h=30mm,β=90∘,e=6.25mm,Rr=12.5mm,αmax=30∘,r1=?.
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).
d2f/dθ2=(240/π)sin4θ.
tanαmax=d2f/dθ2/df/dθ=(240/π)sin4θ/(60/π)(1−cos4θ).
tan30∘=4cot2θ.
θ=40.89∘.
tanα=[df/dθ−e]/[f(θ)+(r2−e2)0.5].
=[(60/π)(1−cos4θ)−e]/[(15/π)(4θ−sin4θ)+(r21−e2)0.5].
r1=42.22mm.
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