International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 5 (2017) pp. 773-778 © Research India Publications. http://www.ripublication.com 773 An Application of Wavelet Transform on the Dynamic Effect of Curvature Changing in a Cam Profile Vincenzo Niola 1 , Giuseppe Quaremba 1 , Gennaro Pellino 1 and Angelo Montanino 1 1 Dipartimento di Ingegneria Industriale – Università degli Studi di Napoli Federico II, via Claudio 21, 80125, Naples, Italy. 1 Dipartimento di Ingegneria Industriale – Università degli Studi di Napoli Federico II, via Claudio 21, 81025, Naples, Italy. 1 Dipartimento di Ingegneria Industriale – Università degli Studi di Napoli Federico II, via Claudio 21, 81025, Naples, Italy. 1 Dipartimento di Ingegneria Industriale – Università degli Studi di Napoli Federico II, via Claudio 21, 81025, Naples, Italy. Abstract In this paper we study numerically the motion of the follower near a characteristic point of a cam. An analytical formulation of the cam profile has been proposed, in terms of a function depending on a given angular parameter. Therefore we investigate the smoothness of the relative trajectory by applying the wavelet analysis. Our proposed procedure proves that the wavelet analysis can be utilized for studying the dynamic response of a mechanical system, which depends on the regularity of the profile of the cam. Keywords: Wavelet analysis, numerical analysis, cam profile, cam motion. INTRODUCTION A cam is mechanical element, which is used to transmit a desired motion to another mechanical element by direct contact. Specifically, the purpose of the cam is the transmission of power, motion or information. Usually, a cam is composed of three different parts: a driving element called itself cam, a driven element called follower and a fixed frame. Cam mechanisms are usually used in most modern applications, especially in automatic machines and instruments, internal combustion engines and control systems. Generally, the design of cam profile is based on well note simple regular curves such as circles, parabolas cycloids, sinusoidal or trapezoidal curves, polynomial functions and Fourier series curves. In the recent literature, many studies have been addressed to circular-arc cams [1-2] have studied the motion equation of an equivalent system model of an automative valve train. On the other side, the Continuous Wavelet Transformation (CWT) represents a time-scale analysis of the smoothness of a signal or, more in general, of a time series or a curve profile. The Wavelet analysis, unlike the Fourier one, is very useful when one analyzes and decompose signal with a not constant frequency. Let us consider the simple case in which we want to find the Fourier expansion of a signal, defined from 0 to 2, that assumes a linear form from 0 to 1 and it is sinusoidal from 1 to 2. In this case, in order to obtain an appraisable approximation of the signal, we must evaluate many coefficients of the Fourier expansion. Qualitatively, the difference between the usual sine wave and a wavelet can be described from the localization property: the sine wave is localized in frequency domain, but not in time domain, while a wavelet is localized both in the frequency and time domain. Furthermore, the duration of its maximum oscillation is relatively small. One can regard a wavelet is a shape of wave of limited duration and zero moments of a given order. The choice of a wavelet and of signal decomposition level depends on the shape of signals and on the experience of the analyst. For its versatility, the wavelet analysis is diffused in many fields, such as Acoustics, Electrodynamics [3], Finance [4], Medicine and Statistics [5], Robotics [6-9], Mechanics [10- 11] and advanced signal processing [12-16]. In this paper, we study the smoothness (such as the regularity of the induced motions) of a determined cam profile, which is composed by subsets of circular arcs. Our study is performed by applying the Continuous Wavelet Transformation. We concentrate our analysis on the point where the profile of the cam changes. MATERIAL AND METHODS Referring to Figure 1, a cam profile can be composed by the following curves. The first two curves are the circle Γα, (α  1, 2), whose radius and center are, respectively, ρα and Cα. The third and the four circle, named respectively Γ3 and Γ4, are centered on the cam rotation axis O; their radiuses are, respectively, r and r + h1. If one assumes a fixed frame OXY,