Modified sine

The modified-sine is a synthesized profile using the cycloid and harmonic elements.  This combination uses the best properties of the cycloid and harmonic; i.e., the harmonic has a lower maximum acceleration than the cycloid, but has an instantaneous acceleration/deceleration at θ/β=0 and θ/β=1.  The first half of the cycloid is used to eliminate the instantaneous acceleration at the beginning of the harmonic, and the last half of the cycloid is used to eliminate the instantaneous deceleration at the end of the harmonic.

A term called "C" Factor is introduced to indicate how much of the cam segment is assigned to the cycloid portion of the modified-sine at each end of the profile.  The modified-sine that is the standard in the industry uses a "C" Factor of 0.25.  This means that one fourth of the cam segment for this modified-sine profile will be a Cycloidal profile and three fourths will be made up of harmonic.  The first half of the cycloid, then, makes up 1/8 of the segment at the beginning and the last half of the cycloid makes up 1/8 of the segment at the end, for a total of 1/4 of the total segment.  A "C" Factor approaching one will cause the modified-sine to be mostly a harmonic profile; while a "C" Factor approaching 1/2 makes the modified-sine to look more like a cycloid.  Lesson 2 in the tutorial section shows a graph that explains this concept further.

Varying the "C" Factor can modify the peak acceleration and thereby the radius of curvature.  Also, varying the "C" Factor can modify the velocity, which in turn will modify the pressure angle

NOTE:          If a "C" Factor other than 0.25 is used, the cam will have to be fabricated via the Post Processor in Cam Designer SE^TM, or a post processor that uses the CAD translation of the cam surface. 

Modified-Sine Properties

•Both the velocity and displacement curves have zero slope at the ends.

•The acceleration is a maximum at (C/2)(β) and a minimum at  (1-C/2)(β)

•This is a symmetrical curve; therefore, the displacement at (θ/β)=0.5 is 1/2 of the total.

•The peak acceleration is less than the maximum acceleration of the Cycloidal and greater than the maximum acceleration of the harmonic.

•The slope of the velocity curve is zero at the mid-point of the segment.

•This profile is also available in just acceleration or deceleration.

NOTE:          

1.          The curves shown in figure 5 are for a rising translating follower or an oscillating follower that is rotating CCW.

2.The X axis is θ/β from 0 to 1

3.The Y axis is based on a displacement of 1.

Figure 5

Modified Sine Profile