Kinematic Analysis of Cam Mechanisms

Abstract

In this chapter, we discuss the kinematic analysis of cam mechanisms. That is, we determine the follower motion, given a cam profile described by the Cartesian coordinates of a discrete set of its points, its follower type, and all the parameters involved. We assume throughout that the cam profile is available as a discrete set of coordinate points {x(ψ _k ), y(ψ _k )} ^m₁ Moreover, we assume that we know the values of the first two derivatives of these Cartesian coordinates with respect to ψ, at the same ψ _k values. This is, indeed, the case if the cam profile was synthesized using the methods described in Chapters 4 and 5. If, on the other hand, the cam profile is available as an engineering blueprint, as a photograph or, even as a plate, then a database of point Cartesian coordinates can be constructed by suitably digitizing the given profile. However, the digitization of profile points yields only Cartesian coordinates but not their derivatives, which we can calculate by using a spline approximation of the cam profile, as outlined in Chapter 8. For translating followers, the follower output is given by the displacement s(t), the velocity $\dot{s}(t)$, and the acceleration $\ddot{s}(t)$. For oscillating followers, the follower output is given by the angular displacement ø(t), the angular velocity ø(t), and the angular acceleration $\ddot{\phi }(t)$. Once more, the basic approach for analysis will be computer-oriented rather than graphical. In Sections 7.2 and 7.3 we derive the analysis equations for translating and oscillating flat-face followers. In Section 7.4 we present the corresponding analysis for translating knife-edge followers, while Sections 7.5 and 7.6 deal with translating and oscillating roller-followers. Finally, in Section 7.7 we derive the analysis equations of cylindrical cams with translating roller-followers.