CIRCULAR ARC CURVE

This curve composed of two circular arcs tangent to each other is only acceptable insofar as it has some improvement over the infinite acceleration, straight-line curve. Although its acceleration is finite at all times, the curve gives large follower accelerations and excessive velocities. Therefore it is used for low speeds only, if at all.

Characteristics:

Let H=radii of circular arcs.

R_p=radius of pitch circle.

l=developed length of cam for angle θ.

The displacement of the follower from 0 to β/2 is

y=H-[H²-L²]^1/2

But we know for radial cams

l=R_pθ

Substituting gives displacement

y=H-[H²-(Rpθ)²]^1/2

Differentiating gives velocity and acceleration

v=dy/dt=ωR_p²θ/[H²-(R_pθ)²]^1/2

a=dv/dt=(ωR_pH)²/[H²-(R_pθ)²]^3/2

This curve is symmetrical about the transition point β/2. No calculated example will be shown since this is not employed in mode machinery.