Geometry-Transition Curve

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Geometry-Transition Curve

The Transition-Curve is not available with the Trial License.

It is ONLY available with the Premium License.

About Transition-Curve

The PSMotion Transition-Curve© is used to eliminate Polygonal-Action - also referred to as Chordal-Action - and any Linear Velocity-Discontinuity as a Chain moves from a Chain-Guide to a Chain-Sprocket.

Polygonal Action

Standard Sprocket and Polygonal Action

Standard Sprocket and Polygonal Action

Usually, the geometry of chain-links and standard sprockets mean that for each rotation of one tooth:

the chain lifts and falls from R1 to R2 and back again to R1

the Linear-Velocity varies between its:

ominimum Linear-Velocity of

omaximum Linear Velocity of

the Linear-Velocity variation is NOT sinusoidal - it is similar to a sinusoidal bumps (), without the valley!

the Linear Acceleration is continually changing, of course

the Linear-Acceleration is discontinuous

each Pin impacts the root of the Sprocket-Tooth

Polygonal-Action creates two(2) problems

Velocity Variation in the Chain

In the general case, if a Driving Sprocket is rotating at constant Angular Velocity, the chain does not move at constant Linear Velocity.

The ratio of Maximum and Minimum Velocity increases as you reduce the number-of-teeth on the drive sprocket.

Tension Variation in the Chain.

As a chain link engages with a tooth, the chain accelerates, and thus there is a tension variation.

Also, the pitch of the chain link is not constant.

Usually, it is recommended that you use more than 17 teeth on a standard sprocket. Bicycle sprockets have fewer, but the derailleur compensates for the velocity and tension-variations.

Add Transition-Curve


Toolbar :

Part-Editor : Geometry Toolbar > Transition-Curve

Menu :

Part-Editor : Add menu > Geometry sub-menu> > Transition-Curve

To add a Transition-Curve

1.Click Geometry-toolbar > Transition-Curve

2.Drag to add a Line

The Transition-Curve is added.

You can see that the Transition Curve is easy to add. However, it must be used with Pulleys and Chains to be useful.


A Tutorial will show you how to apply the Transition Curve to a Long-Link Chain.