Answer to Question #202594 in Mechanical Engineering for Adarsh maurya

Question

From the following data, draw the profile of a cam in which the follower moves 

with simple harmonic motion during ascent while it moves with uniformly 

accelerated motion during descent : Least radius of cam = 50 mm ; Angle of 

ascent = 48° ; Angle of dwell between ascent and descent = 42° ; Angle of descent 

= 60° ; Lift of follower = 40 mm ; Diameter of roller = 30 mm ; Distance between 

the line of action of follower and the axis of cam = 20 mm. If the cam rotates at 

360 r.p.m. anticlockwise, find the maximum velocity and acceleration of the 

follower during descent

Answer 1

$ω = \frac{2πN}{60}=\frac{2π×240}{60} = 25.14 rad/s.$

$v_O=\frac{πωS}{2θ_O} =\frac{π×25.14×0.04}{2×1.571}= 1 m/s.$

$v_R=\frac{πωS}{2θ_R }=\frac{π×25.14×0.04}{2×1.047}= 1.51m/s.$

$a_O= \frac{π^2ω^2}{2(θ_o)^2} = \frac{π^2(25.14)^2×0.042}{(1.571)^2} = 50.6 m/s.$

$a_R=\frac{ π^2ω^2}{2(θR)^2 }=\frac{ π^2(25.14)^2×0.042}{(1.047)^2}= 113.8 m/s.$