Editing Cam (mechanism) (section)

== Displacement diagram ==
[[File:Basic Displacement Diagram.JPG|thumb|left|Fig. 2 Basic displacement diagram for a rotating cam]]
Cams can be characterized by their displacement diagrams, which reflect the changing position a follower would make as the surface of the cam moves in contact with the follower. In the example shown, the cam rotates about an axis. These diagrams relate angular position, usually in degrees, to the radial displacement experienced at that position. Displacement diagrams are traditionally presented as graphs with non-negative values. A simple displacement diagram illustrates the follower motion at a constant velocity rise followed by a similar return with a dwell in between as depicted in figure 2.<ref>{{cite book
| title = Cam Design and Manufacture
| page = 8
| publisher = The Industrial Press, New York.}}</ref> The rise is the motion of the follower away from the cam center, dwell is the motion where the follower is at rest, and return is the motion of the follower toward the cam center.<ref>[https://www.cs.cmu.edu/~rapidproto/mechanisms/chpt6.html Introduction to Mechanisms – Cams]"rise is the motion of the follower away from the cam center, dwell is the motion where the follower is at rest, and return is the motion of the follower toward the cam center"</ref>
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A common type is in the valve [[actuator]]s in internal combustion engines. Here, the cam profile is commonly symmetric and at rotational speeds generally met with, very high acceleration forces develop. Ideally, a convex curve between the onset and maximum position of lift reduces acceleration, but this requires impractically large shaft diameters relative to lift. Thus, in practice, the points at which lift begins and ends mean that a tangent to the base circle appears on the profile. This is continuous with a tangent to the tip circle. In designing the cam, the lift and the dwell angle {{math|''θ''}} are given. If the profile is treated as a large base circle and a small tip circle, joined by a common tangent, giving lift {{math|''L''}}, the relationship can be calculated, given the angle {{math|''φ''}} between one tangent and the axis of symmetry ({{math|''φ''}} being {{math|{{sfrac|''π''|2}} − {{sfrac|''θ''|2}}}}), while {{math|''C''}} is the distance between the centres of the circles (required), and {{math|''R''}} is the radius of the base (given) and {{math|''r''}} that of the tip circle (required):

:{{math|''C'' {{=}} {{sfrac|''L''|1 − sin ''φ''}}}} and {{math|''r'' {{=}} ''R'' − ''L'' {{sfrac|sin ''φ''|1 − sin ''φ''}}}}

[[File:Cam Profile.JPG|thumb|Fig. 3 Cam profile]]