinear contact damping and contact stiffness of single degree of freedom system [3]. Moreover, the same group in Ref. [3] discussed the effect of rolling and sliding contact on the nonlinear dynamics phenomenon [4]. Osorio et al. studied the bifurcation of corner impact at variable cam speeds since the detachment occurred between the cam and the follower [5]. Li and Du used the model of coefficient of restitution to control and analyze the bifurcation diagram of collision constrained vibrational system. On the other hand, phase-plane diagram has been built between the displacement and velocity of the follower due to the energy dissipation outside the phase-plane envelope, while the Poincare' map [6] shows the single and group points of black dots. The aim of this chapter is to study the effect of different contact material properties on the nonlinear dynamics phenomenon for radial cam and translated roller follower system at different cam speeds and different follower guides' clearances.
