Synthesis of displacement functions by Bézier curves in constant-breadth cams with parallel flat-faced double translating and oscillating followers

Conceptual design and dimensional synthesis of cam-linkage mechanisms for gait rehabilitation

“…Flores [31] presented a computational approach for the dimensional optimization of cam mechanisms having offset translating roller followers. Cardona and HidalgoMartínez [32][33][34] presented methods for the optimization of the cam profile based on Bézier curves. Cardona and Zayas [35] analyzed the influence of the inclination and offset of the translating follower in a constant-breadth cam mechanism.…”

Minimization of the sliding velocity in planar cam mechanisms with flat-faced translating followers

“…The ordinate of the contact points between cam and follower P and Q are given by, being R a and θ the radius of the prime circle and the rotation angle of the cam, respectively. The function f(θ) is the displacement function of the single follower and is given by the following expression, where P 1,2 are n th-degree Bézier curves 8,9,18 and β is the total rise angle, i.e. the cam angle required to reach the maximum displacement h of the follower (see Hidalgo-Martínez et al.…”

“…The point C P is the center of curvature of the cam profile, and the point W P is the intersection between the line IP and the inflection circle (see Figure 1). Thus, the value of IW P is The radius of curvature of the cam profile at the point P is and in the case of a double follower, the radius of curvature of the cam profile at the point Q is Note that, for a double follower, the sum of both radii of curvature is constant 8,9,12 where d c is the breadth of the cam or the normal distance between both flat faces. To avoid the undercutting, the radius of curvature at any point must be higher than zero.…”

“…They also explained explicitly the process of displacement function synthesis, with or without double dwell. Cardona et al 9 showed a design procedure which guarantees automatically the global continuity of the law of displacement. This procedure provides the expressions of calculation for both parallel flat-faced double translating follower and parallel flat-faced double oscillating follower.…”

Parameter selection in the design of displacement and motion functions by means of B-splines

“…In previous works [10,11], the authors of this paper have used non-parametric Bézier curves to synthesize the follower displacement functions in constant-breadth cam mechanisms that drive both translating and oscillating followers. The authors' works present the desmodromic condition that the follower displacement functions must meet, as well as the calculation algorithms that permit such functions to be obtained; the procedure that automatically guarantees their 2 C global continuity is also shown.…”