Answer to Question #301067 in Mechanical Engineering for vivek

Question

A reciprocating roller follower has cycloidal motion and its

stroke of 30 mm is completed in 90°of the cam rotation.

The follower is offset against the direction of rotation by

6.25 mm and radius of the roller is 12.5 mm. determine the

base circle radius which would limit the pressure angle to

30°.

Answer 1

$h=30mm,β=90^∘ ,e=6.25mm,R r ​ =12.5mm,α max ​ =30^∘ ,r 1 ​ =?.$

For cycloidal motion,

$y=f(θ)=h[θ/β−(1/2)sin(2πθ/β)].$

$=30[2θ/−(1/2)sin4θ].$

$=(15/π)[4θ−sin4θ].$

$df/dθ=(60/π)(1cos4θ).$

$d^ 2 f/dθ^ 2 =(240/π)sin4θ.$

$tan_{α max} ​ =d^ 2 f/dθ^ 2 /df/dθ=(240/π)sin4θ/(60/π)(1−cos4θ).$

$tan30^ ∘ =4cot2θ.$

$θ=40.89^ ∘ .$

$tanα=[df/dθ−e]/[f(θ)+(r 2 −e 2 ) ^ {0.5} ].$

$=[(60/π)(1−cos4θ)−e]/[(15/π)(4θ−sin4θ)+(r 2 1 ​ −e 2 )^ {0.5} ].$

$r_ 1 ​ =42.22mm.$