GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 56 of 65

Marks: +1, -0

A cam with a translating flat-face follower is desired to have the follower motion

Y(θ)=4[2 π θ-θ^{2}], \;\; 0 ≤ θ ≤ 2 π

Contact stress consideration dictate that the radius of curvature of the cam profile should not be less than

40 {mm}

anywhere. The minimum permissible basic circle radius in ______ mm (round off to one decimal place).

Solution:

Follower motion equation

y=4(2 π θ-θ^{2})

Velocity,

v=\;{d y}/{d θ}

=8(π-θ)

Acceleration,

{a}=\;{ {d}^{2} {y}}/{ {d} θ^{2}}

=-8

For max. value of

y

\;{d y}/{d θ}=0

8(π-θ)=0

θ=π

for minimum value of

y

θ=0,2 π

y=0=y _{\min}

Rourvature

=

Rease

+(y+a) _{\min}

40= {R}_{\;\text "Base "\;}+(0-8)

{R}_{\;\text "Base "\;}=48 {mm}

Go to Question:

Prev Question

Next Question