Equations for Traditional Motion-Laws

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Equations for Traditional Motion-Laws

Motion-law Equations

We evaluate exact values of Position, Velocity, Acceleration, and Jerk values for each motion-law from the equation for each motion-derivative.


Motion-Laws

The important motion-laws are:

Dwell

Constant Velocity

Constant Acceleration - Constant Deceleration

Simple Harmonic Motion

Cycloidal

Polynomial 2-3

Polynomial 3-4-5

Polynomial 4-5-6-7

Modified Sinusoid

Modified Trapezoid


Motion Functions

Actual Velocity, Acceleration, and Jerk

You can calculate the actual motion-values for each motion-derivative of each motion-law if you know the actual total displacement ( ), and the actual total (time) period ( ).

Actual Position =

 

Actual Velocity =

 

Actual Acceleration =

 

Actual Jerk =

 


Dwell

Constant Velocity

 

Parabolic (Constant-Acceleration - Constant-Deceleration) (PAR)

 

 

 

 

 

 

Simple Harmonic Motion (SHM)




Cycloidal




Polynomial 2-3




Polynomial 3-4-5




Polynomial 4-5-6-7




Modified Sinusoid

 

 

 

 

 

 

 

 

 

Modified Trapezoid