# Need equation for modified sine curve for a cam.

• sgt_rock
In summary, the conversation is about finding the equation for creating a cam shape using a modified sine curve. The person suggests looking in Harold A. Rothbart's "Cam Design Handbook" for the equation, but doesn't want to buy the book. Another person mentions that a modified sine curve is a good starting point for designing cams and explains how it divides the event length into three subsections with different lift expressions. They also suggest doing a Google search for more information, including finding the equations in Rothbart's book on page 75.
sgt_rock
I am looking for the equation used to create the cam shape using a "modified sine curve".

I am pretty sure the information is in the "Cam Design Handbook" by Harold A. Rothbart but I don't want to buy the book for just one equation.

Any help would be appreciated.

It's more than likely just literally a modified sine curve. Nice thing about sine curves is that they are infinitely differentiable, so there are no discontinuities in accelerations/forces, etc.

Unless someone else has designed cams before.

Yeah, modified sine curve is a good starting point unless you're doing something particular.

The modified sine curve divides the complete event length, beta, into three subsections and uses a separate lift expression over each subsection. They are as follows:

For a total lift of h ...

for 0<theta<beta/8 .....y=(h/(4+pi))*(pi*theta/beta-(1/4)sin(4 pi theta/beta))
for beta/8<theta<7*beta/8 ..y=(h/(4+pi))*(2+pi*theta/beta-(9/4)*sin(4*pi*theta/(3*beta)+pi/3))
for 7*beta/8<theta<beta ...y=(h/(4+pi))*(4+pi*theta/beta-(1/4)*sin(4*pi*theta/beta))

Do a Google search on "modified sine curve" and you will find several entries, one of which is from GoogleBooks. There you can read a portion of Rothbart's book where you can find these equations on p. 75.

## 1. What is a modified sine curve?

A modified sine curve is a type of curve that resembles a regular sine curve, but with some modifications to its shape. It is commonly used in the design of cams, which are mechanical devices that convert rotational motion into linear motion.

## 2. Why is an equation needed for a modified sine curve for a cam?

An equation is needed to accurately describe the shape of the modified sine curve and its relationship to the rotation of the cam. This equation is essential in the design and manufacturing process of the cam to ensure its proper functioning.

## 3. How is a modified sine curve different from a regular sine curve?

A modified sine curve has some key differences from a regular sine curve. It typically has a sharper peak and flatter valleys, and its amplitude and period may be different. These modifications are necessary to create the desired motion in the cam mechanism.

## 4. What factors influence the equation for a modified sine curve for a cam?

The equation for a modified sine curve for a cam is influenced by several factors, including the desired motion of the cam, the shape and size of the cam, and the type of mechanism it is used in. Other factors, such as friction and wear, may also impact the equation.

## 5. Can the equation for a modified sine curve be simplified?

The equation for a modified sine curve can be simplified in some cases, depending on the specific requirements of the cam and its mechanism. However, it is important to ensure that any simplifications do not compromise the accuracy and functionality of the cam.

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