22-06-2012, 02:49 PM
An analytical design for three circular-arc cams
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Introduction
A cam is a mechanical element, which is used to transmit a desired motion to another mechanical
element by direct surface contact.
Generally, a cam is a mechanism, which is composed of three different fundamental parts from
a kinematic viewpoint [1,2]: a cam, which is a driving element; a follower, which is a driven element
and a fixed frame. Cam mechanisms are usually implemented in most modern applications
and in particular in automatic machines and instruments, internal combustion engines and
control systems [3].
Cam and follower mechanisms can be very cheap, and simple. They have few moving parts and
can be built with very small size.
The design of cam profile has been based on simply geometric curves, [4], such as: parabolic,
harmonic, cycloidal and trapezoidal curves [2,5] and their combinations [1,2,6,7].
In this paper we have addressed attention to cam profiles, which are designed as a collection of
circular arcs. Therefore they are called circular-arc cams [5,8].
An analytical model for three circular-arc cams
An analytical formulation can be proposed for three circular-arc cams in agreement with design
parameters of the model shown in Figs. 1 and 2.
Significant parameters for a mechanical design of a three circular-arc cam are: Fig. 1 [8]; the rise
angle as, the dwell angle ar, the return angle ad, the action angle aa ¼ as þ ar þ ad, the maximum
lift h1.
An analytical design procedure
Eqs. (1)–(11) can be used to deduce a suitable system of equations, which allows solving the coordinates
of the points C1, C2, C3, F and G when suitable data are assumed.
It is possible to distinguish four different design cases by using the proposed analytical description.
In a first case we can consider that the numeric value of the parameters h1, r, as, ar, ad, q1, q2,
and co-ordinates of the points A, C1, C2, D and G are given, and the co-ordinates of points C3, F
are the unknowns. When the action angle aa is equal to 180, the co-ordinate xA of point A is equal
to zero.
Applications
A novel interest can be addressed to approximate design of cam profiles for both new design
purposes and manufacturing needs.
Analytical design formulation is required to obtain efficient design algorithms. In addition,
closed-form formulation can be also useful to characterise cam profiles in both analysis procedures
and synthesis criteria. The approximated profiles with circular-arcs can be of particular
interest also to obtain analytical expressions for kinematic characteristics of any profiles that can
be approximated by segments of proper circular arcs.
Conclusions
In this paper we have proposed an analytical formulation which describes the basic design
characteristics of three circular-arc cams. A design algorithm has been deduced from the formulation,
which solves design problems with great numerical efficiency. Numerical examples have
been reported in the paper to show and discuss the multiple design solutions and the engineering
feasibility of three circular-arc cams.