CUBIC OR CONSTANT PULSE NO.2 CURVE (DWELL-RISE-DWELL CAM)

This curve is similar to the constant acceleration and the pulse no.1 curves. It differs from these , however , in that there is no abrupt change in acceleration at the transition point and also that its acceleration is a continuous curve for the complete rise .similar to the constant acceleration curve , it has the disadvantages of abrupt change in acceleration at the beginning and at the end of the stroke .This cubic curve has characteristics similar to that of the simple harmonic motion curve .It is not often employed but has advantages when used in combination with other curves .No simple construction method is available.

Characteristics:

Displacement y=hθ²/β²(3-2θ/β)

Velocity v=6hωθ/β²(1-θ/β)

Acceleration a=6hω²/β²(1-2θ/β)

Pulse p=-12hω³/β³=constant.

3.8. FOLLOWER CHARACTERISTICS:

In all cams the displacement of the follower is given by the mathematical relationship

y=f(θ)

Where θ=cam angle rotation in radians.

However, since the cam rotates at a angular velocity, the displacement

y=g(t)

and θ=ωt.

Where t=time for cam to rotate through angle θ,

ω=cam angular velocity.

Equations for the follower action are often preferred in the form of the former equation than the latter one, since it is simpler to analyze and use.

The velocity is considered as the instantaneous time rate of change of displacement.

v=dy/dt=slope of the displacement curve at angle θ or time t.

The acceleration being the instantaneous time rate of change of velocity,

a=d2y/dt2=dv/dt

=slope of the velocity curve at angle θ or time t.