8/19/2019 Consider the Radius of Wheel Is

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Consider the radius of wheel isr 

, angular velocity isω 

 and stroke length isl 

.

At0t  =

,0t  =

touches x-axis

0φ   =

From the figure consider the expression.

( )   cos cos x t r l θ φ = +…… !"

Also,

( )

# # #

# # # #

#

# #

sin sin

sin sin

! cos sin

cos ! sin

r l 

r l 

r l 

l 

r 

θ φ 

θ φ 

θ φ 

θ φ 

=

=

− =

 = −  ÷  

$ake

l n

r =

# #cos ! sinnθ φ = −

%ut the

# #cos ! sin cosn l θ φ φ = − +

 in e&uation !".

8/19/2019 Consider the Radius of Wheel Is

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( )   # #! sin cos x t r n l φ φ = − +

a"

'f0φ   =

( )   ! 0 ! x t r l 

r l 

= − + ×

= +

("

'f

)0φ 

  = °

( )   #

# #

#

# #

! 0 x t r x l 

r l r 

r 

r l 

= − + ×

−=

= −