Page 163 - Mechatronics with Experiments

MECHANISMS FOR MOTION TRANSMISSION 149

FIGURE 3.11: Sinusoidal acceleration cam profile: acceleration, speed, and displacement
function for a cam design where half of the shaft revolution is used for the rise motion and the
other half is used for the down motion symmetrically.

then, the mirror image (let us call that x down )

x down ( ) = f(2 rise − ); rise ≤ ≤ 2 rise (3.104)

Hence the mirror image of the displacement cam function x( )is x(2 rise − ),
C 1 1
x( ) = (2 rise − ) − C 1 ⋅ sin( f (2 rise − )); rise ≤ ≤ 2 rise (3.105)
1
f 1 f 2
1
Figure 3.11 shows the acceleration, speed, and displacement curves for one cycle
of the cam motion. If there is a dwell portion for the input shaft rotation range
of , + , then the dwell portion of the cam function following the rise
rise rise dwell
portion would be as follows,
x( ) = x rise ( rise ); rise ≤ ≤ rise + dwell (3.106)
dx( )
= 0 (3.107)
d
2
d x( )
= 0 (3.108)
d 2
and for the down portion of the cam,

C 1 1
x( ) = (2 rise + dwell − ) − C 1 ⋅ sin( f (2 rise + dwell − )); (3.109)
1
f 1 f 2
1
rise + dwell ≤ ≤ 2 rise + dwell (3.110)