Question

A cam with a translating flat-face follower is desired to have the follower motion $y\left(\theta \right)=4[2\pi \theta -{\theta }^2]0\le \theta \le 2\pi$
Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radiusis mm(round of to one decimal place).

Answer 1

$(R_{\text{cruvature}}{)}_{min}=40mm$
For flat face follower,
Displacement equation:
$y=4(2\pi \theta -{\theta }^2)$
$\frac{dy}{d\theta }=V=4(2\pi -2\theta )$
$=8(\pi -\theta )$
$\left(\text{For y to be max}\frac{dy}{d\theta }\right)=0\Rightarrow \theta =\pi$
$a=\frac{dv}{d\theta }=-8$
$(R_{\text{curvature}}{)}_{Min}=R_{Base}+(y+a{)}_{min}$
$(y_{\text{min}}is0at\theta =0,2\pi )$
$40=R_{Base}+[0-8{]}_{min}$
$40=R_{Base}+[-8]$
$R_{Base}=40-(-8)=40+8=48$ mm